http://wiki.googology.top/api.php?action=feedcontributions&feedformat=atom&user=0100000000a7 2026-09-06T12:14:50Z 用户贡献 MediaWiki 1.43.1 http://wiki.googology.top/index.php?title=BTBMS&diff=3777 2026-08-30T16:01:28Z

<p>0100000000a7：​</p> <hr /> <div>BTBMS（Bubby3's Transfinite Bashicu Matrix System）是 Bubby3 创造的序数记号，是现行扩展 [[BMS]] 中强度最高的。它由 Bubby3 最先提出，并由笑姐姐最终给出完整定义。<br /> <br /> === 定义 ===<br /> 一个 BTBM 矩阵形如 &lt;math&gt;A = A_1 \cdots A_n&lt;/math&gt;，其中 &lt;math&gt;A_i&lt;/math&gt; 称为矩阵的顶层列。<br /> <br /> 一个列形如 &lt;math&gt;C = (C_1, \cdots, C_m)&lt;/math&gt;，其中 &lt;math&gt;C_i&lt;/math&gt; 称为列的项。<br /> <br /> 一个项形如 &lt;math&gt;E = v^X&lt;/math&gt;，其中 &lt;math&gt;v&lt;/math&gt; 是正整数，&lt;math&gt;X&lt;/math&gt; 是一个 BTBM 矩阵。称 &lt;math&gt;X&lt;/math&gt; 为 &lt;math&gt;E&lt;/math&gt; 的高度矩阵，&lt;math&gt;v&lt;/math&gt; 为 &lt;math&gt;E&lt;/math&gt; 的值，或称作 &lt;math&gt;E&lt;/math&gt; 的父列标。<br /> 称 &lt;math&gt;E&lt;/math&gt; 为 &lt;math&gt;X&lt;/math&gt; 的直接外部项；&lt;math&gt;E&lt;/math&gt; 所在列为 &lt;math&gt;X&lt;/math&gt; 的直接外部列。若 &lt;math&gt;E&lt;/math&gt; 的高度矩阵为空，则称 &lt;math&gt;E&lt;/math&gt; 为单行项。<br /> <br /> 以后我们常用 &lt;math&gt;A&lt;/math&gt; 表示整个矩阵，&lt;math&gt;X&lt;/math&gt; 表示 &lt;math&gt;A&lt;/math&gt; 的一个子阵。顶层列的高度矩阵称为直接子阵。矩阵 &lt;math&gt;A&lt;/math&gt; 本身，以及 &lt;math&gt;A&lt;/math&gt; 的某个直接子阵的子阵，统称为 &lt;math&gt;A&lt;/math&gt; 的子阵。<br /> <br /> ==== 列标 ====<br /> 如下定义 &lt;math&gt;A&lt;/math&gt; 的列在 &lt;math&gt;A&lt;/math&gt; 中的列标。 &lt;math&gt;A&lt;/math&gt; 最左列的列标为 1；对一个子阵 &lt;math&gt;X&lt;/math&gt;，&lt;math&gt;X&lt;/math&gt; 的最左侧列列标为它的外部列的列标 +1。某个子阵非最左侧列的列标等于它左侧相邻列的列标 +1。<br /> <br /> 对于一个元素，它的值等于它的父列列标。如下寻找它的父列：从该元素所在列 &lt;math&gt;C&lt;/math&gt; 出发，若存在左侧相邻列则取左侧相邻列，否则取外部列。得到的列的列标取遍不大于 &lt;math&gt;C&lt;/math&gt; 的列标的所有正整数。其中列标等于元素的值的列即为该元素父列。<br /> <br /> ==== 合法性约束 ====<br /> 引入如下约束：一个合法矩阵所有列的所有元素的值都小于所在列的列标；对任何列 &lt;math&gt;C&lt;/math&gt;，&lt;math&gt;C&lt;/math&gt; 的任何元素的高度矩阵的所有列都非空，且这些列的首个元素的值都大于等于 &lt;math&gt;C&lt;/math&gt; 的列标。<br /> <br /> ==== 零记号与后继记号 ====<br /> 若 &lt;math&gt;A&lt;/math&gt; 为空矩阵，则 &lt;math&gt;A&lt;/math&gt; 为零记号。<br /> 若 &lt;math&gt;A&lt;/math&gt; 的末列为空列，则 &lt;math&gt;A&lt;/math&gt; 为后继记号，其前驱记号为 &lt;math&gt;A&lt;/math&gt; 去掉末列。<br /> <br /> ==== 展开规则（寻找末列与基本列） ====<br /> 对于合法的极限矩阵，我们如下寻找它的末列。初始令当前层级为 &lt;math&gt;A&lt;/math&gt; 本身。<br /> * 若当前层级的顶层列中的末列的末项（根据合法性约束总是存在）不为单行项，则将当前层级改为该项的高度矩阵，然后继续流程；<br /> * 否则末列即为当前层级的顶层列中的末列。按定义末列的末项为单行项，称为右上元素。该项父列称为根列。<br /> <br /> 若末列恰有 1 项，且根列为末列所在层级的直接外部列时，适用如下特殊展开规则：<br /> 设直接外部列为 &lt;math&gt;C = (E_1, \cdots, E_k, E_{k+1})&lt;/math&gt;，其中 &lt;math&gt;E_{k+1} = v^X&lt;/math&gt;，&lt;math&gt;X&lt;/math&gt; 的顶层列的末列为 &lt;math&gt;A&lt;/math&gt; 的末列。<br /> 此时 &lt;math&gt;A&lt;/math&gt; 的基本列第 &lt;math&gt;n&lt;/math&gt; 项为将 &lt;math&gt;E_{k+1}&lt;/math&gt; 替换为 &lt;math&gt;{E_{k+1}}'&lt;/math&gt; 的 &lt;math&gt;n&lt;/math&gt; 份复制，即将 &lt;math&gt;C&lt;/math&gt; 替换为 &lt;math&gt;C' = (E_1, \cdots, E_k, {E_{k+1}}', \cdots, {E_{k+1}}')&lt;/math&gt;。<br /> 其中 &lt;math&gt;{E_{k+1}}' = v^{X'}&lt;/math&gt; 为去掉 &lt;math&gt;E_{k+1}&lt;/math&gt; 的高度矩阵 &lt;math&gt;X&lt;/math&gt; 的末列得到的项。<br /> <br /> 否则，适用一般展开规则。<br /> 一般展开中，我们定义减一余项。这是在末列删去末项后，将要添加到末列的根列的项。<br /> 令 &lt;math&gt;C_r&lt;/math&gt; 为根列的一个复制，&lt;math&gt;C_t&lt;/math&gt; 为末列的一个复制去掉末项，其列标视为原来列的列标。<br /> 这之后，不断比较 &lt;math&gt;C_r&lt;/math&gt; 与 &lt;math&gt;C_t&lt;/math&gt; 首项的高度，然后删去高度较低的项；高度相同时同时删去。直到 &lt;math&gt;C_r&lt;/math&gt; 与 &lt;math&gt;C_t&lt;/math&gt; 至少有一个为空时，&lt;math&gt;C_r&lt;/math&gt; 中的项即称为减一余项。令阶差等于末列列标减去根列列标。<br /> <br /> 一个元素称为递增的当且仅当它的值不小于根列列标。简单递增 &lt;math&gt;w&lt;/math&gt; 次是指将该矩阵的所有递增元素的值增加阶差的 &lt;math&gt;w&lt;/math&gt; 倍。<br /> 令复制部为根列所在层级中，根列和右侧的所有列构成的矩阵，删去末列。将 &lt;math&gt;C_t'&lt;/math&gt; 为原矩阵末列去掉末项，&lt;math&gt;C_r'&lt;/math&gt; 为减一余项。将 &lt;math&gt;C_t'&lt;/math&gt; 简单递增 &lt;math&gt;w-1&lt;/math&gt; 次得到 &lt;math&gt;C_t''&lt;/math&gt;。<br /> * 若根列不是所在层级末列，令 &lt;math&gt;C_r''&lt;/math&gt; 为对 &lt;math&gt;C_r'&lt;/math&gt; 简单递增 &lt;math&gt;w&lt;/math&gt; 次。递增结果的首列为 &lt;math&gt;C_t'' + C_r''&lt;/math&gt;；其余列为复制部去掉首列后简单递增 &lt;math&gt;w&lt;/math&gt; 次。<br /> * 否则，根列为所在层级的末列，因此末列是根列末项高度矩阵中的列。若减一余项为空，则称 &lt;math&gt;A&lt;/math&gt; 为坏矩阵，不定义其展开。否则，末列实际为减一余项的子列。将减一余项删去末列，然后简单递增 &lt;math&gt;w&lt;/math&gt; 次得到 &lt;math&gt;C_r''&lt;/math&gt;。递增结果为 &lt;math&gt;C_t'' + C_r''&lt;/math&gt; 构成的单列矩阵。<br /> <br /> 这之后，&lt;math&gt;A&lt;/math&gt; 的基本列第 &lt;math&gt;n&lt;/math&gt; 项如下计算：<br /> 将 &lt;math&gt;A&lt;/math&gt; 删去末列，然后对 &lt;math&gt;i=1, \cdots, n&lt;/math&gt;，依次将 &lt;math&gt;A&lt;/math&gt; 的复制部递增 &lt;math&gt;i&lt;/math&gt; 次后，置于删去的末列的位置。（&lt;math&gt;i=1&lt;/math&gt; 时置于 &lt;math&gt;A&lt;/math&gt; 删去的末列的位置；否则置于递增 &lt;math&gt;i-1&lt;/math&gt; 次的复制部删去的末列的位置）得到的矩阵即为所求。<br /> <br /> == 分析 ==<br /> 关于 BTBMS 的强度分析及与 Y 序列等记号的具体对应，详见 [[BTBMS分析]]。<br /> <br /> {{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=BTBMS%E5%88%86%E6%9E%90&diff=3775 2026-08-30T15:39:51Z

<p>0100000000a7：​</p> <hr /> <div>本条目展示 [[BTBMS]] 和 [[ωMN]] 的列表分析。以下分析来自test_alpha0<br /> {| class=&quot;wikitable&quot;<br /> ! BTBMS !! ωMN<br /> |-<br /> | (0) || ()<br /> |-<br /> | (0)(1) || ()(,1)<br /> |-<br /> | (0)(1^(2)) || ()(,,1)<br /> |-<br /> | (0)(1^(2)(2)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)<br /> |-<br /> | (0)(1^(2)(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6)<br /> |-<br /> | (0)(1^(2)(3^(4))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6)(,7,,7)<br /> |-<br /> | (0)(1^(2,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)<br /> |-<br /> | (0)(1^(2,1))(1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,1)<br /> |-<br /> | (0)(1^(2,1))(1)(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,1)(,8,,8)(,9,,8)(,10,8)<br /> |-<br /> | (0)(1^(2,1))(1)(3^(4,3))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4)<br /> |-<br /> | (0)(1^(2,1))(1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4))(4,3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4))(4,3^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4))(4^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)(,10,10,10)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)(,10,10,10,10)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4),3^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)(,10,10,10,,10)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4)(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4)(5^(6,5))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10)(,11,,11)(,12,,11)(,13,11)(,11,11)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(3,3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(3^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(3^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8,8,,8)(,12,8,,8)(,13,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4,3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4,3^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4,3^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)(,12,12,12)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)(,12,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,10,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6)(6))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6)(7^(8,7)))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13)(,14,,14)(,15,,14)(,16,14)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7,7))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14,14)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7^(8)))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14,14,,14)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7^(8)(8)))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14,14,,14)(,15,14,,14)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,3)(5^(6,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)(,12,12,,12)(,13,12,,12)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,3)(5^(6,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)(,12,12,,12)(,13,12,,12)(,14,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,3)(5^(6,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)(,12,12,,12)(,13,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,3)(5^(6,5))(5,5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)(,12,12,,12)(,13,12,,12)(,14,12)(,12,12)<br /> |-<br /> | (0)(1^(2,1))(1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,4,4)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1)(4^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,4,4)(,13,13,,13)(,14,13,,13)(,15,4)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1)(4^(5,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,4,4)(,13,13,,13)(,14,13,,13)(,15,13)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1)(4^(5,4))(4,4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,4,4)(,13,13,,13)(,14,13,,13)(,15,13)(,13,13,13)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1)(4^(5,4))(4,4,4)(4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1)(4^(5,4))(4,4,4)(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1)(5^(6,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)(,15,15,,15)(,16,15,,15)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1)(5^(6,5))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)(,15,15,,15)(,16,15,,15)(,17,15)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1)(5^(6,5))(5,5,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)(,15,15,,15)(,16,15,,15)(,17,15)(,15,15,15)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1)(5^(6,5))(5,5,5)(7^(8,5))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,3))(3,3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,3))(3,3,3)(5^(6,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,12,12,12)(,16,16,16,,16)(,17,16,16,,16)(,18,16)<br /> |-<br /> | (0)(1^(2,1))(1,1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,12,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(1^(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1^(3)(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)(,13,4)<br /> |-<br /> | (0)(1^(2,1))(1^(3,1))(1,1)(4^(5,4))(4^(6,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)(,13,8)<br /> |-<br /> | (0)(1^(2,1))(1^(3,1))(1^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)(,13,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1^(3,1))(1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)(,13,8)(,8,8,,8)(,15,8,,8)(,16,4)<br /> |-<br /> | (0)(1^(2,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9)<br /> |-<br /> | (0)(1^(2,1))(2,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,4)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1,1)(4^(5,4))(5,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1))(1,1)(5^(6,5))(6,5)(5^(8,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1))(1^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1))(1^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)(,8,8,,8)(,16,8,,8)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1))(4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1))(4,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,4)<br /> |-<br /> | (0)(1^(2,1))(2,1)(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,9)<br /> |-<br /> | (0)(1^(2,1))(2,1)(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,12)<br /> |-<br /> | (0)(1^(2,1))(2,1)(3^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2,1)(3^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,12,12,,12)(,13,12,,12)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2,1)(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,12,12,,12)(,13,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1))(2,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1))(2,1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,13)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1,1)(4^(5,4))(5,4^(6,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,8,8,,8)(,16,8,,8)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,4)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4,1^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4,1^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,8,8,,8)(,17,8,,8)(,18,4)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,9)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(2,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(2,1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,4)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(3,1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,8,8)(,8,8,,8)(,14,8,,8)(,15,4)<br /> |-<br /> | (0)(1^(2,1))(2,2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12)(,8,8,,8)(,14,8,,8)(,15,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(2^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(2^(4,1))(4^(5,1),4^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,12,12,12)(,14,14,14,,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(2^(4,1),2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,12,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(2^(4,1),2^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(3,2^(4,1),2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(3^(4,1),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14,14,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(3^(4,1),3^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14,14,14)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3),2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14,14,14,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3),2^(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14,14,14,,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3)(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,13,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,13,12,12,,12)(,16,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4,1)(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,14,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4,1)(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4^(5))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15,15,,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4^(5,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15,15,,15)(,16,15,,15)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4^(5,4))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15,15,,15)(,16,15,,15)(,17,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,8,8,,8)(,16,8,,8)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,13,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4,1^(5,1))(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15)(,8,8,,8)(,17,8,,8)(,18,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1),4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1),4^(5,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,,15)(,16,15,15,,15)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,,15)(,16,15,15,,15)(,17,8,8)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1^(6)))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,,15)(,16,15,15,,15)(,17,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1^(6,1)))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,,15)(,16,15,15,,15)(,17,8,8)(,8,8,,8)(,19,8,,8)(,20,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3,2^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3,2^(4,2)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,12,12,12,,12)(,17,12,12,,12)(,18,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,16,16)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3^(4,2)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,16,16,16,16)(,12,12,12,,12)(,18,12,12,,12)(,19,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3^(4,2),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,16,16,16,16,16)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,16,16,16,16,,16)(,17,16,16,16,,16)(,18,16)<br /> |-<br /> | (0)(1^(2,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3,1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,8,8,,8)(,17,8,,8)(,18,4)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,1),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,3),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)(,17,16,16,,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,3),3)(3^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)(,17,16,16,,16)(,16,16,16,,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,3),3)(3^(5,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)(,17,16,16,,16)(,16,16,16,,16)(,21,16,16,,16)(,22,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,3),3)(3^(5,3))(5^(6,5),5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)(,17,16,16,,16)(,16,16,16,,16)(,21,16,16,,16)(,22,16)(,21,16,16,16)(,24,24,24,24,,24)(,25,24,24,24,,24)(,26,24)(,25,24,24,24,,24)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4,1^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,8,8,,8)(,18,8,,8)(,19,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,1),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,4),4)(5,4^(6)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)(,18,17,17,17)(,17,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,4),4)(5,4^(6,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)(,18,17,17,17)(,17,17,17,,17)(,23,17,17,,17)(,24,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13)(,8,8,,8)(,15,8,,8)(,16,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,1))(1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13)(,8,8,,8)(,15,8,,8)(,16,8)(,15,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,1),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3),3)(4,3^(5,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,,13)(,14,13,13,13)(,13,13,13,,13)(,19,13,13,,13)(,20,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3),3)(4,3^(5,3))(5^(6,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,,13)(,14,13,13,13)(,18,18,18,18,,18)(,19,18,18,18,,18)(,20,18)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3),3)(4,3^(5,3))(5^(6,5),5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,,13)(,14,13,13,13)(,18,18,18,18,,18)(,19,18,18,18,,18)(,20,18)(,19,18,18,18,,18)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1))(4^(5,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1))(4^(5,4),4)(5,4^(6,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)(,18,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1),1)(4,1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,,8)(,14,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,15,8,,8)(,16,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,15,8,,8)(,16,8)(,15,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(1^(5,1),1)(5,1^(6,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,15,8,,8)(,16,8)(,15,8,,8)(,15,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(4^(5,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,14,14,14,,14)(,15,14,14,,14)(,16,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(4^(5,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(4^(5,4),4)(5,4^(6,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)(,15,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,12)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,12,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(2,1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,12,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,10)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(3,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,10,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11,,11)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11,,11)(,12,11,,11)(,13,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4^(5,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11,,11)(,12,11,,11)(,13,11)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4^(5,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11,,11)(,12,11,,11)(,13,11)(,12,11,,11)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1,1)(5^(6,5),5)(6,5^(7,5),5)(7,5^(8,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,14,14,,14)(,24,14,,14)(,25,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,21,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1)(5,1^(6,1),1)(6) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,21,14,,14)(,24)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1)(5,1^(6,1),1)(6,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,21,14,,14)(,24,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1)(5,1^(6,1),1)(6,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1)(5,1^(6,1),1)(6,1^(7)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1))(6^(7,6),6)(7,6^(8,6),6)(8,6^(9,6))(7,6^(10,6)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12)(,17,12,12)(,20,20,20,,20)(,21,20,20,,20)(,22,20,20,20)(,21,20,20,20)(,20,20,20,,20)(,25,20,20,,20)(,26,20)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12)(,17,12,,12)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12)(,17,12,,12)(,17,12,,12)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12)(,17,12,,12)(,20,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12,12)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1^(8)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1^(8,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,,4)(,12,,4)(,13,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1^(8,1))(6) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,5)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(2,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,5,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5,5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,1),5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,1),5^(6,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,1,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,16,16,16,,16)(,17,16,16,,16)(,18,12,12)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,5),5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,5),5)(6,5^(7,5),5)(7,5^(8,5))(6) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,8,8)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,4,,4)(,10,,4)(,11,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1))(1^(7,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,4,,4)(,10,,4)(,11,4)(,10,4)(,13,13,,13)(,14,13,,13)(,15,13,13)(,14,13,,13)(,17,13,13)(,13,13,,13)(,19,13,,13)(,20,13)(,19,13,,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1))(1^(7,1),1)(7,1^(8,1),1)(8,1^(9,1))(7,1^(10,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,4,,4)(,10,,4)(,11,4)(,10,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,5)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1))(2,1^(7,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,5,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,6)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(3,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,6,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,1),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,1^(6))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,4)(,4,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7)(,8,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7)(,8,7,,7)(,8,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4)(6,4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4)(6,4^(7,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7,7)(,7,7,,7)(,11,7,,7)(,12,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4)(6,4^(7,4))(4^(8,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7,7)(,7,7,,7)(,11,7,,7)(,12,7)(,11,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4)(6,4^(7,4))(7^(8,7)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7,7)(,10,10,10,,10)(,11,10,10,,10)(,12,10)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,2) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)<br /> |-<br /> | (0)(1^(2,1),1)(2,2)(2,1^(4,1),1)(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8)(,8,7,,7)(,10,10)<br /> |-<br /> | (0)(1^(2,1),1)(2,2)(2,2) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8)(,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,7,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(1^(4,1),1)(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,7,7,,7)(,10,10)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(2,1^(4,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,8,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,1),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,2)) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,9,9,,9)(,11,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,9,9,,9)(,11,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3),3)(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,10)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3),3)(4,4,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,10,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3),3)(4,4,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,10,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3),3)(4,4,3^(5,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,10,9,9)(,9,9,9,,9)(,12,9,9,,9)(,13,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,2) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3)) || ()(,,1)(,2)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3),2) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,6)(,10,10,,10)(,11,11,11)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3),2^(3)) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,6)(,10,10,,10)(,11,11,11)(,10,10,,10)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3)(3)) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1)) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,,6)(,10,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(1^(4,1),1) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,,6)(,10,6)(,9,6)(,12,12,,12)(,13,13,13)(,12,12,,12)(,15,12,,12)(,16,12)(,15,12,,12)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(1^(4,1),1)(4,4) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,9)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(1^(4,1),1)(4^(5)) || ()(,,1)(,2)(,,1)(,4)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(2) || ()(,,1)(,2)(,2)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3) || ()(,,1)(,2)(,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,1),3) || ()(,,1)(,2)(,3,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,1),3^(4)) || ()(,,1)(,2)(,3,,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,1),3^(4)(4)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,1),3^(4,1)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,1^(5))) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,6)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,2)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,2^(5))) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,7)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3))(4) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3))(4,3^(5,3)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,14)(,14,14,14,,14)(,19,14,14,,14)(,20,14)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3))(4^(5,3),4) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,14)(,18,18,18,18,18)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3))(4^(5,4)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,14)(,18,18,18,18,,18)(,19,18,18,18,,18)(,20,18)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4,3^(5,3),3) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)(,15,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4,4) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,9)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5)) || ()(,,1)(,2)(,3,,3)(,4)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5)(5)) || ()(,,1)(,2)(,3,,3)(,4)(,,1)(,6)(,1)(,8,,8)(,9,9)(,10,10,,10)(,11,11)(,8,,8)(,13,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,1)) || ()(,,1)(,2)(,3,,3)(,4)(,,1)(,6)(,1)(,8,,8)(,9,9)(,10,10,,10)(,11,11)(,8,,8)(,13,,8)(,14,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,2)) || ()(,,1)(,2)(,3,,3)(,4,4)(,3,,3)(,6,,3)(,7)(,1)(,9,,9)(,10,10)(,11,11,,11)(,12,12,12)(,11,11,,11)(,14,11,,11)(,15,10)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,3)) || ()(,,1)(,2)(,3,,3)(,4,4)(,3,,3)(,6,,3)(,7)(,1)(,9,,9)(,10,10)(,11,11,,11)(,12,12,12)(,11,11,,11)(,14,11,,11)(,15,11)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,3))(3^(6,3),3) || ()(,,1)(,2)(,3,,3)(,4,4)(,3,,3)(,6,,3)(,7)(,1)(,9,,9)(,10,10)(,11,11,,11)(,12,12,12)(,11,11,,11)(,14,11,,11)(,15,11)(,14,11,,11)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,3))(5^(6,5)) || ()(,,1)(,2)(,3,,3)(,4,4)(,5,5,,5)(,6)(,1)(,8,,8)(,9,9)(,10,10,,10)(,11,11,11)(,12,12,12,,12)(,13,12,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1) || ()(,,1)(,2,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1)(4,4) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)(,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1)(4^(5,1))(5^(6,5),5)(6,6) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)(,8,8)(,9,9,,9)(,10,10,10)(,11,11,11,,11)(,12,12)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1)(4^(5,1))(5^(6,5),5)(6^(7,5),5) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)(,8,8)(,9,9,,9)(,10,10,10,,9)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1)(4^(5,1),1) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)(,8,8,,5)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,2) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2^(4)) || ()(,,1)(,2,,1)(,2)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2^(4,1))(4) || ()(,,1)(,2,,1)(,2)(,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2^(4,1))(4^(5,4),4)(5^(6,4),4) || ()(,,1)(,2,,1)(,2)(,4,,4)(,5,5,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2^(4,1),1) || ()(,,1)(,2,,1)(,2,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3) || ()(,,1)(,2,,1)(,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3,1) || ()(,,1)(,2,,1)(,3)(,1)(,5,,5)(,6,6,,5)(,7,5)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3,1^(4,1),1) || ()(,,1)(,2,,1)(,3)(,1)(,5,,5)(,6,6,,5)(,7,,5)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3,2) || ()(,,1)(,2,,1)(,3)(,1)(,5,,5)(,6,6,,5)(,7,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3,3) || ()(,,1)(,2,,1)(,3)(,1)(,5,,5)(,6,6,,5)(,7,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3^(4)) || ()(,,1)(,2,,1)(,3)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3^(4,1)) || ()(,,1)(,2,,1)(,3)(,,1)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9)(,7,,7)(,11,,7)(,12,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3^(4,1))(4) || ()(,,1)(,2,,1)(,3)(,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3^(4,1))(4^(5,4),4)(5^(6,4),4) || ()(,,1)(,2,,1)(,3)(,4,,4)(,5,5,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2) || ()(,,1)(,2,,1)(,3,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3) || ()(,,1)(,2,,1)(,3,3)(,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,1) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,1^(4,1),1) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4)) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,7)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),1) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,7,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),1)(4^(5,1),4)(5,4) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),1)(4^(5,1),4)(5,4^(6,1),1) || (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),1)(4^(5,1),4)(5,4^(6,1),1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),2) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,3) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,9)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3^(4)) || ()(,,1)(,2,,1)(,3,3)(,4)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,3)(,4,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3^(4,1),2) || ()(,,1)(,2,,1)(,3,3)(,4,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3)(,4,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2,2) || ()(,,1)(,2,,1)(,3,3)(,4,4,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2^(3)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2^(3,1)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1^(4))) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,7)(,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1^(4,1),1)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),1)(4^(5,4)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,9)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),1)(4^(5,4))(4^(6,1),1)(6^(7,6)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,9)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,16)(,16,16,16,,14)(,21,21,21,21)(,22,22,22,22,,22)(,23,22,22,22,,22)(,24,21)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,8)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,15)(,16,16,16,16)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2)(4^(5,2)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,9)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,16)(,16,16,16,16)(,21,21,21,21,,21)(,22,21,21,21,,21)(,23,16)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2)(4^(5,2),4) || <br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2)(4^(5,4)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2)(4^(5,4))(4) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,17)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2,2) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,17,17,17,17,17)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,2)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,17,17,17,17,,17)(,21,17,17,17,,17)(,22,17)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(3,2^(4,2)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,17)(,17,17,17,17,,17)(,22,17,17,17,,17)(,23,17)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(3,3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,17)(,21,21)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(3^(4,2),3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,17)(,21,21,21,21,21,21)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(3^(4,3)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,17)(,21,21,21,21,21,,21)(,22,21,21,21,21,,21)(,23,21)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3,3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,11)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,2)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5,5)(,4,4,,4)(,7,4,,4)(,8,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,2),2) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5,5,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,2),3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5,5,,4)(,6,6,6,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,3)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5,5,,4)(,6,6,6,6)(,7,7,7,7,,7)(,8)(,1)(,10,,10)(,11,11,,10)(,12,12,12)(,13,13,13,,13)(,14,14,14,14,,13)(,15,15,15,15,15)(,16,16,16,16,16,,16)(,17,16,16,16,16,,16)(,18,14)<br /> |-<br /> | (0)(1^(2,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(1^(3,1),1)(3^(4)) || ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5)(,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(1^(3,1),1)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(1^(3,1),1)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5,,1)(,6,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(1^(3,1),1)(3^(4,3),3,3) || ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5,,1)(,6,6)(,7,7,,7)(,8,8,8,,7)(,9,9,9,9,,7)<br /> |-<br /> | (0)(1^(2,1),1,1)(1^(3,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5,,1)(,6,6,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2) || ()(,,1)(,2,,1)(,3,3,,1)(,2)<br /> |-<br /> | (0)(1^(2,1),1,1)(2,1^(3,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,2)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,7,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2,1^(3,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,2)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,7,,6)(,10,10,,6)(,11,11,11,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2,2) || ()(,,1)(,2,,1)(,3,3,,1)(,2)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,7,7)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3)) || ()(,,1)(,2,,1)(,3,3,,1)(,2)(,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3)(4) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3)(4^(5,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3)(4^(5,1),3) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3)(4^(5,1),4) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3,3) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3^(4)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3^(4,1)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1^(5))) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,9)(,9,,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1^(5,1),1)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1^(5,1),1,1)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,,9)(,17,17,,9)(,18,18,18,,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,2)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,10)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,2^(5,1),1)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,10,,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4,3^(5,3)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,23)(,23,23,23,23,,23)(,28,23,23,23,,23)(,29,22)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4,4) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,23)(,27,27)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4^(5,3),4) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,23)(,27,27,27,27,27,27)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4^(5,3),4^(5,3)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,23)(,27,27,27,27,27,,27)(,28,27,27,27,27,,27)(,29,22)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4^(5,3)(5)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,,23)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4^(5,4)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3),3) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3),3,3) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7,7,7,,6)(,8,8,8,8,,6)(,7,7,7,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1,1)(3) || ()(,,1)(,2,,1)(,3,3,,1)(,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1,1)(3^(4,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,,1)(,5,5,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,1),2) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,3)) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,5,,5)(,6,5,,5)(,7,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,3),3)(4^(5,3),3) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,5,,5)(,6,6,6,,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,3),3,3) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,5,,5)(,6,6,6,,5)(,7,7,7,7,,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,2,,1)(,3,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1)(4^(5,1),4,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,2,,1)(,3,3,,1)(,3,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1)(4^(5,1),4,1)(4) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1)(4^(5,1),4,1)(4^(6,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1)(4^(5,1),4,1)(4^(6,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3,,1)(,6,6,,1)(,6,6,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),2) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),2,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3) || ()(,,1)(,2,,1)(,3,3,,1)(,4)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,1^(4,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,1^(4,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,,6)(,10,10,,6)(,11,11,11,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,7)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,7,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,7,,6)(,10,10,10,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1,1)(4^(5,1),4,1)(5,4) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1,1)(4^(5,1),4,1)(5,4^(6,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1,1)(4^(5,1),4,1)(5,4^(6,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8,,6)(,10,10,10,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),2) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),2,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8,8,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,3) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4)) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,4,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4,,1)(,5,5,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),2) || ()(,,1)(,2,,1)(,3,3,,1)(,4,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),2,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),3,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,2) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,2)) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)(,5,5,5,,5)(,6)(,1)(,8,,8)(,9,9,,8)(,10,10,10,,8)(,11,11,11,11)(,12,12,12,12,,12)(,13,12,12,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,2),2)(3^(4)) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)(,5,5,5,,5)(,6)(,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,2),2)(3^(4,2),2) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)(,5,5,5,,5)(,6,6,6,6,,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,2),2,2) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)(,5,5,5,,5)(,6,6,6,6,,5)(,7,7,7,7,7,,5)<br /> |-<br /> | (0)(1^(2,1),1,1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4,,1)<br /> |-<br /> | (0)(1^(2,1),1^(2)) || ()(,,1)(,,2)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2) || ()(,,1)(,,2)(,2)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2,1) || ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2,1^(3,1))(3^(4,3),3^(4)) || ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,5)(,8,8,,8)(,9,9,,9)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2,1^(3,1),1) || ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2,1^(3,1),1^(3)) || ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,,5)(,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2,2) || ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3)) || ()(,,1)(,,2)(,2)(,,1)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),1) || ()(,,1)(,,2)(,2,,1)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),1,1) || ()(,,1)(,,2)(,2,,1)(,4,4,,1)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),1^(3)) || ()(,,1)(,,2)(,2,,1)(,4,,4)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2) || ()(,,1)(,,2)(,2,,1)(,4,,4)(,4,4)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2,1) || ()(,,1)(,,2)(,2,,1)(,4,,4)(,4,4,,1)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2,1^(3)) || ()(,,1)(,,2)(,2,,1)(,4,,4)(,4,4,,1)(,6,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2,2) || ()(,,1)(,,2)(,2,,1)(,4,,4)(,4,4,,1)(,6,6,,6)(,6,6,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3)) || ()(,,1)(,,2)(,,2)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3) || ()(,,1)(,,2)(,3)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,1^(4,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,1^(4,1),1^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,5)(,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,1^(4,1),1^(4))(4^(5,1),4^(5)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,5)(,8,,8)(,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,5,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1))(1^(5,1),1^(5)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,5,,5)(,9,,9)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,6,,5)(,9,9,,9)(,10,9,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),1^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,6,,5)(,9,9,,9)(,10,9,,5)(,11,11,,11)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,6,,5)(,9,9,,9)(,10,9,9)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),2,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,6,,5)(,9,9,,9)(,10,9,9)(,9,9,9,,5)(,12,12,12,,12)(,13,12,12,12)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),2^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3^(4,1),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,8,,8)(,10,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2),2,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,9,9,,8)(,10,10,10,10,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,9,,9)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2),2^(3))(3^(4,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,9,,9)(,10,9,9)(,11,11,11,,11)(,12,11,11,,11)(,13,9)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2),2^(3))(3^(4,3),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,9,,9)(,10,9,9)(,11,11,11,,11)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1),1^(2),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(9)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3,2^(4,1),2^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,1),3^(4),3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,,10)(,11,10,,10)(,12,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,,10)(,11,10,,10)(,12,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,3),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,,10)(,11,11,,11)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,3),3^(4),3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,,10)(,11,11,,11)(,12,11,11,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,7)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,7,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,7,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,2^(4,1),2^(4),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,7,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,2^(4,1),2^(4),1)(4) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3^(4,1),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3^(4,1),3^(4),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8)(,9,9,9,,9)(,10,9,9,,9)(,11,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,2),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8)(,9,9,9,,9)(,10,10,10,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,2),2^(3),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8)(,9,9,9,,9)(,10,10,10,,10)(,11,10,10,10,,9)<br /> |-<br /> | (0)(1^(2,1),1^(2),1,1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2,1^(3,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2,1^(3,1),1^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,5)(,10,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2,1^(3,1),1^(3),1^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,5)(,10,,10)(,11,10,,5)(,12,12,,12)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3,2^(4,1),2^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3^(4,1),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,11,11)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3^(4,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,11,11,,11)(,12,11,,11)(,13,11)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3^(4,3),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,11,11,,11)(,12,12,,12)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3^(4,3),3^(4),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,11,11,,11)(,12,12,,12)(,13,12,12,,11)(,14,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6,,5)(,11,11,,11)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,7)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3,2^(4,1),2^(4),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,7,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3,2^(4,1),2^(4),1^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,7,6,,5)(,10,10,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3,2^(4,1),2^(4),1^(4))(4) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3,3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4))(2^(5,1),2^(5),1^(5)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8)(,6,,6)(,11,6,,5)(,12,12,,12)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4))(2^(5,1),2^(5),1^(5))(5^(6,1),5^(6)) || <br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4))(4^(5,4),4^(5),4^(5)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8)(,10,10,,10)(,11,11,,11)(,12,11,11,,10)(,13,13,13,,13)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4),1^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,,5)(,10,10,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2,1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,8,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2,1^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,8,,5)(,10,10,10,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,8,,5)(,10,10,10,,10)(,10,10,10,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,2),2^(3),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,9,8)(,10,10,,10)(,11,11,,11)(,12,11,11,,10)(,13,13,13,,13)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,9,8,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2)(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(8,5)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2) || <br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3))(3) || <br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,11,11,,11)(,15,11,11,,10)(,16,16,16,,16)(,17,16,16,,16)(,18,10)(,16,16,16,,16)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,11,11,,11)(,15,11,,11)(,16,5)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1))(3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1))(3,2^(4,1),2^(4,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,11,11,,11)(,16,11,,11)(,17,10)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1))(3,3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,15)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,,15)(,16,15,15,,15)(,17,15)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,2),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,,15)(,16,16,16,,16)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,2),2^(3,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,,15)(,16,16,16,,16)(,17,16,16,,16)(,18,5)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,2),2^(3,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,,15)(,16,16,16,,16)(,17,16,16,,16)(,18,15)<br /> |-<br /> | (0)(1^(2,1),1^(2,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2,1),1^(2,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11,,10)(,15,15,15,,15)(,16,15,15,,15)(,17,10)<br /> |-<br /> | (0)(1^(2,1)(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,,11)<br /> |-<br /> | (0)(1^(2,1)(2,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,,11)(,15,10)<br /> |-<br /> | (0)(1^(2,1)(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,13)<br /> |-<br /> | (0)(1^(2,1)(3,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,13,5)<br /> |-<br /> | (0)(1^(2,1)(3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,14,14)<br /> |-<br /> | (0)(1^(2,1)(3^(4))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,14,14,,14)<br /> |-<br /> | (0)(1^(2,1)(3^(4,3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,14,14,,14)(,15,15,,15)(,16,15,,15)(,17,14)<br /> |-<br /> | (0)(1^(2,1,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10,10)<br /> |-<br /> | (0)(1^(2,1^(3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)<br /> |-<br /> | (0)(1^(2,1^(3,1))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)<br /> |-<br /> | (0)(1^(2,1^(3,1)))(1^(3,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,13,13,,13)(,18,13,,13)(,19,13)(,18,13,,13)<br /> |-<br /> | (0)(1^(2,1^(3,1)))(2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,14)<br /> |-<br /> | (0)(1^(2,1^(3,1)))(2^(3,1^(4,1))) || <br /> |-<br /> | (0)(1^(2,1^(3,1)))(2^(3,1^(4,1)))(3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,15)<br /> |-<br /> | (0)(1^(2,1^(3,1)),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,15,14,14,,13)<br /> |-<br /> | (0)(1^(2,1^(3,1))(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,15,14,,14)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,16)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13,13)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13,13)(,13,13,,13)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13,13)(,13,13,,13)(,18,13,,13)(,19,5)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1)))(1^(3,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,,5)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1)))(2,1^(3,1),1) || <br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1))(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,7,,6)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1))(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,8)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1))(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,9)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,9,9)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3^(4,3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,9,9,,9)(,10,9,,9)(,11,9)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3^(4,3^(5,3)))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,9,9,,9)(,10,10,,10)(,11,10,,10)(,12,9)<br /> |-<br /> | (0)(1^(2,1^(3,1),1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)<br /> |-<br /> | (0)(1^(2,1^(3,1),1^(3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)(,9,,9)<br /> |-<br /> | (0)(1^(2,1^(3,1),1^(3,1))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)(,9,,9)(,10,,9)(,11,5)<br /> |-<br /> | (0)(1^(2,1^(3,1^(4)))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)(,9,,9)(,10,,9)(,11,5)(,5,,5)<br /> |-<br /> | (0)(1^(2,1^(3,1^(4,1)))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)(,9,,9)(,10,,9)(,11,5)(,5,,5)(,13,,5)(,14,5)<br /> |-<br /> | (0)(1^(2,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)<br /> |-<br /> | (0)(1^(2^(3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,5,,5)<br /> |-<br /> | (0)(1^(2^(3,1))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,5,,5)(,10,,5)(,11,5)<br /> |-<br /> | (0)(1^(2^(3,1))(2^(4))) || <br /> |-<br /> | (0)(1^(2^(3,1),1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,6,6,,5)(,10,10,,10)(,11,10,,10)(,12,10,,5)<br /> |-<br /> | (0)(1^(2^(3,1),2^(3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,6,,6)<br /> |-<br /> | (0)(1^(2^(3,2))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,6,,6)(,10,,6)(,11,6)<br /> |-<br /> | (0)(1^(2^(3,2))(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,7,,6)<br /> |-<br /> | (0)(1^(2^(3,2))(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,8)<br /> |-<br /> | (0)(1^(2^(3,2))(3,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,8,5)<br /> |-<br /> | (0)(1^(2^(3,2))(3,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,8,6)<br /> |-<br /> | (0)(1^(2^(3,2))(3,2^(4,2))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,8,6)(,6,,6)(,11,,6)(,12,6)<br /> |-<br /> | (0)(1^(2^(3,2))(3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,9,9)<br /> |-<br /> | (0)(1^(2^(3,2),1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)<br /> |-<br /> | (0)(1^(2^(3,2),1)(3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9)<br /> |-<br /> | (0)(1^(2^(3,2),1)(3^(4,2),3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,9)<br /> |-<br /> | (0)(1^(2^(3,2),1)(3^(4,2),3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,9)(,10,10,10,10)<br /> |-<br /> | (0)(1^(2^(3,2),1,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,9,,5)<br /> |-<br /> | (0)(1^(2^(3,2),1^(3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,,9)<br /> |-<br /> | (0)(1^(2^(3,2),1^(3^(4,3),1))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,,9)(,10,9,,9)(,11,9,9,,5)<br /> |-<br /> | (0)(1^(2^(3,2),2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,6)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,6)(,8)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3,2^(4,2),1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,6)(,8,6,,5)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3,2^(4,2),2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,6)(,8,,6)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,7)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4))) || ()(,,1)(,,2)(,3)(,,1)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,1),3^(4))) || ()(,,1)(,,2)(,3)(,,2)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,2))) || ()(,,1)(,,2)(,3)(,,2)(,5)(,1)(,7,,7)(,8,,8)(,9,9)(,8,,8)(,11,,8)(,12,8)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,2),1)) || ()(,,1)(,,2)(,3,,1)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,2),2)) || ()(,,1)(,,2)(,3,,2)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,2),3)) || ()(,,1)(,,2)(,3,,2)(,4,4)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,2),3^(4))) || <br /> |-<br /> | (0)(1^(2^(3,2),2,1)) || ()(,,1)(,,2)(,3,,2)(,4,4,,1)<br /> |-<br /> | (0)(1^(2^(3,2),2,2)) || ()(,,1)(,,2)(,3,,2)(,4,4,,2)<br /> |-<br /> | (0)(1^(2^(3,2),2^(3))) || ()(,,1)(,,2)(,,3)<br /> |-<br /> | (0)(1^(2^(3^(4)))) || ()(,,1)(,,2)(,,3)(,4)(,1)(,6,,6)(,7,,7)(,8,,8)(,9,,8)(,10,8)(,6,,6)<br /> |-<br /> | Limit || ()(,,1)(,,2,2)<br /> |}<br /> <br /> [[分类:分析]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=BTBMS%E5%88%86%E6%9E%90&diff=3774 2026-08-30T15:37:52Z

<p>0100000000a7：​</p> <hr /> <div>本条目展示 [[BTBMS]] 和 [[ωMN]] 的列表分析。以下分析来自test_alpha0<br /> {| class=&quot;wikitable&quot;<br /> ! BTBMS !! ωMN<br /> |-<br /> | (0) || ()<br /> |-<br /> | (0)(1) || ()(,1)<br /> |-<br /> | (0)(1^(2)) || ()(,,1)<br /> |-<br /> | (0)(1^(2)(2)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)<br /> |-<br /> | (0)(1^(2)(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6)<br /> |-<br /> | (0)(1^(2)(3^(4))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6)(,7,,7)<br /> |-<br /> | (0)(1^(2,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)<br /> |-<br /> | (0)(1^(2,1))(1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,1)<br /> |-<br /> | (0)(1^(2,1))(1)(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,1)(,8,,8)(,9,,8)(,10,8)<br /> |-<br /> | (0)(1^(2,1))(1)(3^(4,3))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4)<br /> |-<br /> | (0)(1^(2,1))(1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4))(4,3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4))(4,3^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4))(4^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)(,10,10,10)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)(,10,10,10,10)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4),3^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)(,10,10,10,,10)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4)(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4)(5^(6,5))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10)(,11,,11)(,12,,11)(,13,11)(,11,11)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(3,3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(3^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(3^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8,8,,8)(,12,8,,8)(,13,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4,3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4,3^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4,3^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)(,12,12,12)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)(,12,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,10,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6)(6))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6)(7^(8,7)))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13)(,14,,14)(,15,,14)(,16,14)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7,7))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14,14)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7^(8)))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14,14,,14)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7^(8)(8)))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14,14,,14)(,15,14,,14)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,3)(5^(6,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)(,12,12,,12)(,13,12,,12)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,3)(5^(6,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)(,12,12,,12)(,13,12,,12)(,14,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,3)(5^(6,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)(,12,12,,12)(,13,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,3)(5^(6,5))(5,5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)(,12,12,,12)(,13,12,,12)(,14,12)(,12,12)<br /> |-<br /> | (0)(1^(2,1))(1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,4,4)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1)(4^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,4,4)(,13,13,,13)(,14,13,,13)(,15,4)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1)(4^(5,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,4,4)(,13,13,,13)(,14,13,,13)(,15,13)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1)(4^(5,4))(4,4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,4,4)(,13,13,,13)(,14,13,,13)(,15,13)(,13,13,13)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1)(4^(5,4))(4,4,4)(4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1)(4^(5,4))(4,4,4)(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1)(5^(6,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)(,15,15,,15)(,16,15,,15)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1)(5^(6,5))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)(,15,15,,15)(,16,15,,15)(,17,15)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1)(5^(6,5))(5,5,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)(,15,15,,15)(,16,15,,15)(,17,15)(,15,15,15)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1)(5^(6,5))(5,5,5)(7^(8,5))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,3))(3,3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,3))(3,3,3)(5^(6,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,12,12,12)(,16,16,16,,16)(,17,16,16,,16)(,18,16)<br /> |-<br /> | (0)(1^(2,1))(1,1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,12,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(1^(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1^(3)(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)(,13,4)<br /> |-<br /> | (0)(1^(2,1))(1^(3,1))(1,1)(4^(5,4))(4^(6,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)(,13,8)<br /> |-<br /> | (0)(1^(2,1))(1^(3,1))(1^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)(,13,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1^(3,1))(1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)(,13,8)(,8,8,,8)(,15,8,,8)(,16,4)<br /> |-<br /> | (0)(1^(2,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9)<br /> |-<br /> | (0)(1^(2,1))(2,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,4)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1,1)(4^(5,4))(5,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1))(1,1)(5^(6,5))(6,5)(5^(8,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1))(1^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1))(1^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)(,8,8,,8)(,16,8,,8)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1))(4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1))(4,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,4)<br /> |-<br /> | (0)(1^(2,1))(2,1)(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,9)<br /> |-<br /> | (0)(1^(2,1))(2,1)(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,12)<br /> |-<br /> | (0)(1^(2,1))(2,1)(3^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2,1)(3^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,12,12,,12)(,13,12,,12)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2,1)(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,12,12,,12)(,13,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1))(2,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1))(2,1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,13)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1,1)(4^(5,4))(5,4^(6,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,8,8,,8)(,16,8,,8)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,4)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4,1^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4,1^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,8,8,,8)(,17,8,,8)(,18,4)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,9)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(2,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(2,1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,4)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(3,1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,8,8)(,8,8,,8)(,14,8,,8)(,15,4)<br /> |-<br /> | (0)(1^(2,1))(2,2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12)(,8,8,,8)(,14,8,,8)(,15,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(2^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(2^(4,1))(4^(5,1),4^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,12,12,12)(,14,14,14,,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(2^(4,1),2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,12,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(2^(4,1),2^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(3,2^(4,1),2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(3^(4,1),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14,14,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(3^(4,1),3^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14,14,14)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3),2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14,14,14,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3),2^(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14,14,14,,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3)(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,13,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,13,12,12,,12)(,16,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4,1)(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,14,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4,1)(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4^(5))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15,15,,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4^(5,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15,15,,15)(,16,15,,15)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4^(5,4))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15,15,,15)(,16,15,,15)(,17,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,8,8,,8)(,16,8,,8)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,13,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4,1^(5,1))(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15)(,8,8,,8)(,17,8,,8)(,18,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1),4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1),4^(5,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,,15)(,16,15,15,,15)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,,15)(,16,15,15,,15)(,17,8,8)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1^(6)))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,,15)(,16,15,15,,15)(,17,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1^(6,1)))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,,15)(,16,15,15,,15)(,17,8,8)(,8,8,,8)(,19,8,,8)(,20,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3,2^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3,2^(4,2)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,12,12,12,,12)(,17,12,12,,12)(,18,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,16,16)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3^(4,2)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,16,16,16,16)(,12,12,12,,12)(,18,12,12,,12)(,19,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3^(4,2),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,16,16,16,16,16)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,16,16,16,16,,16)(,17,16,16,16,,16)(,18,16)<br /> |-<br /> | (0)(1^(2,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3,1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,8,8,,8)(,17,8,,8)(,18,4)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,1),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,3),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)(,17,16,16,,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,3),3)(3^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)(,17,16,16,,16)(,16,16,16,,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,3),3)(3^(5,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)(,17,16,16,,16)(,16,16,16,,16)(,21,16,16,,16)(,22,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,3),3)(3^(5,3))(5^(6,5),5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)(,17,16,16,,16)(,16,16,16,,16)(,21,16,16,,16)(,22,16)(,21,16,16,16)(,24,24,24,24,,24)(,25,24,24,24,,24)(,26,24)(,25,24,24,24,,24)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4,1^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,8,8,,8)(,18,8,,8)(,19,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,1),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,4),4)(5,4^(6)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)(,18,17,17,17)(,17,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,4),4)(5,4^(6,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)(,18,17,17,17)(,17,17,17,,17)(,23,17,17,,17)(,24,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13)(,8,8,,8)(,15,8,,8)(,16,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,1))(1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13)(,8,8,,8)(,15,8,,8)(,16,8)(,15,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,1),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3),3)(4,3^(5,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,,13)(,14,13,13,13)(,13,13,13,,13)(,19,13,13,,13)(,20,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3),3)(4,3^(5,3))(5^(6,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,,13)(,14,13,13,13)(,18,18,18,18,,18)(,19,18,18,18,,18)(,20,18)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3),3)(4,3^(5,3))(5^(6,5),5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,,13)(,14,13,13,13)(,18,18,18,18,,18)(,19,18,18,18,,18)(,20,18)(,19,18,18,18,,18)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1))(4^(5,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1))(4^(5,4),4)(5,4^(6,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)(,18,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1),1)(4,1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,,8)(,14,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,15,8,,8)(,16,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,15,8,,8)(,16,8)(,15,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(1^(5,1),1)(5,1^(6,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,15,8,,8)(,16,8)(,15,8,,8)(,15,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(4^(5,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,14,14,14,,14)(,15,14,14,,14)(,16,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(4^(5,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(4^(5,4),4)(5,4^(6,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)(,15,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,12)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,12,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(2,1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,12,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,10)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(3,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,10,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11,,11)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11,,11)(,12,11,,11)(,13,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4^(5,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11,,11)(,12,11,,11)(,13,11)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4^(5,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11,,11)(,12,11,,11)(,13,11)(,12,11,,11)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1,1)(5^(6,5),5)(6,5^(7,5),5)(7,5^(8,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,14,14,,14)(,24,14,,14)(,25,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,21,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1)(5,1^(6,1),1)(6) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,21,14,,14)(,24)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1)(5,1^(6,1),1)(6,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,21,14,,14)(,24,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1)(5,1^(6,1),1)(6,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1)(5,1^(6,1),1)(6,1^(7)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1))(6^(7,6),6)(7,6^(8,6),6)(8,6^(9,6))(7,6^(10,6)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12)(,17,12,12)(,20,20,20,,20)(,21,20,20,,20)(,22,20,20,20)(,21,20,20,20)(,20,20,20,,20)(,25,20,20,,20)(,26,20)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12)(,17,12,,12)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12)(,17,12,,12)(,17,12,,12)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12)(,17,12,,12)(,20,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12,12)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1^(8)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1^(8,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,,4)(,12,,4)(,13,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1^(8,1))(6) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,5)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(2,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,5,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5,5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,1),5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,1),5^(6,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,1,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,16,16,16,,16)(,17,16,16,,16)(,18,12,12)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,5),5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,5),5)(6,5^(7,5),5)(7,5^(8,5))(6) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,8,8)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,4,,4)(,10,,4)(,11,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1))(1^(7,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,4,,4)(,10,,4)(,11,4)(,10,4)(,13,13,,13)(,14,13,,13)(,15,13,13)(,14,13,,13)(,17,13,13)(,13,13,,13)(,19,13,,13)(,20,13)(,19,13,,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1))(1^(7,1),1)(7,1^(8,1),1)(8,1^(9,1))(7,1^(10,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,4,,4)(,10,,4)(,11,4)(,10,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,5)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1))(2,1^(7,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,5,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,6)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(3,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,6,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,1),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,1^(6))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,4)(,4,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7)(,8,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7)(,8,7,,7)(,8,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4)(6,4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4)(6,4^(7,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7,7)(,7,7,,7)(,11,7,,7)(,12,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4)(6,4^(7,4))(4^(8,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7,7)(,7,7,,7)(,11,7,,7)(,12,7)(,11,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4)(6,4^(7,4))(7^(8,7)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7,7)(,10,10,10,,10)(,11,10,10,,10)(,12,10)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,2) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)<br /> |-<br /> | (0)(1^(2,1),1)(2,2)(2,1^(4,1),1)(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8)(,8,7,,7)(,10,10)<br /> |-<br /> | (0)(1^(2,1),1)(2,2)(2,2) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8)(,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,7,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(1^(4,1),1)(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,7,7,,7)(,10,10)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(2,1^(4,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,8,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,1),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,2)) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,9,9,,9)(,11,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,9,9,,9)(,11,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3),3)(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,10)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3),3)(4,4,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,10,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3),3)(4,4,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,10,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3),3)(4,4,3^(5,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,10,9,9)(,9,9,9,,9)(,12,9,9,,9)(,13,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,2) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3)) || ()(,,1)(,2)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3),2) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,6)(,10,10,,10)(,11,11,11)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3),2^(3)) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,6)(,10,10,,10)(,11,11,11)(,10,10,,10)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3)(3)) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1)) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,,6)(,10,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(1^(4,1),1) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,,6)(,10,6)(,9,6)(,12,12,,12)(,13,13,13)(,12,12,,12)(,15,12,,12)(,16,12)(,15,12,,12)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(1^(4,1),1)(4,4) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,9)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(1^(4,1),1)(4^(5)) || ()(,,1)(,2)(,,1)(,4)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(2) || ()(,,1)(,2)(,2)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3) || ()(,,1)(,2)(,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,1),3) || ()(,,1)(,2)(,3,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,1),3^(4)) || ()(,,1)(,2)(,3,,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,1),3^(4)(4)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,1),3^(4,1)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,1^(5))) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,6)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,2)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,2^(5))) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,7)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3))(4) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3))(4,3^(5,3)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,14)(,14,14,14,,14)(,19,14,14,,14)(,20,14)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3))(4^(5,3),4) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,14)(,18,18,18,18,18)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3))(4^(5,4)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,14)(,18,18,18,18,,18)(,19,18,18,18,,18)(,20,18)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4,3^(5,3),3) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)(,15,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4,4) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,9)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5)) || ()(,,1)(,2)(,3,,3)(,4)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5)(5)) || ()(,,1)(,2)(,3,,3)(,4)(,,1)(,6)(,1)(,8,,8)(,9,9)(,10,10,,10)(,11,11)(,8,,8)(,13,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,1)) || ()(,,1)(,2)(,3,,3)(,4)(,,1)(,6)(,1)(,8,,8)(,9,9)(,10,10,,10)(,11,11)(,8,,8)(,13,,8)(,14,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,2)) || ()(,,1)(,2)(,3,,3)(,4,4)(,3,,3)(,6,,3)(,7)(,1)(,9,,9)(,10,10)(,11,11,,11)(,12,12,12)(,11,11,,11)(,14,11,,11)(,15,10)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,3)) || ()(,,1)(,2)(,3,,3)(,4,4)(,3,,3)(,6,,3)(,7)(,1)(,9,,9)(,10,10)(,11,11,,11)(,12,12,12)(,11,11,,11)(,14,11,,11)(,15,11)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,3))(3^(6,3),3) || ()(,,1)(,2)(,3,,3)(,4,4)(,3,,3)(,6,,3)(,7)(,1)(,9,,9)(,10,10)(,11,11,,11)(,12,12,12)(,11,11,,11)(,14,11,,11)(,15,11)(,14,11,,11)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,3))(5^(6,5)) || ()(,,1)(,2)(,3,,3)(,4,4)(,5,5,,5)(,6)(,1)(,8,,8)(,9,9)(,10,10,,10)(,11,11,11)(,12,12,12,,12)(,13,12,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1) || ()(,,1)(,2,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1)(4,4) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)(,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1)(4^(5,1))(5^(6,5),5)(6,6) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)(,8,8)(,9,9,,9)(,10,10,10)(,11,11,11,,11)(,12,12)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1)(4^(5,1))(5^(6,5),5)(6^(7,5),5) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)(,8,8)(,9,9,,9)(,10,10,10,,9)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1)(4^(5,1),1) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)(,8,8,,5)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,2) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2^(4)) || ()(,,1)(,2,,1)(,2)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2^(4,1))(4) || ()(,,1)(,2,,1)(,2)(,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2^(4,1))(4^(5,4),4)(5^(6,4),4) || ()(,,1)(,2,,1)(,2)(,4,,4)(,5,5,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2^(4,1),1) || ()(,,1)(,2,,1)(,2,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3) || ()(,,1)(,2,,1)(,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3,1) || ()(,,1)(,2,,1)(,3)(,1)(,5,,5)(,6,6,,5)(,7,5)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3,1^(4,1),1) || ()(,,1)(,2,,1)(,3)(,1)(,5,,5)(,6,6,,5)(,7,,5)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3,2) || ()(,,1)(,2,,1)(,3)(,1)(,5,,5)(,6,6,,5)(,7,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3,3) || ()(,,1)(,2,,1)(,3)(,1)(,5,,5)(,6,6,,5)(,7,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3^(4)) || ()(,,1)(,2,,1)(,3)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3^(4,1)) || ()(,,1)(,2,,1)(,3)(,,1)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9)(,7,,7)(,11,,7)(,12,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3^(4,1))(4) || ()(,,1)(,2,,1)(,3)(,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3^(4,1))(4^(5,4),4)(5^(6,4),4) || ()(,,1)(,2,,1)(,3)(,4,,4)(,5,5,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2) || ()(,,1)(,2,,1)(,3,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3) || ()(,,1)(,2,,1)(,3,3)(,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,1) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,1^(4,1),1) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4)) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,7)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),1) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,7,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),1)(4^(5,1),4)(5,4) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),1)(4^(5,1),4)(5,4^(6,1),1) || (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),1)(4^(5,1),4)(5,4^(6,1),1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),2) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,3) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,9)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3^(4)) || ()(,,1)(,2,,1)(,3,3)(,4)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,3)(,4,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3^(4,1),2) || ()(,,1)(,2,,1)(,3,3)(,4,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3)(,4,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2,2) || ()(,,1)(,2,,1)(,3,3)(,4,4,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2^(3)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2^(3,1)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1^(4))) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,7)(,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1^(4,1),1)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),1)(4^(5,4)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,9)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),1)(4^(5,4))(4^(6,1),1)(6^(7,6)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,9)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,16)(,16,16,16,,14)(,21,21,21,21)(,22,22,22,22,,22)(,23,22,22,22,,22)(,24,21)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,8)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,15)(,16,16,16,16)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2)(4^(5,2)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,9)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,16)(,16,16,16,16)(,21,21,21,21,,21)(,22,21,21,21,,21)(,23,16)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2)(4^(5,2),4) || <br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2)(4^(5,4)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2)(4^(5,4))(4) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,17)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2,2) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,17,17,17,17,17)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,2)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,17,17,17,17,,17)(,21,17,17,17,,17)(,22,17)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(3,2^(4,2)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,17)(,17,17,17,17,,17)(,22,17,17,17,,17)(,23,17)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(3,3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,17)(,21,21)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(3^(4,2),3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,17)(,21,21,21,21,21,21)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(3^(4,3)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,17)(,21,21,21,21,21,,21)(,22,21,21,21,21,,21)(,23,21)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3,3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,11)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,2)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5,5)(,4,4,,4)(,7,4,,4)(,8,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,2),2) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5,5,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,2),3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5,5,,4)(,6,6,6,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,3)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5,5,,4)(,6,6,6,6)(,7,7,7,7,,7)(,8)(,1)(,10,,10)(,11,11,,10)(,12,12,12)(,13,13,13,,13)(,14,14,14,14,,13)(,15,15,15,15,15)(,16,16,16,16,16,,16)(,17,16,16,16,16,,16)(,18,14)<br /> |-<br /> | (0)(1^(2,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(1^(3,1),1)(3^(4)) || ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5)(,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(1^(3,1),1)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(1^(3,1),1)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5,,1)(,6,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(1^(3,1),1)(3^(4,3),3,3) || ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5,,1)(,6,6)(,7,7,,7)(,8,8,8,,7)(,9,9,9,9,,7)<br /> |-<br /> | (0)(1^(2,1),1,1)(1^(3,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5,,1)(,6,6,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2) || ()(,,1)(,2,,1)(,3,3,,1)(,2)<br /> |-<br /> | (0)(1^(2,1),1,1)(2,1^(3,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,2)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,7,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2,1^(3,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,2)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,7,,6)(,10,10,,6)(,11,11,11,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2,2) || ()(,,1)(,2,,1)(,3,3,,1)(,2)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,7,7)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3)) || ()(,,1)(,2,,1)(,3,3,,1)(,2)(,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3)(4) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3)(4^(5,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3)(4^(5,1),3) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3)(4^(5,1),4) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3,3) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3^(4)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3^(4,1)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1^(5))) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,9)(,9,,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1^(5,1),1)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1^(5,1),1,1)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,,9)(,17,17,,9)(,18,18,18,,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,2)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,10)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,2^(5,1),1)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,10,,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4,3^(5,3)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,23)(,23,23,23,23,,23)(,28,23,23,23,,23)(,29,22)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4,4) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,23)(,27,27)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4^(5,3),4) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,23)(,27,27,27,27,27,27)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4^(5,3),4^(5,3)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,23)(,27,27,27,27,27,,27)(,28,27,27,27,27,,27)(,29,22)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4^(5,3)(5)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,,23)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4^(5,4)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3),3) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3),3,3) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7,7,7,,6)(,8,8,8,8,,6)(,7,7,7,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1,1)(3) || ()(,,1)(,2,,1)(,3,3,,1)(,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1,1)(3^(4,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,,1)(,5,5,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,1),2) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,3)) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,5,,5)(,6,5,,5)(,7,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,3),3)(4^(5,3),3) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,5,,5)(,6,6,6,,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,3),3,3) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,5,,5)(,6,6,6,,5)(,7,7,7,7,,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,2,,1)(,3,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1)(4^(5,1),4,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,2,,1)(,3,3,,1)(,3,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1)(4^(5,1),4,1)(4) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1)(4^(5,1),4,1)(4^(6,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1)(4^(5,1),4,1)(4^(6,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3,,1)(,6,6,,1)(,6,6,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),2) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),2,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3) || ()(,,1)(,2,,1)(,3,3,,1)(,4)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,1^(4,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,1^(4,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,,6)(,10,10,,6)(,11,11,11,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,7)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,7,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,7,,6)(,10,10,10,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1,1)(4^(5,1),4,1)(5,4) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1,1)(4^(5,1),4,1)(5,4^(6,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1,1)(4^(5,1),4,1)(5,4^(6,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8,,6)(,10,10,10,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),2) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),2,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8,8,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,3) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4)) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,4,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4,,1)(,5,5,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),2) || ()(,,1)(,2,,1)(,3,3,,1)(,4,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),2,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),3,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,2) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,2)) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)(,5,5,5,,5)(,6)(,1)(,8,,8)(,9,9,,8)(,10,10,10,,8)(,11,11,11,11)(,12,12,12,12,,12)(,13,12,12,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,2),2)(3^(4)) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)(,5,5,5,,5)(,6)(,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,2),2)(3^(4,2),2) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)(,5,5,5,,5)(,6,6,6,6,,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,2),2,2) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)(,5,5,5,,5)(,6,6,6,6,,5)(,7,7,7,7,7,,5)<br /> |-<br /> | (0)(1^(2,1),1,1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4,,1)<br /> |-<br /> | (0)(1^(2,1),1^(2)) || ()(,,1)(,,2)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2) || ()(,,1)(,,2)(,2)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2,1) || ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2,1^(3,1))(3^(4,3),3^(4)) || ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,5)(,8,8,,8)(,9,9,,9)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2,1^(3,1),1) || ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2,1^(3,1),1^(3)) || ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,,5)(,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2,2) || ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3)) || ()(,,1)(,,2)(,2)(,,1)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),1) || ()(,,1)(,,2)(,2,,1)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),1,1) || ()(,,1)(,,2)(,2,,1)(,4,4,,1)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),1^(3)) || ()(,,1)(,,2)(,2,,1)(,4,,4)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2) || ()(,,1)(,,2)(,2,,1)(,4,,4)(,4,4)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2,1) || ()(,,1)(,,2)(,2,,1)(,4,,4)(,4,4,,1)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2,1^(3)) || ()(,,1)(,,2)(,2,,1)(,4,,4)(,4,4,,1)(,6,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2,2) || ()(,,1)(,,2)(,2,,1)(,4,,4)(,4,4,,1)(,6,6,,6)(,6,6,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3)) || ()(,,1)(,,2)(,,2)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3) || ()(,,1)(,,2)(,3)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,1^(4,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,1^(4,1),1^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,5)(,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,1^(4,1),1^(4))(4^(5,1),4^(5)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,5)(,8,,8)(,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,5,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1))(1^(5,1),1^(5)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,5,,5)(,9,,9)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,6,,5)(,9,9,,9)(,10,9,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),1^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,6,,5)(,9,9,,9)(,10,9,,5)(,11,11,,11)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,6,,5)(,9,9,,9)(,10,9,9)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),2,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,6,,5)(,9,9,,9)(,10,9,9)(,9,9,9,,5)(,12,12,12,,12)(,13,12,12,12)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),2^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3^(4,1),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,8,,8)(,10,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2),2,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,9,9,,8)(,10,10,10,10,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,9,,9)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2),2^(3))(3^(4,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,9,,9)(,10,9,9)(,11,11,11,,11)(,12,11,11,,11)(,13,9)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2),2^(3))(3^(4,3),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,9,,9)(,10,9,9)(,11,11,11,,11)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1),1^(2),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(9)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3,2^(4,1),2^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,1),3^(4),3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,,10)(,11,10,,10)(,12,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,,10)(,11,10,,10)(,12,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,3),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,,10)(,11,11,,11)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,3),3^(4),3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,,10)(,11,11,,11)(,12,11,11,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,7)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,7,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,7,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,2^(4,1),2^(4),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,7,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,2^(4,1),2^(4),1)(4) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3^(4,1),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3^(4,1),3^(4),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8)(,9,9,9,,9)(,10,9,9,,9)(,11,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,2),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8)(,9,9,9,,9)(,10,10,10,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,2),2^(3),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8)(,9,9,9,,9)(,10,10,10,,10)(,11,10,10,10,,9)<br /> |-<br /> | (0)(1^(2,1),1^(2),1,1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2,1^(3,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2,1^(3,1),1^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,5)(,10,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2,1^(3,1),1^(3),1^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,5)(,10,,10)(,11,10,,5)(,12,12,,12)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3,2^(4,1),2^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3^(4,1),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,11,11)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3^(4,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,11,11,,11)(,12,11,,11)(,13,11)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3^(4,3),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,11,11,,11)(,12,12,,12)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3^(4,3),3^(4),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,11,11,,11)(,12,12,,12)(,13,12,12,,11)(,14,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6,,5)(,11,11,,11)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,7)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3,2^(4,1),2^(4),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,7,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3,2^(4,1),2^(4),1^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,7,6,,5)(,10,10,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3,2^(4,1),2^(4),1^(4))(4) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3,3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4))(2^(5,1),2^(5),1^(5)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8)(,6,,6)(,11,6,,5)(,12,12,,12)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4))(2^(5,1),2^(5),1^(5))(5^(6,1),5^(6)) || <br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4))(4^(5,4),4^(5),4^(5)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8)(,10,10,,10)(,11,11,,11)(,12,11,11,,10)(,13,13,13,,13)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4),1^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,,5)(,10,10,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2,1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,8,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2,1^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,8,,5)(,10,10,10,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,8,,5)(,10,10,10,,10)(,10,10,10,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,2),2^(3),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,9,8)(,10,10,,10)(,11,11,,11)(,12,11,11,,10)(,13,13,13,,13)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,9,8,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2)(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(8,5)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2) || <br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3))(3) || <br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,11,11,,11)(,15,11,11,,10)(,16,16,16,,16)(,17,16,16,,16)(,18,10)(,16,16,16,,16)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,11,11,,11)(,15,11,,11)(,16,5)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1))(3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1))(3,2^(4,1),2^(4,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,11,11,,11)(,16,11,,11)(,17,10)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1))(3,3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,15)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,,15)(,16,15,15,,15)(,17,15)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,2),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,,15)(,16,16,16,,16)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,2),2^(3,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,,15)(,16,16,16,,16)(,17,16,16,,16)(,18,5)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,2),2^(3,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,,15)(,16,16,16,,16)(,17,16,16,,16)(,18,15)<br /> |-<br /> | (0)(1^(2,1),1^(2,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2,1),1^(2,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11,,10)(,15,15,15,,15)(,16,15,15,,15)(,17,10)<br /> |-<br /> | (0)(1^(2,1)(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,,11)<br /> |-<br /> | (0)(1^(2,1)(2,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,,11)(,15,10)<br /> |-<br /> | (0)(1^(2,1)(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,13)<br /> |-<br /> | (0)(1^(2,1)(3,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,13,5)<br /> |-<br /> | (0)(1^(2,1)(3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,14,14)<br /> |-<br /> | (0)(1^(2,1)(3^(4))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,14,14,,14)<br /> |-<br /> | (0)(1^(2,1)(3^(4,3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,14,14,,14)(,15,15,,15)(,16,15,,15)(,17,14)<br /> |-<br /> | (0)(1^(2,1,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10,10)<br /> |-<br /> | (0)(1^(2,1^(3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)<br /> |-<br /> | (0)(1^(2,1^(3,1))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)<br /> |-<br /> | (0)(1^(2,1^(3,1)))(1^(3,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,13,13,,13)(,18,13,,13)(,19,13)(,18,13,,13)<br /> |-<br /> | (0)(1^(2,1^(3,1)))(2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,14)<br /> |-<br /> | (0)(1^(2,1^(3,1)))(2^(3,1^(4,1))) || <br /> |-<br /> | (0)(1^(2,1^(3,1)))(2^(3,1^(4,1)))(3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,15)<br /> |-<br /> | (0)(1^(2,1^(3,1)),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,15,14,14,,13)<br /> |-<br /> | (0)(1^(2,1^(3,1))(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,15,14,,14)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,16)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13,13)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13,13)(,13,13,,13)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13,13)(,13,13,,13)(,18,13,,13)(,19,5)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1)))(1^(3,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,,5)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1)))(2,1^(3,1),1) || <br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1))(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,7,,6)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1))(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,8)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1))(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,9)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,9,9)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3^(4,3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,9,9,,9)(,10,9,,9)(,11,9)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3^(4,3^(5,3)))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,9,9,,9)(,10,10,,10)(,11,10,,10)(,12,9)<br /> |-<br /> | (0)(1^(2,1^(3,1),1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)<br /> |-<br /> | (0)(1^(2,1^(3,1),1^(3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)(,9,,9)<br /> |-<br /> | (0)(1^(2,1^(3,1),1^(3,1))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)(,9,,9)(,10,,9)(,11,5)<br /> |-<br /> | (0)(1^(2,1^(3,1^(4)))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)(,9,,9)(,10,,9)(,11,5)(,5,,5)<br /> |-<br /> | (0)(1^(2,1^(3,1^(4,1)))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)(,9,,9)(,10,,9)(,11,5)(,5,,5)(,13,,5)(,14,5)<br /> |-<br /> | (0)(1^(2,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)<br /> |-<br /> | (0)(1^(2^(3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,5,,5)<br /> |-<br /> | (0)(1^(2^(3,1))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,5,,5)(,10,,5)(,11,5)<br /> |-<br /> | (0)(1^(2^(3,1))(2^(4))) || <br /> |-<br /> | (0)(1^(2^(3,1),1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,6,6,,5)(,10,10,,10)(,11,10,,10)(,12,10,,5)<br /> |-<br /> | (0)(1^(2^(3,1),2^(3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,6,,6)<br /> |-<br /> | (0)(1^(2^(3,2))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,6,,6)(,10,,6)(,11,6)<br /> |-<br /> | (0)(1^(2^(3,2))(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,7,,6)<br /> |-<br /> | (0)(1^(2^(3,2))(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,8)<br /> |-<br /> | (0)(1^(2^(3,2))(3,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,8,5)<br /> |-<br /> | (0)(1^(2^(3,2))(3,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,8,6)<br /> |-<br /> | (0)(1^(2^(3,2))(3,2^(4,2))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,8,6)(,6,,6)(,11,,6)(,12,6)<br /> |-<br /> | (0)(1^(2^(3,2))(3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,9,9)<br /> |-<br /> | (0)(1^(2^(3,2),1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)<br /> |-<br /> | (0)(1^(2^(3,2),1)(3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9)<br /> |-<br /> | (0)(1^(2^(3,2),1)(3^(4,2),3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,9)<br /> |-<br /> | (0)(1^(2^(3,2),1)(3^(4,2),3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,9)(,10,10,10,10)<br /> |-<br /> | (0)(1^(2^(3,2),1,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,9,,5)<br /> |-<br /> | (0)(1^(2^(3,2),1^(3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,,9)<br /> |-<br /> | (0)(1^(2^(3,2),1^(3^(4,3),1))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,,9)(,10,9,,9)(,11,9,9,,5)<br /> |-<br /> | (0)(1^(2^(3,2),2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,6)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,6)(,8)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3,2^(4,2),1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,6)(,8,6,,5)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3,2^(4,2),2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,6)(,8,,6)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,7)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4))) || ()(,,1)(,,2)(,3)(,,1)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,1),3^(4))) || ()(,,1)(,,2)(,3)(,,2)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,2))) || ()(,,1)(,,2)(,3)(,,2)(,5)(,1)(,7,,7)(,8,,8)(,9,9)(,8,,8)(,11,,8)(,12,8)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,2),1)) || ()(,,1)(,,2)(,3,,1)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,2),2)) || ()(,,1)(,,2)(,3,,2)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,2),3)) || ()(,,1)(,,2)(,3,,2)(,4,4)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,2),3^(4))) || <br /> |-<br /> | (0)(1^(2^(3,2),2,1)) || ()(,,1)(,,2)(,3,,2)(,4,4,,1)<br /> |-<br /> | (0)(1^(2^(3,2),2,2)) || ()(,,1)(,,2)(,3,,2)(,4,4,,2)<br /> |-<br /> | (0)(1^(2^(3,2),2^(3))) || ()(,,1)(,,2)(,,3)<br /> |-<br /> | (0)(1^(2^(3^(4)))) || ()(,,1)(,,2)(,,3)(,4)(,1)(,6,,6)(,7,,7)(,8,,8)(,9,,8)(,10,8)(,6,,6)<br /> |-<br /> | Limit || ()(,,1)(,,2,2)<br /> |}</div>

0100000000a7 http://wiki.googology.top/index.php?title=BTBMS%E5%88%86%E6%9E%90&diff=3773 2026-08-30T15:32:52Z

<p>0100000000a7：​</p> <hr /> <div>本条目展示[[BTBMS]] 和 [[ωMN]]的列表分析。以下分析来自test_alpha0<br /> {| class=&quot;wikitable&quot;<br /> ! BTBMS !! ωMN<br /> |-<br /> | (0) || ()<br /> |-<br /> | (0)(1) || ()(,1)<br /> |-<br /> | (0)(1^(2)) || ()(,,1)<br /> |-<br /> | (0)(1^(2)(2)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)<br /> |-<br /> | (0)(1^(2)(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6)<br /> |-<br /> | (0)(1^(2)(3^(4))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6)(,7,,7)<br /> |-<br /> | (0)(1^(2,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)<br /> |-<br /> | (0)(1^(2,1))(1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,1)<br /> |-<br /> | (0)(1^(2,1))(1)(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,1)(,8,,8)(,9,,8)(,10,8)<br /> |-<br /> | (0)(1^(2,1))(1)(3^(4,3))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4)<br /> |-<br /> | (0)(1^(2,1))(1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4))(4,3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4))(4,3^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4))(4^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)(,10,10,10)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)(,10,10,10,10)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4),3^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)(,10,10,10,,10)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4)(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4)(5^(6,5))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10)(,11,,11)(,12,,11)(,13,11)(,11,11)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(3,3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(3^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(3^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8,8,,8)(,12,8,,8)(,13,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4,3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4,3^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4,3^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1))(4^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)(,12,12,12)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)(,12,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,10,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6)(6))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6)(7^(8,7)))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13)(,14,,14)(,15,,14)(,16,14)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7,7))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14,14)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7^(8)))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14,14,,14)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7^(8)(8)))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14,14,,14)(,15,14,,14)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,3)(5^(6,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)(,12,12,,12)(,13,12,,12)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,3)(5^(6,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)(,12,12,,12)(,13,12,,12)(,14,8)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,3)(5^(6,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)(,12,12,,12)(,13,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1))(1,1)(3^(4,3))(3,3)(5^(6,5))(5,5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)(,12,12,,12)(,13,12,,12)(,14,12)(,12,12)<br /> |-<br /> | (0)(1^(2,1))(1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,4,4)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1)(4^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,4,4)(,13,13,,13)(,14,13,,13)(,15,4)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1)(4^(5,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,4,4)(,13,13,,13)(,14,13,,13)(,15,13)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1)(4^(5,4))(4,4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,4,4)(,13,13,,13)(,14,13,,13)(,15,13)(,13,13,13)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1)(4^(5,4))(4,4,4)(4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1)(4^(5,4))(4,4,4)(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1)(5^(6,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)(,15,15,,15)(,16,15,,15)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1)(5^(6,5))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)(,15,15,,15)(,16,15,,15)(,17,15)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1)(5^(6,5))(5,5,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)(,15,15,,15)(,16,15,,15)(,17,15)(,15,15,15)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1)(5^(6,5))(5,5,5)(7^(8,5))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,1,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,3))(3,3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(1,1,1)(3^(4,3))(3,3,3)(5^(6,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,12,12,12)(,16,16,16,,16)(,17,16,16,,16)(,18,16)<br /> |-<br /> | (0)(1^(2,1))(1,1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,12,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(1^(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1^(3)(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)(,13,4)<br /> |-<br /> | (0)(1^(2,1))(1^(3,1))(1,1)(4^(5,4))(4^(6,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)(,13,8)<br /> |-<br /> | (0)(1^(2,1))(1^(3,1))(1^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)(,13,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(1^(3,1))(1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)(,13,8)(,8,8,,8)(,15,8,,8)(,16,4)<br /> |-<br /> | (0)(1^(2,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9)<br /> |-<br /> | (0)(1^(2,1))(2,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,4)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1,1)(4^(5,4))(5,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1))(1,1)(5^(6,5))(6,5)(5^(8,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1))(1^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1))(1^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)(,8,8,,8)(,16,8,,8)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1))(4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13)<br /> |-<br /> | (0)(1^(2,1))(2,1)(1^(4,1))(4,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,4)<br /> |-<br /> | (0)(1^(2,1))(2,1)(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,9)<br /> |-<br /> | (0)(1^(2,1))(2,1)(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,12)<br /> |-<br /> | (0)(1^(2,1))(2,1)(3^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2,1)(3^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,12,12,,12)(,13,12,,12)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2,1)(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,12,12,,12)(,13,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1))(2,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1))(2,1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,13)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1,1)(4^(5,4))(5,4^(6,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,8,8,,8)(,16,8,,8)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,4)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4,1^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4,1^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,8,8,,8)(,17,8,,8)(,18,4)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,9)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(2,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(2,1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,4)<br /> |-<br /> | (0)(1^(2,1))(2,1^(3,1))(3,1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,8,8)(,8,8,,8)(,14,8,,8)(,15,4)<br /> |-<br /> | (0)(1^(2,1))(2,2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12)(,8,8,,8)(,14,8,,8)(,15,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(2^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(2^(4,1))(4^(5,1),4^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,12,12,12)(,14,14,14,,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(2^(4,1),2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,12,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(2^(4,1),2^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(3,2^(4,1),2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(3^(4,1),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14,14,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3))(3^(4,1),3^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14,14,14)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3),2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14,14,14,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3),2^(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14,14,14,,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3)(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1),2^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,13,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,13,12,12,,12)(,16,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4,1)(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,14,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4,1)(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4^(5))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15,15,,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4^(5,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15,15,,15)(,16,15,,15)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1)(4^(5,4))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15,15,,15)(,16,15,,15)(,17,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,8,8,,8)(,16,8,,8)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,13,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,14)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4,1^(5,1))(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15)(,8,8,,8)(,17,8,,8)(,18,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1),4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,15)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1),4^(5,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,,15)(,16,15,15,,15)(,17,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1,1))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,,15)(,16,15,15,,15)(,17,8,8)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1^(6)))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,,15)(,16,15,15,,15)(,17,8,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1^(6,1)))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,,15)(,16,15,15,,15)(,17,8,8)(,8,8,,8)(,19,8,,8)(,20,4)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3,2^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3,2^(4,2)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,12,12,12,,12)(,17,12,12,,12)(,18,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,16,16)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3^(4,2)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,16,16,16,16)(,12,12,12,,12)(,18,12,12,,12)(,19,12)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3^(4,2),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,16,16,16,16,16)<br /> |-<br /> | (0)(1^(2,1))(2^(3,2))(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,16,16,16,16,,16)(,17,16,16,16,,16)(,18,16)<br /> |-<br /> | (0)(1^(2,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,4)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3,1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,8,8,,8)(,17,8,,8)(,18,4)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,1),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,3),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)(,17,16,16,,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,3),3)(3^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)(,17,16,16,,16)(,16,16,16,,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,3),3)(3^(5,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)(,17,16,16,,16)(,16,16,16,,16)(,21,16,16,,16)(,22,16)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1))(3^(4,3),3)(3^(5,3))(5^(6,5),5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)(,17,16,16,,16)(,16,16,16,,16)(,21,16,16,,16)(,22,16)(,21,16,16,16)(,24,24,24,24,,24)(,25,24,24,24,,24)(,26,24)(,25,24,24,24,,24)<br /> |-<br /> | (0)(1^(2,1),1)(1^(3,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4,1^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,8,8,,8)(,18,8,,8)(,19,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,1),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,4),4)(5,4^(6)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)(,18,17,17,17)(,17,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,4),4)(5,4^(6,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)(,18,17,17,17)(,17,17,17,,17)(,23,17,17,,17)(,24,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13)(,8,8,,8)(,15,8,,8)(,16,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,1))(1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13)(,8,8,,8)(,15,8,,8)(,16,8)(,15,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,1),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3),3)(4,3^(5,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,,13)(,14,13,13,13)(,13,13,13,,13)(,19,13,13,,13)(,20,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3),3)(4,3^(5,3))(5^(6,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,,13)(,14,13,13,13)(,18,18,18,18,,18)(,19,18,18,18,,18)(,20,18)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3),3)(4,3^(5,3))(5^(6,5),5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,,13)(,14,13,13,13)(,18,18,18,18,,18)(,19,18,18,18,,18)(,20,18)(,19,18,18,18,,18)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1))(4^(5,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1))(4^(5,4),4)(5,4^(6,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)(,18,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1),1)(4,1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,,8)(,14,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,15,8,,8)(,16,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,15,8,,8)(,16,8)(,15,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(1^(5,1),1)(5,1^(6,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,15,8,,8)(,16,8)(,15,8,,8)(,15,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(4^(5,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,14,14,14,,14)(,15,14,14,,14)(,16,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(4^(5,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(4^(5,4),4)(5,4^(6,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)(,15,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,12)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,12,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(2,1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,12,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,10)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(3,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,10,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11,,11)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11,,11)(,12,11,,11)(,13,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4^(5,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11,,11)(,12,11,,11)(,13,11)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4^(5,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11,,11)(,12,11,,11)(,13,11)(,12,11,,11)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1,1)(5^(6,5),5)(6,5^(7,5),5)(7,5^(8,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,14,14,,14)(,24,14,,14)(,25,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,21,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1)(5,1^(6,1),1)(6) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,21,14,,14)(,24)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1)(5,1^(6,1),1)(6,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,21,14,,14)(,24,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1)(5,1^(6,1),1)(6,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14,14)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1)(5,1^(6,1),1)(6,1^(7)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1))(6^(7,6),6)(7,6^(8,6),6)(8,6^(9,6))(7,6^(10,6)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12)(,17,12,12)(,20,20,20,,20)(,21,20,20,,20)(,22,20,20,20)(,21,20,20,20)(,20,20,20,,20)(,25,20,20,,20)(,26,20)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12)(,17,12,,12)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12)(,17,12,,12)(,17,12,,12)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12)(,17,12,,12)(,20,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12,12)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1^(8)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1^(8,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,,4)(,12,,4)(,13,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1^(8,1))(6) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,5)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(2,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,5,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5,5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,1),5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,1),5^(6,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,1,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,16,16,16,,16)(,17,16,16,,16)(,18,12,12)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,5)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,5),5) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,5),5)(6,5^(7,5),5)(7,5^(8,5))(6) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,8,8)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,4,,4)(,10,,4)(,11,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1))(1^(7,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,4,,4)(,10,,4)(,11,4)(,10,4)(,13,13,,13)(,14,13,,13)(,15,13,13)(,14,13,,13)(,17,13,13)(,13,13,,13)(,19,13,,13)(,20,13)(,19,13,,13)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1))(1^(7,1),1)(7,1^(8,1),1)(8,1^(9,1))(7,1^(10,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,4,,4)(,10,,4)(,11,4)(,10,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,5)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1))(2,1^(7,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,5,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,6)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(3,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,6,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,1),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,1^(6))) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,4)(,4,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7)(,8,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7)(,8,7,,7)(,8,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4)(6,4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4)(6,4^(7,4)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7,7)(,7,7,,7)(,11,7,,7)(,12,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4)(6,4^(7,4))(4^(8,4),4) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7,7)(,7,7,,7)(,11,7,,7)(,12,7)(,11,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4)(6,4^(7,4))(7^(8,7)) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7,7)(,10,10,10,,10)(,11,10,10,,10)(,12,10)<br /> |-<br /> | (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2,2) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)<br /> |-<br /> | (0)(1^(2,1),1)(2,2)(2,1^(4,1),1)(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8)(,8,7,,7)(,10,10)<br /> |-<br /> | (0)(1^(2,1),1)(2,2)(2,2) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8)(,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,7,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(1^(4,1),1)(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,7,7,,7)(,10,10)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(2) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(2,1^(4,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,8,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,1),3) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,2)) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,9,9,,9)(,11,8)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,9,9,,9)(,11,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3),3)(4,4) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,10)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3),3)(4,4,1) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,10,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3),3)(4,4,3) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,10,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3),3)(4,4,3^(5,3)) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,10,9,9)(,9,9,9,,9)(,12,9,9,,9)(,13,9)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,1^(3,1),1) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2,2,2) || ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3)) || ()(,,1)(,2)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3),2) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,6)(,10,10,,10)(,11,11,11)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3),2^(3)) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,6)(,10,10,,10)(,11,11,11)(,10,10,,10)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3)(3)) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1)) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,,6)(,10,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(1^(4,1),1) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,,6)(,10,6)(,9,6)(,12,12,,12)(,13,13,13)(,12,12,,12)(,15,12,,12)(,16,12)(,15,12,,12)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(1^(4,1),1)(4,4) || ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,9)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(1^(4,1),1)(4^(5)) || ()(,,1)(,2)(,,1)(,4)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(2) || ()(,,1)(,2)(,2)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3) || ()(,,1)(,2)(,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,1),3) || ()(,,1)(,2)(,3,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,1),3^(4)) || ()(,,1)(,2)(,3,,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,1),3^(4)(4)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,1),3^(4,1)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,1^(5))) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,6)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,2)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,2^(5))) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,7)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3))(4) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3))(4,3^(5,3)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,14)(,14,14,14,,14)(,19,14,14,,14)(,20,14)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3))(4^(5,3),4) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,14)(,18,18,18,18,18)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3))(4^(5,4)) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,14)(,18,18,18,18,,18)(,19,18,18,18,,18)(,20,18)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4,3^(5,3),3) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)(,15,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4,4) || ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,9)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5)) || ()(,,1)(,2)(,3,,3)(,4)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5)(5)) || ()(,,1)(,2)(,3,,3)(,4)(,,1)(,6)(,1)(,8,,8)(,9,9)(,10,10,,10)(,11,11)(,8,,8)(,13,,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,1)) || ()(,,1)(,2)(,3,,3)(,4)(,,1)(,6)(,1)(,8,,8)(,9,9)(,10,10,,10)(,11,11)(,8,,8)(,13,,8)(,14,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,2)) || ()(,,1)(,2)(,3,,3)(,4,4)(,3,,3)(,6,,3)(,7)(,1)(,9,,9)(,10,10)(,11,11,,11)(,12,12,12)(,11,11,,11)(,14,11,,11)(,15,10)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,3)) || ()(,,1)(,2)(,3,,3)(,4,4)(,3,,3)(,6,,3)(,7)(,1)(,9,,9)(,10,10)(,11,11,,11)(,12,12,12)(,11,11,,11)(,14,11,,11)(,15,11)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,3))(3^(6,3),3) || ()(,,1)(,2)(,3,,3)(,4,4)(,3,,3)(,6,,3)(,7)(,1)(,9,,9)(,10,10)(,11,11,,11)(,12,12,12)(,11,11,,11)(,14,11,,11)(,15,11)(,14,11,,11)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,3))(5^(6,5)) || ()(,,1)(,2)(,3,,3)(,4,4)(,5,5,,5)(,6)(,1)(,8,,8)(,9,9)(,10,10,,10)(,11,11,11)(,12,12,12,,12)(,13,12,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1) || ()(,,1)(,2,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1)(4,4) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)(,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1)(4^(5,1))(5^(6,5),5)(6,6) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)(,8,8)(,9,9,,9)(,10,10,10)(,11,11,11,,11)(,12,12)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1)(4^(5,1))(5^(6,5),5)(6^(7,5),5) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)(,8,8)(,9,9,,9)(,10,10,10,,9)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1)(4^(5,1),1) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)(,8,8,,5)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2,2) || ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2^(4)) || ()(,,1)(,2,,1)(,2)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2^(4,1))(4) || ()(,,1)(,2,,1)(,2)(,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2^(4,1))(4^(5,4),4)(5^(6,4),4) || ()(,,1)(,2,,1)(,2)(,4,,4)(,5,5,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(2^(4,1),1) || ()(,,1)(,2,,1)(,2,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3) || ()(,,1)(,2,,1)(,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3,1) || ()(,,1)(,2,,1)(,3)(,1)(,5,,5)(,6,6,,5)(,7,5)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3,1^(4,1),1) || ()(,,1)(,2,,1)(,3)(,1)(,5,,5)(,6,6,,5)(,7,,5)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3,2) || ()(,,1)(,2,,1)(,3)(,1)(,5,,5)(,6,6,,5)(,7,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3,3) || ()(,,1)(,2,,1)(,3)(,1)(,5,,5)(,6,6,,5)(,7,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3^(4)) || ()(,,1)(,2,,1)(,3)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3^(4,1)) || ()(,,1)(,2,,1)(,3)(,,1)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9)(,7,,7)(,11,,7)(,12,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3^(4,1))(4) || ()(,,1)(,2,,1)(,3)(,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3^(4,1))(4^(5,4),4)(5^(6,4),4) || ()(,,1)(,2,,1)(,3)(,4,,4)(,5,5,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),1)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2) || ()(,,1)(,2,,1)(,3,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3) || ()(,,1)(,2,,1)(,3,3)(,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,1) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,1^(4,1),1) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4)) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,7)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),1) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,7,,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),1)(4^(5,1),4)(5,4) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),1)(4^(5,1),4)(5,4^(6,1),1) || (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),1)(4^(5,1),4)(5,4^(6,1),1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),2) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3,3) || ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,9)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3^(4)) || ()(,,1)(,2,,1)(,3,3)(,4)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,3)(,4,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3^(4,1),2) || ()(,,1)(,2,,1)(,3,3)(,4,3)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3)(,4,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2,2) || ()(,,1)(,2,,1)(,3,3)(,4,4,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2^(3)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1),2^(3,1)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1^(4))) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,7)(,7,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,1^(4,1),1)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,,7)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,8)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),1)(4^(5,4)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,9)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),1)(4^(5,4))(4^(6,1),1)(6^(7,6)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,9)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,16)(,16,16,16,,14)(,21,21,21,21)(,22,22,22,22,,22)(,23,22,22,22,,22)(,24,21)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,8)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,15)(,16,16,16,16)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2)(4^(5,2)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,9)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,16)(,16,16,16,16)(,21,21,21,21,,21)(,22,21,21,21,,21)(,23,16)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2)(4^(5,2),4) || <br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2)(4^(5,4)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2)(4^(5,4))(4) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,17)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2,2) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,17,17,17,17,17)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(2^(4,2)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,17,17,17,17,,17)(,21,17,17,17,,17)(,22,17)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(3,2^(4,2)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,17)(,17,17,17,17,,17)(,22,17,17,17,,17)(,23,17)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(3,3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,17)(,21,21)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(3^(4,2),3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,17)(,21,21,21,21,21,21)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2))(3^(4,3)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,17)(,21,21,21,21,21,,21)(,22,21,21,21,21,,21)(,23,21)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,,17)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3,3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,11)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,,1)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,2)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5,5)(,4,4,,4)(,7,4,,4)(,8,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,2),2) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5,5,,4)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,2),3) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5,5,,4)(,6,6,6,6)<br /> |-<br /> | (0)(1^(2,1),1)(2^(3,2),2)(3^(4,3)) || ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5,5,,4)(,6,6,6,6)(,7,7,7,7,,7)(,8)(,1)(,10,,10)(,11,11,,10)(,12,12,12)(,13,13,13,,13)(,14,14,14,14,,13)(,15,15,15,15,15)(,16,16,16,16,16,,16)(,17,16,16,16,16,,16)(,18,14)<br /> |-<br /> | (0)(1^(2,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(1^(3,1),1)(3^(4)) || ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5)(,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(1^(3,1),1)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(1^(3,1),1)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5,,1)(,6,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(1^(3,1),1)(3^(4,3),3,3) || ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5,,1)(,6,6)(,7,7,,7)(,8,8,8,,7)(,9,9,9,9,,7)<br /> |-<br /> | (0)(1^(2,1),1,1)(1^(3,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5,,1)(,6,6,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2) || ()(,,1)(,2,,1)(,3,3,,1)(,2)<br /> |-<br /> | (0)(1^(2,1),1,1)(2,1^(3,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,2)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,7,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2,1^(3,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,2)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,7,,6)(,10,10,,6)(,11,11,11,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2,2) || ()(,,1)(,2,,1)(,3,3,,1)(,2)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,7,7)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3)) || ()(,,1)(,2,,1)(,3,3,,1)(,2)(,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3)(4) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3)(4^(5,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3)(4^(5,1),3) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3)(4^(5,1),4) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3,3) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3^(4)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3^(4,1)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1^(5))) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,9)(,9,,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1^(5,1),1)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1^(5,1),1,1)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,,9)(,17,17,,9)(,18,18,18,,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,2)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,10)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,2^(5,1),1)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,10,,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4,3^(5,3)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,23)(,23,23,23,23,,23)(,28,23,23,23,,23)(,29,22)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4,4) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,23)(,27,27)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4^(5,3),4) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,23)(,27,27,27,27,27,27)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4^(5,3),4^(5,3)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,23)(,27,27,27,27,27,,27)(,28,27,27,27,27,,27)(,29,22)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4^(5,3)(5)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,,23)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4^(5,4)) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3),3) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3),3,3) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7,7,7,,6)(,8,8,8,8,,6)(,7,7,7,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1,1)(3) || ()(,,1)(,2,,1)(,3,3,,1)(,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),1,1)(3^(4,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,,1)(,5,5,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,1),2) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,3)) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,5,,5)(,6,5,,5)(,7,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,3),3)(4^(5,3),3) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,5,,5)(,6,6,6,,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,3),3,3) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,5,,5)(,6,6,6,,5)(,7,7,7,7,,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,2,,1)(,3,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1)(4^(5,1),4,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,2,,1)(,3,3,,1)(,3,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1)(4^(5,1),4,1)(4) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1)(4^(5,1),4,1)(4^(6,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1)(4^(5,1),4,1)(4^(6,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3,,1)(,6,6,,1)(,6,6,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),2) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),2,1) || ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3) || ()(,,1)(,2,,1)(,3,3,,1)(,4)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,1^(4,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,1^(4,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,,6)(,10,10,,6)(,11,11,11,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,7)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,7,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,7,,6)(,10,10,10,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1,1)(4^(5,1),4,1)(5,4) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1,1)(4^(5,1),4,1)(5,4^(6,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1,1)(4^(5,1),4,1)(5,4^(6,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8,,6)(,10,10,10,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),2) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8,8)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),2,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8,8,,6)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,3) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,9)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4)) || ()(,,1)(,2,,1)(,3,3,,1)(,4)(,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),1) || ()(,,1)(,2,,1)(,3,3,,1)(,4,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4,,1)(,5,5,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),2) || ()(,,1)(,2,,1)(,3,3,,1)(,4,3)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),2,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4,3,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),3) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),3,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,1),2,2) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,2)) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)(,5,5,5,,5)(,6)(,1)(,8,,8)(,9,9,,8)(,10,10,10,,8)(,11,11,11,11)(,12,12,12,12,,12)(,13,12,12,12,,12)(,14,12)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,2),2)(3^(4)) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)(,5,5,5,,5)(,6)(,,1)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,2),2)(3^(4,2),2) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)(,5,5,5,,5)(,6,6,6,6,,5)<br /> |-<br /> | (0)(1^(2,1),1,1)(2^(3,2),2,2) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)(,5,5,5,,5)(,6,6,6,6,,5)(,7,7,7,7,7,,5)<br /> |-<br /> | (0)(1^(2,1),1,1,1) || ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4,,1)<br /> |-<br /> | (0)(1^(2,1),1^(2)) || ()(,,1)(,,2)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2) || ()(,,1)(,,2)(,2)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2,1) || ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2,1^(3,1))(3^(4,3),3^(4)) || ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,5)(,8,8,,8)(,9,9,,9)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2,1^(3,1),1) || ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2,1^(3,1),1^(3)) || ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,,5)(,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2,2) || ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3)) || ()(,,1)(,,2)(,2)(,,1)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),1) || ()(,,1)(,,2)(,2,,1)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),1,1) || ()(,,1)(,,2)(,2,,1)(,4,4,,1)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),1^(3)) || ()(,,1)(,,2)(,2,,1)(,4,,4)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2) || ()(,,1)(,,2)(,2,,1)(,4,,4)(,4,4)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2,1) || ()(,,1)(,,2)(,2,,1)(,4,,4)(,4,4,,1)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2,1^(3)) || ()(,,1)(,,2)(,2,,1)(,4,,4)(,4,4,,1)(,6,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2,2) || ()(,,1)(,,2)(,2,,1)(,4,,4)(,4,4,,1)(,6,6,,6)(,6,6,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3)) || ()(,,1)(,,2)(,,2)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3) || ()(,,1)(,,2)(,3)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,1^(4,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,1^(4,1),1^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,5)(,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,1^(4,1),1^(4))(4^(5,1),4^(5)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,5)(,8,,8)(,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,5,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1))(1^(5,1),1^(5)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,5,,5)(,9,,9)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,6,,5)(,9,9,,9)(,10,9,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),1^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,6,,5)(,9,9,,9)(,10,9,,5)(,11,11,,11)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,6,,5)(,9,9,,9)(,10,9,9)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),2,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,6,,5)(,9,9,,9)(,10,9,9)(,9,9,9,,5)(,12,12,12,,12)(,13,12,12,12)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),2^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3^(4,1),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,1),2^(3),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,8,,8)(,10,6)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2),2,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,9,9,,8)(,10,10,10,10,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,9,,9)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2),2^(3))(3^(4,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,9,,9)(,10,9,9)(,11,11,11,,11)(,12,11,11,,11)(,13,9)<br /> |-<br /> | (0)(1^(2,1),1^(2))(2^(3,2),2^(3))(3^(4,3),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,9,,9)(,10,9,9)(,11,11,11,,11)(,12,12,12,,12)<br /> |-<br /> | (0)(1^(2,1),1^(2),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(9)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3,2^(4,1),2^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,1),3^(4),3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,,10)(,11,10,,10)(,12,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,,10)(,11,10,,10)(,12,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,3),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,,10)(,11,11,,11)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,3),3^(4),3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,,10)(,11,11,,11)(,12,11,11,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,7)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,7,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,7,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,2^(4,1),2^(4),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,7,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,2^(4,1),2^(4),1)(4) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3^(4,1),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3^(4,1),3^(4),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8)(,9,9,9,,9)(,10,9,9,,9)(,11,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,2),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8)(,9,9,9,,9)(,10,10,10,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1)(2^(3,2),2^(3),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8)(,9,9,9,,9)(,10,10,10,,10)(,11,10,10,10,,9)<br /> |-<br /> | (0)(1^(2,1),1^(2),1,1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2,1^(3,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2,1^(3,1),1^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,5)(,10,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2,1^(3,1),1^(3),1^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,5)(,10,,10)(,11,10,,5)(,12,12,,12)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3,2^(4,1),2^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3^(4,1),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,11,11)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3^(4,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,11,11,,11)(,12,11,,11)(,13,11)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3^(4,3),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,11,11,,11)(,12,12,,12)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3^(4,3),3^(4),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,11,11,,11)(,12,12,,12)(,13,12,12,,11)(,14,14,14,,14)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6,,5)(,11,11,,11)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,7)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3,2^(4,1),2^(4),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,7,6,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3,2^(4,1),2^(4),1^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,7,6,,5)(,10,10,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3,2^(4,1),2^(4),1^(4))(4) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3,3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8)(,6,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4))(2^(5,1),2^(5),1^(5)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8)(,6,,6)(,11,6,,5)(,12,12,,12)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4))(2^(5,1),2^(5),1^(5))(5^(6,1),5^(6)) || <br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4))(4^(5,4),4^(5),4^(5)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8)(,10,10,,10)(,11,11,,11)(,12,11,11,,10)(,13,13,13,,13)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4),1^(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,,5)(,10,10,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2,1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,8,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2,1^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,8,,5)(,10,10,10,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2,2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,8,,5)(,10,10,10,,10)(,10,10,10,10)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,,8)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2))(2^(3,2),2^(3),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,9,8)(,10,10,,10)(,11,11,,11)(,12,11,11,,10)(,13,13,13,,13)<br /> |-<br /> | (0)(1^(2,1),1^(2),1^(2),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,9,8,,5)<br /> |-<br /> | (0)(1^(2,1),1^(2)(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)<br /> |-<br /> | (0)(1^(2,1),1^(2,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(8,5)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2) || <br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3))(3) || <br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,11,11,,11)(,15,11,11,,10)(,16,16,16,,16)(,17,16,16,,16)(,18,10)(,16,16,16,,16)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,11,11,,11)(,15,11,,11)(,16,5)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1))(3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1))(3,2^(4,1),2^(4,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,11,11,,11)(,16,11,,11)(,17,10)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1))(3,3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1),2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,15)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,,15)(,16,15,15,,15)(,17,15)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,2),2^(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,,15)(,16,16,16,,16)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,2),2^(3,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,,15)(,16,16,16,,16)(,17,16,16,,16)(,18,5)<br /> |-<br /> | (0)(1^(2,1),1^(2,1))(2^(3,2),2^(3,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,,15)(,16,16,16,,16)(,17,16,16,,16)(,18,15)<br /> |-<br /> | (0)(1^(2,1),1^(2,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11,,10)<br /> |-<br /> | (0)(1^(2,1),1^(2,1),1^(2,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11,,10)(,15,15,15,,15)(,16,15,15,,15)(,17,10)<br /> |-<br /> | (0)(1^(2,1)(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,,11)<br /> |-<br /> | (0)(1^(2,1)(2,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,,11)(,15,10)<br /> |-<br /> | (0)(1^(2,1)(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,13)<br /> |-<br /> | (0)(1^(2,1)(3,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,13,5)<br /> |-<br /> | (0)(1^(2,1)(3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,14,14)<br /> |-<br /> | (0)(1^(2,1)(3^(4))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,14,14,,14)<br /> |-<br /> | (0)(1^(2,1)(3^(4,3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,14,14,,14)(,15,15,,15)(,16,15,,15)(,17,14)<br /> |-<br /> | (0)(1^(2,1,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10,10)<br /> |-<br /> | (0)(1^(2,1^(3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)<br /> |-<br /> | (0)(1^(2,1^(3,1))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)<br /> |-<br /> | (0)(1^(2,1^(3,1)))(1^(3,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,13,13,,13)(,18,13,,13)(,19,13)(,18,13,,13)<br /> |-<br /> | (0)(1^(2,1^(3,1)))(2) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,14)<br /> |-<br /> | (0)(1^(2,1^(3,1)))(2^(3,1^(4,1))) || <br /> |-<br /> | (0)(1^(2,1^(3,1)))(2^(3,1^(4,1)))(3) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,15)<br /> |-<br /> | (0)(1^(2,1^(3,1)),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,15,14,14,,13)<br /> |-<br /> | (0)(1^(2,1^(3,1))(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,15,14,,14)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,16)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13,13)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13,13)(,13,13,,13)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13,13)(,13,13,,13)(,18,13,,13)(,19,5)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1)))(1^(3,1),1) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,,5)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1)))(2,1^(3,1),1) || <br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1))(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,7,,6)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1))(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,8)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,1^(4,1))(4)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,9)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,9,9)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3^(4,3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,9,9,,9)(,10,9,,9)(,11,9)<br /> |-<br /> | (0)(1^(2,1^(3,1))(3^(4,3^(5,3)))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,9,9,,9)(,10,10,,10)(,11,10,,10)(,12,9)<br /> |-<br /> | (0)(1^(2,1^(3,1),1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)<br /> |-<br /> | (0)(1^(2,1^(3,1),1^(3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)(,9,,9)<br /> |-<br /> | (0)(1^(2,1^(3,1),1^(3,1))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)(,9,,9)(,10,,9)(,11,5)<br /> |-<br /> | (0)(1^(2,1^(3,1^(4)))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)(,9,,9)(,10,,9)(,11,5)(,5,,5)<br /> |-<br /> | (0)(1^(2,1^(3,1^(4,1)))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)(,9,,9)(,10,,9)(,11,5)(,5,,5)(,13,,5)(,14,5)<br /> |-<br /> | (0)(1^(2,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)<br /> |-<br /> | (0)(1^(2^(3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,5,,5)<br /> |-<br /> | (0)(1^(2^(3,1))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,5,,5)(,10,,5)(,11,5)<br /> |-<br /> | (0)(1^(2^(3,1))(2^(4))) || <br /> |-<br /> | (0)(1^(2^(3,1),1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,6,6,,5)(,10,10,,10)(,11,10,,10)(,12,10,,5)<br /> |-<br /> | (0)(1^(2^(3,1),2^(3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,6,,6)<br /> |-<br /> | (0)(1^(2^(3,2))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,6,,6)(,10,,6)(,11,6)<br /> |-<br /> | (0)(1^(2^(3,2))(2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,7,,6)<br /> |-<br /> | (0)(1^(2^(3,2))(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,8)<br /> |-<br /> | (0)(1^(2^(3,2))(3,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,8,5)<br /> |-<br /> | (0)(1^(2^(3,2))(3,2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,8,6)<br /> |-<br /> | (0)(1^(2^(3,2))(3,2^(4,2))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,8,6)(,6,,6)(,11,,6)(,12,6)<br /> |-<br /> | (0)(1^(2^(3,2))(3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,9,9)<br /> |-<br /> | (0)(1^(2^(3,2),1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)<br /> |-<br /> | (0)(1^(2^(3,2),1)(3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9)<br /> |-<br /> | (0)(1^(2^(3,2),1)(3^(4,2),3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,9)<br /> |-<br /> | (0)(1^(2^(3,2),1)(3^(4,2),3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,9)(,10,10,10,10)<br /> |-<br /> | (0)(1^(2^(3,2),1,1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,9,,5)<br /> |-<br /> | (0)(1^(2^(3,2),1^(3))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,,9)<br /> |-<br /> | (0)(1^(2^(3,2),1^(3^(4,3),1))) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,,9)(,10,9,,9)(,11,9,9,,5)<br /> |-<br /> | (0)(1^(2^(3,2),2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,6)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,6)(,8)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3,2^(4,2),1)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,6)(,8,6,,5)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3,2^(4,2),2)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,6)(,8,,6)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3,3)) || ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,7)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4))) || ()(,,1)(,,2)(,3)(,,1)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,1),3^(4))) || ()(,,1)(,,2)(,3)(,,2)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,2))) || ()(,,1)(,,2)(,3)(,,2)(,5)(,1)(,7,,7)(,8,,8)(,9,9)(,8,,8)(,11,,8)(,12,8)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,2),1)) || ()(,,1)(,,2)(,3,,1)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,2),2)) || ()(,,1)(,,2)(,3,,2)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,2),3)) || ()(,,1)(,,2)(,3,,2)(,4,4)<br /> |-<br /> | (0)(1^(2^(3,2),2)(3^(4,2),3^(4))) || <br /> |-<br /> | (0)(1^(2^(3,2),2,1)) || ()(,,1)(,,2)(,3,,2)(,4,4,,1)<br /> |-<br /> | (0)(1^(2^(3,2),2,2)) || ()(,,1)(,,2)(,3,,2)(,4,4,,2)<br /> |-<br /> | (0)(1^(2^(3,2),2^(3))) || ()(,,1)(,,2)(,,3)<br /> |-<br /> | (0)(1^(2^(3^(4)))) || ()(,,1)(,,2)(,,3)(,4)(,1)(,6,,6)(,7,,7)(,8,,8)(,9,,8)(,10,8)(,6,,6)<br /> |-<br /> | Limit || ()(,,1)(,,2,2)<br /> |}</div>

0100000000a7 http://wiki.googology.top/index.php?title=BTBMS%E5%88%86%E6%9E%90&diff=3772 2026-08-30T15:26:35Z

<p>0100000000a7：​创建页面，内容为“本条目展示BTBMS 和 ωMN的列表分析。以下分析来自test_alpha0 (0) = () (0)(1) = ()(,1) (0)(1^(2)) = ()(,,1) (0)(1^(2)(2)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4) (0)(1^(2)(3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6) (0)(1^(2)(3^(4))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6)(,7,,7) (0)(1^(2,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4) (0)(1^(2,1))(1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,1) (0)(1^(2,1))(1)(3^(4,3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,1)(…”</p> <hr /> <div>本条目展示[[BTBMS]] 和 [[ωMN]]的列表分析。以下分析来自test_alpha0<br /> <br /> (0) = ()<br /> (0)(1) = ()(,1)<br /> (0)(1^(2)) = ()(,,1)<br /> (0)(1^(2)(2)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)<br /> (0)(1^(2)(3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6)<br /> (0)(1^(2)(3^(4))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6)(,7,,7)<br /> (0)(1^(2,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)<br /> (0)(1^(2,1))(1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,1)<br /> (0)(1^(2,1))(1)(3^(4,3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,1)(,8,,8)(,9,,8)(,10,8)<br /> (0)(1^(2,1))(1)(3^(4,3))(3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4)<br /> (0)(1^(2,1))(1,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)<br /> (0)(1^(2,1))(1,1)(3^(4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)<br /> (0)(1^(2,1))(1,1)(3^(4))(4,3,3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)<br /> (0)(1^(2,1))(1,1)(3^(4))(4,3^(5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)(,8,8,,8)<br /> (0)(1^(2,1))(1,1)(3^(4))(4^(5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)(,10,10,10)(,8,8,,8)<br /> (0)(1^(2,1))(1,1)(3^(4),3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)(,10,10,10,10)<br /> (0)(1^(2,1))(1,1)(3^(4),3^(4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,8)(,10,10,10,,10)<br /> (0)(1^(2,1))(1,1)(3^(4)(4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)<br /> (0)(1^(2,1))(1,1)(3^(4)(5^(6,5))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10)(,11,,11)(,12,,11)(,13,11)(,11,11)<br /> (0)(1^(2,1))(1,1)(3^(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)<br /> (0)(1^(2,1))(1,1)(3^(4,1))(3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8)<br /> (0)(1^(2,1))(1,1)(3^(4,1))(3,3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8,8)<br /> (0)(1^(2,1))(1,1)(3^(4,1))(3,3,3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8,8,8)<br /> (0)(1^(2,1))(1,1)(3^(4,1))(3^(5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8,8,,8)<br /> (0)(1^(2,1))(1,1)(3^(4,1))(3^(5,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,8,8,,8)(,12,8,,8)(,13,4)<br /> (0)(1^(2,1))(1,1)(3^(4,1))(4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9)<br /> (0)(1^(2,1))(1,1)(3^(4,1))(4,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,4)<br /> (0)(1^(2,1))(1,1)(3^(4,1))(4,3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8)<br /> (0)(1^(2,1))(1,1)(3^(4,1))(4,3,3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)<br /> (0)(1^(2,1))(1,1)(3^(4,1))(4,3^(5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)(,8,8,,8)<br /> (0)(1^(2,1))(1,1)(3^(4,1))(4,3^(5,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,4)<br /> (0)(1^(2,1))(1,1)(3^(4,1))(4^(5,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)(,12,12,12)(,8,8,,8)<br /> (0)(1^(2,1))(1,1)(3^(4,1),3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,9,8,8)(,12,12,12,12)<br /> (0)(1^(2,1))(1,1)(3^(4,1)(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,10,4)<br /> (0)(1^(2,1))(1,1)(3^(4,1)(5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11)<br /> (0)(1^(2,1))(1,1)(3^(4,1)(5,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,4)<br /> (0)(1^(2,1))(1,1)(3^(4,1)(5,5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11)<br /> (0)(1^(2,1))(1,1)(3^(4,1)(5^(6))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)<br /> (0)(1^(2,1))(1,1)(3^(4,1)(5^(6)(6))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)<br /> (0)(1^(2,1))(1,1)(3^(4,1)(5^(6)(7^(8,7)))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13)(,14,,14)(,15,,14)(,16,14)<br /> (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)<br /> (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14)<br /> (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7,1))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14,4)<br /> (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7,7))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14,14)<br /> (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7^(8)))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14,14,,14)<br /> (0)(1^(2,1))(1,1)(3^(4,1)(5^(6,1)(7^(8)(8)))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,4)(,11,11,,11)(,12,11,,11)(,13,4)(,14,14,,14)(,15,14,,14)<br /> (0)(1^(2,1))(1,1)(3^(4,3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)<br /> (0)(1^(2,1))(1,1)(3^(4,3))(3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8)<br /> (0)(1^(2,1))(1,1)(3^(4,3))(3,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,4)<br /> (0)(1^(2,1))(1,1)(3^(4,3))(3,3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)<br /> (0)(1^(2,1))(1,1)(3^(4,3))(3,3)(5^(6,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)(,12,12,,12)(,13,12,,12)(,14,4)<br /> (0)(1^(2,1))(1,1)(3^(4,3))(3,3)(5^(6,3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)(,12,12,,12)(,13,12,,12)(,14,8)<br /> (0)(1^(2,1))(1,1)(3^(4,3))(3,3)(5^(6,5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)(,12,12,,12)(,13,12,,12)(,14,12)<br /> (0)(1^(2,1))(1,1)(3^(4,3))(3,3)(5^(6,5))(5,5) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8)(,12,12,,12)(,13,12,,12)(,14,12)(,12,12)<br /> (0)(1^(2,1))(1,1,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)<br /> (0)(1^(2,1))(1,1,1)(1,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,4,4)<br /> (0)(1^(2,1))(1,1,1)(1,1)(4^(5,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,4,4)(,13,13,,13)(,14,13,,13)(,15,4)<br /> (0)(1^(2,1))(1,1,1)(1,1)(4^(5,4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,4,4)(,13,13,,13)(,14,13,,13)(,15,13)<br /> (0)(1^(2,1))(1,1,1)(1,1)(4^(5,4))(4,4,4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,4,4)(,13,13,,13)(,14,13,,13)(,15,13)(,13,13,13)<br /> (0)(1^(2,1))(1,1,1)(1,1)(4^(5,4))(4,4,4)(4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,8)<br /> (0)(1^(2,1))(1,1,1)(1,1)(4^(5,4))(4,4,4)(4,4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,8,8)<br /> (0)(1^(2,1))(1,1,1)(1,1,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,8,8,8)<br /> (0)(1^(2,1))(1,1,1)(3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12)<br /> (0)(1^(2,1))(1,1,1)(3^(4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)<br /> (0)(1^(2,1))(1,1,1)(3^(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)<br /> (0)(1^(2,1))(1,1,1)(3^(4,1)(5^(6,1))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)(,15,15,,15)(,16,15,,15)(,17,4)<br /> (0)(1^(2,1))(1,1,1)(3^(4,1)(5^(6,5))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)(,15,15,,15)(,16,15,,15)(,17,15)<br /> (0)(1^(2,1))(1,1,1)(3^(4,1)(5^(6,5))(5,5,5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)(,15,15,,15)(,16,15,,15)(,17,15)(,15,15,15)<br /> (0)(1^(2,1))(1,1,1)(3^(4,1)(5^(6,5))(5,5,5)(7^(8,5))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)<br /> (0)(1^(2,1))(1,1,1)(3^(4,1,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)<br /> (0)(1^(2,1))(1,1,1)(3^(4,3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)<br /> (0)(1^(2,1))(1,1,1)(3^(4,3))(3,3,3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,12,12,12)<br /> (0)(1^(2,1))(1,1,1)(3^(4,3))(3,3,3)(5^(6,5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,12,12,12)(,16,16,16,,16)(,17,16,16,,16)(,18,16)<br /> (0)(1^(2,1))(1,1,1,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,12,12,12,12)<br /> (0)(1^(2,1))(1^(3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)<br /> (0)(1^(2,1))(1^(3)(3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)<br /> (0)(1^(2,1))(1^(3,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)(,13,4)<br /> (0)(1^(2,1))(1^(3,1))(1,1)(4^(5,4))(4^(6,4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)(,13,8)<br /> (0)(1^(2,1))(1^(3,1))(1^(4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)(,13,8)(,8,8,,8)<br /> (0)(1^(2,1))(1^(3,1))(1^(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,8,8,,8)(,12,8,,8)(,13,8)(,8,8,,8)(,15,8,,8)(,16,4)<br /> (0)(1^(2,1))(2) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9)<br /> (0)(1^(2,1))(2,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,4)<br /> (0)(1^(2,1))(2,1)(1,1)(4^(5,4))(5,4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)<br /> (0)(1^(2,1))(2,1)(1,1,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,8)<br /> (0)(1^(2,1))(2,1)(1^(4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)<br /> (0)(1^(2,1))(2,1)(1^(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,4)<br /> (0)(1^(2,1))(2,1)(1^(4,1))(1,1)(5^(6,5))(6,5)(5^(8,5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)<br /> (0)(1^(2,1))(2,1)(1^(4,1))(1^(5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)(,8,8,,8)<br /> (0)(1^(2,1))(2,1)(1^(4,1))(1^(5,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)(,8,8,,8)(,16,8,,8)(,17,4)<br /> (0)(1^(2,1))(2,1)(1^(4,1))(4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13)<br /> (0)(1^(2,1))(2,1)(1^(4,1))(4,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,4)<br /> (0)(1^(2,1))(2,1)(2) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,9)<br /> (0)(1^(2,1))(2,1)(3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,12)<br /> (0)(1^(2,1))(2,1)(3^(4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,12,12,,12)<br /> (0)(1^(2,1))(2,1)(3^(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,12,12,,12)(,13,12,,12)(,14,4)<br /> (0)(1^(2,1))(2,1)(3^(4,3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8)(,12,12,,12)(,13,12,,12)(,14,12)<br /> (0)(1^(2,1))(2,1,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)<br /> (0)(1^(2,1))(2,1,1,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,13)<br /> (0)(1^(2,1))(2,1^(3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)<br /> (0)(1^(2,1))(2,1^(3,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,4)<br /> (0)(1^(2,1))(2,1^(3,1))(1,1)(4^(5,4))(5,4^(6,4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)<br /> (0)(1^(2,1))(2,1^(3,1))(1,1,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,8,8,8)<br /> (0)(1^(2,1))(2,1^(3,1))(1^(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,8,8,,8)(,16,8,,8)(,17,4)<br /> (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13)<br /> (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,4)<br /> (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4,1,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)<br /> (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4,1^(5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,8,8,,8)<br /> (0)(1^(2,1))(2,1^(3,1))(1^(4,1))(4,1^(5,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,8,8,,8)(,17,8,,8)(,18,4)<br /> (0)(1^(2,1))(2,1^(3,1))(2) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,9)<br /> (0)(1^(2,1))(2,1^(3,1))(2,1,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,9,8,8)<br /> (0)(1^(2,1))(2,1^(3,1))(2,1^(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,4)<br /> (0)(1^(2,1))(2,1^(3,1))(3,1^(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,8,8)(,8,8,,8)(,14,8,,8)(,15,4)<br /> (0)(1^(2,1))(2,2) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12)<br /> (0)(1^(2,1))(2^(3,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12)(,8,8,,8)(,14,8,,8)(,15,4)<br /> (0)(1^(2,1))(2^(3,1),2) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,12)<br /> (0)(1^(2,1))(2^(3,1),2^(3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)<br /> (0)(1^(2,1))(2^(3,1),2^(3))(2^(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,12,12,12)<br /> (0)(1^(2,1))(2^(3,1),2^(3))(2^(4,1))(4^(5,1),4^(5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,12,12,12)(,14,14,14,,14)<br /> (0)(1^(2,1))(2^(3,1),2^(3))(2^(4,1),2) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,12,12,12,12)<br /> (0)(1^(2,1))(2^(3,1),2^(3))(2^(4,1),2^(4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,12,12,12,,12)<br /> (0)(1^(2,1))(2^(3,1),2^(3))(3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13)<br /> (0)(1^(2,1))(2^(3,1),2^(3))(3,2^(4,1),2) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)<br /> (0)(1^(2,1))(2^(3,1),2^(3))(3,3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14)<br /> (0)(1^(2,1))(2^(3,1),2^(3))(3^(4,1),3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14,14,14)<br /> (0)(1^(2,1))(2^(3,1),2^(3))(3^(4,1),3^(4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14,14,14)(,12,12,12,,12)<br /> (0)(1^(2,1))(2^(3,1),2^(3),2) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14,14,14,14)<br /> (0)(1^(2,1))(2^(3,1),2^(3),2^(3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,12)(,14,14,14,14,,14)<br /> (0)(1^(2,1))(2^(3,1),2^(3)(3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)<br /> (0)(1^(2,1))(2^(3,1),2^(3,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,4)<br /> (0)(1^(2,1))(2^(3,1)(3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,13,12,12,,12)<br /> (0)(1^(2,1))(2^(3,1)(3,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,13,12,12,,12)(,16,4)<br /> (0)(1^(2,1))(2^(3,1)(4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,14)<br /> (0)(1^(2,1))(2^(3,1)(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,14,4)<br /> (0)(1^(2,1))(2^(3,1)(4,1)(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,14,8)(,14,4)<br /> (0)(1^(2,1))(2^(3,1)(4,1)(5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15)<br /> (0)(1^(2,1))(2^(3,1)(4,4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15,15)<br /> (0)(1^(2,1))(2^(3,1)(4^(5))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15,15,,15)<br /> (0)(1^(2,1))(2^(3,1)(4^(5,1))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15,15,,15)(,16,15,,15)(,17,4)<br /> (0)(1^(2,1))(2^(3,1)(4^(5,4))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8)(,15,15,,15)(,16,15,,15)(,17,15)<br /> (0)(1^(2,1))(2^(3,1,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)<br /> (0)(1^(2,1))(2^(3,1^(4))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,8,8,,8)<br /> (0)(1^(2,1))(2^(3,1^(4,1))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,8,8,,8)(,16,8,,8)(,17,4)<br /> (0)(1^(2,1))(2^(3,1^(4,1))(3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,13,12,12,,12)<br /> (0)(1^(2,1))(2^(3,1^(4,1))(4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,14)<br /> (0)(1^(2,1))(2^(3,1^(4,1))(4,1^(5,1))(5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15)<br /> (0)(1^(2,1))(2^(3,1^(4,1))(4,4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15)<br /> (0)(1^(2,1))(2^(3,1^(4,1))(4^(5))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15)(,8,8,,8)<br /> (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15)(,8,8,,8)(,17,8,,8)(,18,4)<br /> (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1),4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,15)<br /> (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1),4^(5,1))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,,15)(,16,15,15,,15)(,17,4)<br /> (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1,1))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,,15)(,16,15,15,,15)(,17,8,8)<br /> (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1^(6)))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,,15)(,16,15,15,,15)(,17,8,8)(,8,8,,8)<br /> (0)(1^(2,1))(2^(3,1^(4,1))(4^(5,1^(6,1)))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,8,8)(,15,15,15,,15)(,16,15,15,,15)(,17,8,8)(,8,8,,8)(,19,8,,8)(,20,4)<br /> (0)(1^(2,1))(2^(3,2)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)<br /> (0)(1^(2,1))(2^(3,2))(3,2^(4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,12,12,12,,12)<br /> (0)(1^(2,1))(2^(3,2))(3,2^(4,2)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,12,12,12,,12)(,17,12,12,,12)(,18,12)<br /> (0)(1^(2,1))(2^(3,2))(3,3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,16,16)<br /> (0)(1^(2,1))(2^(3,2))(3^(4,2)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,16,16,16,16)(,12,12,12,,12)(,18,12,12,,12)(,19,12)<br /> (0)(1^(2,1))(2^(3,2))(3^(4,2),3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,16,16,16,16,16)<br /> (0)(1^(2,1))(2^(3,2))(3^(4,3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,8)(,12,12,12,,12)(,13,12,12,,12)(,14,12)(,13,12,12,12)(,16,16,16,16,,16)(,17,16,16,16,,16)(,18,16)<br /> (0)(1^(2,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)<br /> (0)(1^(2,1),1)(1^(3,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,4)<br /> (0)(1^(2,1),1)(1^(3,1))(3,1^(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,8,8,,8)(,17,8,,8)(,18,4)<br /> (0)(1^(2,1),1)(1^(3,1))(3,3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16)<br /> (0)(1^(2,1),1)(1^(3,1))(3^(4,1),3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,16)<br /> (0)(1^(2,1),1)(1^(3,1))(3^(4,3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)<br /> (0)(1^(2,1),1)(1^(3,1))(3^(4,3),3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)(,17,16,16,,16)<br /> (0)(1^(2,1),1)(1^(3,1))(3^(4,3),3)(3^(5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)(,17,16,16,,16)(,16,16,16,,16)<br /> (0)(1^(2,1),1)(1^(3,1))(3^(4,3),3)(3^(5,3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)(,17,16,16,,16)(,16,16,16,,16)(,21,16,16,,16)(,22,16)<br /> (0)(1^(2,1),1)(1^(3,1))(3^(4,3),3)(3^(5,3))(5^(6,5),5) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,8)(,16,16,16,,16)(,17,16,16,,16)(,18,16)(,17,16,16,,16)(,16,16,16,,16)(,21,16,16,,16)(,22,16)(,21,16,16,16)(,24,24,24,24,,24)(,25,24,24,24,,24)(,26,24)(,25,24,24,24,,24)<br /> (0)(1^(2,1),1)(1^(3,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,8,8,,8)(,13,8,,8)(,14,8)(,13,8,,8)<br /> (0)(1^(2,1),1)(2) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9)<br /> (0)(1^(2,1),1)(2,1,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)<br /> (0)(1^(2,1),1)(2,1^(3,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,4)<br /> (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4,1^(5,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,8,8,,8)(,18,8,,8)(,19,8)<br /> (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,1),4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)<br /> (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)<br /> (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,4),4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)<br /> (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,4),4)(5,4^(6)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)(,18,17,17,17)(,17,17,17,,17)<br /> (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1))(4^(5,4),4)(5,4^(6,4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)(,18,17,17,17)(,17,17,17,,17)(,23,17,17,,17)(,24,17)<br /> (0)(1^(2,1),1)(2,1^(3,1))(1^(4,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,,8)<br /> (0)(1^(2,1),1)(2,1^(3,1))(2) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,9)<br /> (0)(1^(2,1),1)(2,1^(3,1))(3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13)<br /> (0)(1^(2,1),1)(2,1^(3,1))(3^(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13)(,8,8,,8)(,15,8,,8)(,16,8)<br /> (0)(1^(2,1),1)(2,1^(3,1))(3^(4,1))(1^(5,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13)(,8,8,,8)(,15,8,,8)(,16,8)(,15,8,,8)<br /> (0)(1^(2,1),1)(2,1^(3,1))(3^(4,1),3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,13)<br /> (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)<br /> (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3),3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,,13)<br /> (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3),3)(4,3^(5,3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,,13)(,14,13,13,13)(,13,13,13,,13)(,19,13,13,,13)(,20,13)<br /> (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3),3)(4,3^(5,3))(5^(6,5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,,13)(,14,13,13,13)(,18,18,18,18,,18)(,19,18,18,18,,18)(,20,18)<br /> (0)(1^(2,1),1)(2,1^(3,1))(3^(4,3),3)(4,3^(5,3))(5^(6,5),5) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,8)(,13,13,13,,13)(,14,13,13,,13)(,15,13)(,14,13,13,,13)(,14,13,13,13)(,18,18,18,18,,18)(,19,18,18,18,,18)(,20,18)(,19,18,18,18,,18)<br /> (0)(1^(2,1),1)(2,1^(3,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1))(4^(5,4),4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1))(4^(5,4),4)(5,4^(6,4),4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,8)(,17,17,17,,17)(,18,17,17,,17)(,19,17)(,18,17,17,,17)(,18,17,17,,17)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,,8)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(1^(4,1),1)(4,1^(5,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,8,8,,8)(,14,8,,8)(,15,8)(,14,8,,8)(,14,8,,8)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(2) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,15,8,,8)(,16,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(1^(5,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,15,8,,8)(,16,8)(,15,8,,8)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(1^(5,1),1)(5,1^(6,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,8,8,,8)(,15,8,,8)(,16,8)(,15,8,,8)(,15,8,,8)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(4^(5,4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,14,14,14,,14)(,15,14,14,,14)(,16,14)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(4^(5,4),4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1))(4^(5,4),4)(5,4^(6,4),4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,8)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)(,15,14,14,,14)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(2,1^(4,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,9,8,,8)(,9,8,,8)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,12)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,12,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(2,1^(5,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)(,12,8)(,9,8,,8)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,10)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(3,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,10,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4,4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4^(5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11,,11)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4^(5,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11,,11)(,12,11,,11)(,13,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4^(5,4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11,,11)(,12,11,,11)(,13,11)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1)(4^(5,4),4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8)(,11,11,,11)(,12,11,,11)(,13,11)(,12,11,,11)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,4)(,8,8,,8)(,9,8,,8)(,10,8,8)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1,1)(5^(6,5),5)(6,5^(7,5),5)(7,5^(8,5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,14,14,,14)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,14,14,,14)(,24,14,,14)(,25,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,21,14,,14)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1)(5,1^(6,1),1)(6) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,21,14,,14)(,24)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1)(5,1^(6,1),1)(6,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14)(,21,14,,14)(,24,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1)(5,1^(6,1),1)(6,1,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,4)(,14,14,,14)(,15,14,,14)(,16,14,14)(,14,14,,14)(,18,14,,14)(,19,14,14)(,14,14,,14)(,21,14,,14)(,22,14,14)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(1^(5,1),1)(5,1^(6,1),1)(6,1^(7)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,4,,4)(,8,,4)(,9,4)(,4,,4)(,11,,4)(,12,4)(,4,,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1))(6^(7,6),6)(7,6^(8,6),6)(8,6^(9,6))(7,6^(10,6)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12)(,17,12,12)(,20,20,20,,20)(,21,20,20,,20)(,22,20,20,20)(,21,20,20,20)(,20,20,20,,20)(,25,20,20,,20)(,26,20)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12)(,17,12,,12)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12)(,17,12,,12)(,17,12,,12)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12)(,17,12,,12)(,20,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,12,12,,12)(,17,12,,12)(,18,12,12)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1^(8)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1^(8,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,4,,4)(,12,,4)(,13,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(1^(6,1),1)(6,1^(7,1),1)(7,1^(8,1))(6) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,4,,4)(,9,,4)(,10,4)(,9)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(2) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,5)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(2,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,5,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5,5) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,1),5) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,8)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,1),5^(6,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,1,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,4)(,4,4)(,12,12,,12)(,13,12,,12)(,14,12,12)(,13,12,12)(,16,16,16,,16)(,17,16,16,,16)(,18,12,12)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,5)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,8)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,5),5) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1))(5^(6,5),5)(6,5^(7,5),5)(7,5^(8,5))(6) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,4)(,8,8,,8)(,9,8,,8)(,10,8,8)(,9)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,4,,4)(,10,,4)(,11,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1))(1^(7,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,4,,4)(,10,,4)(,11,4)(,10,4)(,13,13,,13)(,14,13,,13)(,15,13,13)(,14,13,,13)(,17,13,13)(,13,13,,13)(,19,13,,13)(,20,13)(,19,13,,13)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1))(1^(7,1),1)(7,1^(8,1),1)(8,1^(9,1))(7,1^(10,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,4,,4)(,10,,4)(,11,4)(,10,,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1))(2) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,5)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(2,1^(5,1),1)(5,1^(6,1))(2,1^(7,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,5,,4)(,8,4)(,5,,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(3) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,6)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(3,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,6,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4,4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,1),4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,7)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,1^(6))) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,4)(,4,,4)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7)(,8,7,,7)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7)(,8,7,,7)(,8,7,,7)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4)(6,4,4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7,7)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4)(6,4^(7,4)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7,7)(,7,7,,7)(,11,7,,7)(,12,7)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4)(6,4^(7,4))(4^(8,4),4) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7,7)(,7,7,,7)(,11,7,,7)(,12,7)(,11,7,,7)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1))(4^(5,4),4)(5,4^(6,4),4)(6,4^(7,4))(7^(8,7)) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,4)(,7,7,,7)(,8,7,,7)(,9,7,7)(,10,10,10,,10)(,11,10,10,,10)(,12,10)<br /> (0)(1^(2,1),1)(2,1^(3,1),1)(3,1^(4,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,,4)(,6,,4)<br /> (0)(1^(2,1),1)(2,2) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)<br /> (0)(1^(2,1),1)(2,2)(2,1^(4,1),1)(4,4) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8)(,8,7,,7)(,10,10)<br /> (0)(1^(2,1),1)(2,2)(2,2) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8)(,8,8)<br /> (0)(1^(2,1),1)(2,2,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)<br /> (0)(1^(2,1),1)(2,2,1^(3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,7,7,,7)<br /> (0)(1^(2,1),1)(2,2,1^(3,1))(1^(4,1),1)(4,4) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,7,7,,7)(,10,10)<br /> (0)(1^(2,1),1)(2,2,1^(3,1))(2) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,8)<br /> (0)(1^(2,1),1)(2,2,1^(3,1))(2,1^(4,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,8,7,,7)<br /> (0)(1^(2,1),1)(2,2,1^(3,1))(3) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9)<br /> (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,1),3) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,9)<br /> (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,2)) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,9,9,,9)(,11,8)<br /> (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,9,9,,9)(,11,9)<br /> (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3),3)(4,4) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,10)<br /> (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3),3)(4,4,1) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,10,7)<br /> (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3),3)(4,4,3) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,10,9)<br /> (0)(1^(2,1),1)(2,2,1^(3,1))(3^(4,3),3)(4,4,3^(5,3)) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,7)(,9,9,9,,9)(,10,10,9,9)(,9,9,9,,9)(,12,9,9,,9)(,13,9)<br /> (0)(1^(2,1),1)(2,2,1^(3,1),1) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,,7)<br /> (0)(1^(2,1),1)(2,2,2) = ()(,,1)(,2)(,1)(,4,,4)(,5,5)(,4,4)(,7,7,,7)(,8,8,8)<br /> (0)(1^(2,1),1)(2^(3)) = ()(,,1)(,2)(,,1)<br /> (0)(1^(2,1),1)(2^(3),2) = ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,6)(,10,10,,10)(,11,11,11)<br /> (0)(1^(2,1),1)(2^(3),2^(3)) = ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,6)(,10,10,,10)(,11,11,11)(,10,10,,10)<br /> (0)(1^(2,1),1)(2^(3)(3)) = ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,,6)<br /> (0)(1^(2,1),1)(2^(3,1)) = ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,,6)(,10,6)<br /> (0)(1^(2,1),1)(2^(3,1))(1^(4,1),1) = ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,,6)(,10,6)(,9,6)(,12,12,,12)(,13,13,13)(,12,12,,12)(,15,12,,12)(,16,12)(,15,12,,12)<br /> (0)(1^(2,1),1)(2^(3,1))(1^(4,1),1)(4,4) = ()(,,1)(,2)(,,1)(,4)(,1)(,6,,6)(,7,7)(,6,,6)(,9,9)<br /> (0)(1^(2,1),1)(2^(3,1))(1^(4,1),1)(4^(5)) = ()(,,1)(,2)(,,1)(,4)(,,1)<br /> (0)(1^(2,1),1)(2^(3,1))(2) = ()(,,1)(,2)(,2)<br /> (0)(1^(2,1),1)(2^(3,1))(3) = ()(,,1)(,2)(,3)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,1),3) = ()(,,1)(,2)(,3,3)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,1),3^(4)) = ()(,,1)(,2)(,3,,3)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,1),3^(4)(4)) = ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,1),3^(4,1)) = ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,6)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,1^(5))) = ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,6)(,6,,6)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,2)) = ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,7)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,2^(5))) = ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,7)(,6,,6)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,3)) = ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,3))(4) = ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,3))(4,3^(5,3)) = ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,14)(,14,14,14,,14)(,19,14,14,,14)(,20,14)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,3))(4^(5,3),4) = ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,14)(,18,18,18,18,18)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,3))(4^(5,4)) = ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,14)(,18,18,18,18,,18)(,19,18,18,18,,18)(,20,18)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3) = ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4,3^(5,3),3) = ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,8,,8)(,10,8)(,6,6)(,12,12,,12)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)(,15,14,14,,14)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4,4) = ()(,,1)(,2)(,3,,3)(,4)(,1)(,6,,6)(,7,7)(,8,8,,8)(,9,9)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5)) = ()(,,1)(,2)(,3,,3)(,4)(,,1)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5)(5)) = ()(,,1)(,2)(,3,,3)(,4)(,,1)(,6)(,1)(,8,,8)(,9,9)(,10,10,,10)(,11,11)(,8,,8)(,13,,8)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,1)) = ()(,,1)(,2)(,3,,3)(,4)(,,1)(,6)(,1)(,8,,8)(,9,9)(,10,10,,10)(,11,11)(,8,,8)(,13,,8)(,14,8)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,2)) = ()(,,1)(,2)(,3,,3)(,4,4)(,3,,3)(,6,,3)(,7)(,1)(,9,,9)(,10,10)(,11,11,,11)(,12,12,12)(,11,11,,11)(,14,11,,11)(,15,10)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,3)) = ()(,,1)(,2)(,3,,3)(,4,4)(,3,,3)(,6,,3)(,7)(,1)(,9,,9)(,10,10)(,11,11,,11)(,12,12,12)(,11,11,,11)(,14,11,,11)(,15,11)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,3))(3^(6,3),3) = ()(,,1)(,2)(,3,,3)(,4,4)(,3,,3)(,6,,3)(,7)(,1)(,9,,9)(,10,10)(,11,11,,11)(,12,12,12)(,11,11,,11)(,14,11,,11)(,15,11)(,14,11,,11)<br /> (0)(1^(2,1),1)(2^(3,1))(3^(4,3),3)(4^(5,3))(5^(6,5)) = ()(,,1)(,2)(,3,,3)(,4,4)(,5,5,,5)(,6)(,1)(,8,,8)(,9,9)(,10,10,,10)(,11,11,11)(,12,12,12,,12)(,13,12,12,,12)(,14,12)<br /> (0)(1^(2,1),1)(2^(3,1),1) = ()(,,1)(,2,,1)<br /> (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1) = ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)<br /> (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1)(4,4) = ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)(,8,8)<br /> (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1)(4^(5,1))(5^(6,5),5)(6,6) = ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)(,8,8)(,9,9,,9)(,10,10,10)(,11,11,11,,11)(,12,12)<br /> (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1)(4^(5,1))(5^(6,5),5)(6^(7,5),5) = ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)(,8,8)(,9,9,,9)(,10,10,10,,9)<br /> (0)(1^(2,1),1)(2^(3,1),1)(2,1^(4,1),1)(4^(5,1),1) = ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,,5)(,8,8,,5)<br /> (0)(1^(2,1),1)(2^(3,1),1)(2,2) = ()(,,1)(,2,,1)(,2)(,1)(,5,,5)(,6,6,,5)(,6,6)<br /> (0)(1^(2,1),1)(2^(3,1),1)(2^(4)) = ()(,,1)(,2,,1)(,2)(,,1)<br /> (0)(1^(2,1),1)(2^(3,1),1)(2^(4,1))(4) = ()(,,1)(,2,,1)(,2)(,4)<br /> (0)(1^(2,1),1)(2^(3,1),1)(2^(4,1))(4^(5,4),4)(5^(6,4),4) = ()(,,1)(,2,,1)(,2)(,4,,4)(,5,5,,4)<br /> (0)(1^(2,1),1)(2^(3,1),1)(2^(4,1),1) = ()(,,1)(,2,,1)(,2,,1)<br /> (0)(1^(2,1),1)(2^(3,1),1)(3) = ()(,,1)(,2,,1)(,3)<br /> (0)(1^(2,1),1)(2^(3,1),1)(3,1) = ()(,,1)(,2,,1)(,3)(,1)(,5,,5)(,6,6,,5)(,7,5)<br /> (0)(1^(2,1),1)(2^(3,1),1)(3,1^(4,1),1) = ()(,,1)(,2,,1)(,3)(,1)(,5,,5)(,6,6,,5)(,7,,5)<br /> (0)(1^(2,1),1)(2^(3,1),1)(3,2) = ()(,,1)(,2,,1)(,3)(,1)(,5,,5)(,6,6,,5)(,7,6)<br /> (0)(1^(2,1),1)(2^(3,1),1)(3,3) = ()(,,1)(,2,,1)(,3)(,1)(,5,,5)(,6,6,,5)(,7,7)<br /> (0)(1^(2,1),1)(2^(3,1),1)(3^(4)) = ()(,,1)(,2,,1)(,3)(,,1)<br /> (0)(1^(2,1),1)(2^(3,1),1)(3^(4,1)) = ()(,,1)(,2,,1)(,3)(,,1)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9)(,7,,7)(,11,,7)(,12,7)<br /> (0)(1^(2,1),1)(2^(3,1),1)(3^(4,1))(4) = ()(,,1)(,2,,1)(,3)(,4)<br /> (0)(1^(2,1),1)(2^(3,1),1)(3^(4,1))(4^(5,4),4)(5^(6,4),4) = ()(,,1)(,2,,1)(,3)(,4,,4)(,5,5,,4)<br /> (0)(1^(2,1),1)(2^(3,1),1)(3^(4,1),1) = ()(,,1)(,2,,1)(,3,,1)<br /> (0)(1^(2,1),1)(2^(3,1),2) = ()(,,1)(,2,,1)(,3,3)<br /> (0)(1^(2,1),1)(2^(3,1),2)(3) = ()(,,1)(,2,,1)(,3,3)(,4)<br /> (0)(1^(2,1),1)(2^(3,1),2)(3,1) = ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,6)<br /> (0)(1^(2,1),1)(2^(3,1),2)(3,1^(4,1),1) = ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,,6)<br /> (0)(1^(2,1),1)(2^(3,1),2)(3,2) = ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,7)<br /> (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4)) = ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,7)(,6,,6)<br /> (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),1) = ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,7,,6)<br /> (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),1)(4^(5,1),4)(5,4) = ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,8)<br /> (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),1)(4^(5,1),4)(5,4^(6,1),1) = (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),1)(4^(5,1),4)(5,4^(6,1),1)<br /> (0)(1^(2,1),1)(2^(3,1),2)(3,2^(4,1),2) = ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,8,8)<br /> (0)(1^(2,1),1)(2^(3,1),2)(3,3) = ()(,,1)(,2,,1)(,3,3)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8)(,9,9)<br /> (0)(1^(2,1),1)(2^(3,1),2)(3^(4)) = ()(,,1)(,2,,1)(,3,3)(,4)(,,1)<br /> (0)(1^(2,1),1)(2^(3,1),2)(3^(4,1),1) = ()(,,1)(,2,,1)(,3,3)(,4,,1)<br /> (0)(1^(2,1),1)(2^(3,1),2)(3^(4,1),2) = ()(,,1)(,2,,1)(,3,3)(,4,3)<br /> (0)(1^(2,1),1)(2^(3,1),2)(3^(4,1),3) = ()(,,1)(,2,,1)(,3,3)(,4,4)<br /> (0)(1^(2,1),1)(2^(3,1),2,2) = ()(,,1)(,2,,1)(,3,3)(,4,4,4)<br /> (0)(1^(2,1),1)(2^(3,1),2^(3)) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)<br /> (0)(1^(2,1),1)(2^(3,1),2^(3,1)) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,7)<br /> (0)(1^(2,1),1)(2^(3,1^(4))) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,7)(,7,,7)<br /> (0)(1^(2,1),1)(2^(3,1^(4,1),1)) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,,7)<br /> (0)(1^(2,1),1)(2^(3,2)) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,8)<br /> (0)(1^(2,1),1)(2^(3,2))(2^(4,1),1)(4^(5,4)) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,9)<br /> (0)(1^(2,1),1)(2^(3,2))(2^(4,1),1)(4^(5,4))(4^(6,1),1)(6^(7,6)) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,9)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,16)(,16,16,16,,14)(,21,21,21,21)(,22,22,22,22,,22)(,23,22,22,22,,22)(,24,21)<br /> (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,8)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,15)(,16,16,16,16)<br /> (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2)(4^(5,2)) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,9)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,16)(,16,16,16,16)(,21,21,21,21,,21)(,22,21,21,21,,21)(,23,16)<br /> (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2)(4^(5,2),4) = <br /> (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2)(4^(5,4)) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)<br /> (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2)(4^(5,4))(4) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,17)<br /> (0)(1^(2,1),1)(2^(3,2))(2^(4,1),2,2) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,17,17,17,17,17)<br /> (0)(1^(2,1),1)(2^(3,2))(2^(4,2)) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,17,17,17,17,,17)(,21,17,17,17,,17)(,22,17)<br /> (0)(1^(2,1),1)(2^(3,2))(3) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18)<br /> (0)(1^(2,1),1)(2^(3,2))(3,2^(4,2)) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,17)(,17,17,17,17,,17)(,22,17,17,17,,17)(,23,17)<br /> (0)(1^(2,1),1)(2^(3,2))(3,3) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,17)(,21,21)<br /> (0)(1^(2,1),1)(2^(3,2))(3^(4,2),3) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,17)(,21,21,21,21,21,21)<br /> (0)(1^(2,1),1)(2^(3,2))(3^(4,3)) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,17)(,21,21,21,21,21,,21)(,22,21,21,21,21,,21)(,23,21)<br /> (0)(1^(2,1),1)(2^(3,2),2) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,10,10,,10)(,12,10)(,7,7)(,14,14,,14)(,15,15,15,,14)(,16,16,16,16)(,17,17,17,17,,17)(,18,17,17,17,,17)(,19,17)(,18,17,17,17,,17)<br /> (0)(1^(2,1),1)(2^(3,2),2)(3,3) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,1)(,7,,7)(,8,8,,7)(,9,9,9)(,10,10,10,,10)(,11,11)<br /> (0)(1^(2,1),1)(2^(3,2),2)(3^(4)) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5)(,,1)<br /> (0)(1^(2,1),1)(2^(3,2),2)(3^(4,1),1) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,,1)<br /> (0)(1^(2,1),1)(2^(3,2),2)(3^(4,1),3) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5)<br /> (0)(1^(2,1),1)(2^(3,2),2)(3^(4,2)) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5,5)(,4,4,,4)(,7,4,,4)(,8,4)<br /> (0)(1^(2,1),1)(2^(3,2),2)(3^(4,2),2) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5,5,,4)<br /> (0)(1^(2,1),1)(2^(3,2),2)(3^(4,2),3) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5,5,,4)(,6,6,6,6)<br /> (0)(1^(2,1),1)(2^(3,2),2)(3^(4,3)) = ()(,,1)(,2,,1)(,3,3)(,4,4,,4)(,5,5,5,,4)(,6,6,6,6)(,7,7,7,7,,7)(,8)(,1)(,10,,10)(,11,11,,10)(,12,12,12)(,13,13,13,,13)(,14,14,14,14,,13)(,15,15,15,15,15)(,16,16,16,16,16,,16)(,17,16,16,16,16,,16)(,18,14)<br /> (0)(1^(2,1),1,1) = ()(,,1)(,2,,1)(,3,3,,1)<br /> (0)(1^(2,1),1,1)(1^(3,1),1)(3^(4)) = ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5)(,,1)<br /> (0)(1^(2,1),1,1)(1^(3,1),1)(3^(4,1),1) = ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5,,1)<br /> (0)(1^(2,1),1,1)(1^(3,1),1)(3^(4,1),3) = ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5,,1)(,6,6)<br /> (0)(1^(2,1),1,1)(1^(3,1),1)(3^(4,3),3,3) = ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5,,1)(,6,6)(,7,7,,7)(,8,8,8,,7)(,9,9,9,9,,7)<br /> (0)(1^(2,1),1,1)(1^(3,1),1,1) = ()(,,1)(,2,,1)(,3,3,,1)(,,1)(,5,,1)(,6,6,,1)<br /> (0)(1^(2,1),1,1)(2) = ()(,,1)(,2,,1)(,3,3,,1)(,2)<br /> (0)(1^(2,1),1,1)(2,1^(3,1),1) = ()(,,1)(,2,,1)(,3,3,,1)(,2)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,7,,6)<br /> (0)(1^(2,1),1,1)(2,1^(3,1),1,1) = ()(,,1)(,2,,1)(,3,3,,1)(,2)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,7,,6)(,10,10,,6)(,11,11,11,,6)<br /> (0)(1^(2,1),1,1)(2,2) = ()(,,1)(,2,,1)(,3,3,,1)(,2)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,7,7)<br /> (0)(1^(2,1),1,1)(2^(3)) = ()(,,1)(,2,,1)(,3,3,,1)(,2)(,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),1) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3)(4) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3)(4^(5,1),1) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3)(4^(5,1),3) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,5)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3)(4^(5,1),4) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3,3) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,6)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3^(4)) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1),3^(4,1)) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,9)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1^(5))) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,9)(,9,,9)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1^(5,1),1)) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,,9)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,1^(5,1),1,1)) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,,9)(,17,17,,9)(,18,18,18,,9)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,2)) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,10)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,2^(5,1),1)) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,10,,9)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3)) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4,3^(5,3)) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,23)(,23,23,23,23,,23)(,28,23,23,23,,23)(,29,22)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4,4) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,23)(,27,27)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4^(5,3),4) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,23)(,27,27,27,27,27,27)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4^(5,3),4^(5,3)) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,23)(,27,27,27,27,27,,27)(,28,27,27,27,27,,27)(,29,22)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4^(5,3)(5)) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,13)(,9,9)(,18,18,,18)(,19,19,19,,18)(,20,20,20,20,,18)(,19,19,19,,18)(,22,22,22,22)(,23,23,23,23,,23)(,24,23,23,23,,23)(,25,22)(,24,23,23,23,,23)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3))(4^(5,4)) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3),3) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7)(,1)(,9,,9)(,10,10,,9)(,11,11,11,,9)(,10,10,,9)(,13,13,13)(,14,14,14,,14)(,15,14,14,,14)(,16,14)(,15,14,14,,14)<br /> (0)(1^(2,1),1,1)(2^(3,1),1)(3^(4,3),3,3) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5)(,6,6,,6)(,7,7,7,,6)(,8,8,8,8,,6)(,7,7,7,,6)<br /> (0)(1^(2,1),1,1)(2^(3,1),1,1) = ()(,,1)(,2,,1)(,3,3,,1)(,2,,1)(,5,5,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),1,1)(3) = ()(,,1)(,2,,1)(,3,3,,1)(,3)<br /> (0)(1^(2,1),1,1)(2^(3,1),1,1)(3^(4,1),1,1) = ()(,,1)(,2,,1)(,3,3,,1)(,3,,1)(,5,5,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),2) = ()(,,1)(,2,,1)(,3,3,,1)(,3,3)<br /> (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,1),1) = ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,1),2) = ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,3)<br /> (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,1),3) = ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,5)<br /> (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,3)) = ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,5,,5)(,6,5,,5)(,7,5)<br /> (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,3),3)(4^(5,3),3) = ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,5,,5)(,6,6,6,,5)<br /> (0)(1^(2,1),1,1)(2^(3,1),2)(3^(4,3),3,3) = ()(,,1)(,2,,1)(,3,3,,1)(,3,3)(,5,5,,5)(,6,6,6,,5)(,7,7,7,7,,5)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1) = ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1) = ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,2,,1)(,3,3,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1)(4^(5,1),4,1) = ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,2,,1)(,3,3,,1)(,3,3,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1)(4^(5,1),4,1)(4) = ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1)(4^(5,1),4,1)(4^(6,1),1) = ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),1,1)(4^(5,1),4,1)(4^(6,1),1,1) = ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3,,1)(,6,6,,1)(,6,6,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),2) = ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3,3)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(2^(4,1),2,1) = ()(,,1)(,2,,1)(,3,3,,1)(,3,3,,1)(,3,3,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3) = ()(,,1)(,2,,1)(,3,3,,1)(,4)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,1^(4,1),1) = ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,,6)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,1^(4,1),1,1) = ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,,6)(,10,10,,6)(,11,11,11,,6)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2) = ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,7)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1) = ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,7,,6)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1,1) = ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,7,,6)(,10,10,10,,6)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1,1)(4^(5,1),4,1)(5,4) = ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1,1)(4^(5,1),4,1)(5,4^(6,1),1) = ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8,,6)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),1,1)(4^(5,1),4,1)(5,4^(6,1),1,1) = ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8,,6)(,10,10,10,,6)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),2) = ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8,8)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,2^(4,1),2,1) = ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,8,8,,6)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3,3) = ()(,,1)(,2,,1)(,3,3,,1)(,4)(,1)(,6,,6)(,7,7,,6)(,8,8,8,,6)(,9,9)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4)) = ()(,,1)(,2,,1)(,3,3,,1)(,4)(,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),1) = ()(,,1)(,2,,1)(,3,3,,1)(,4,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),1,1) = ()(,,1)(,2,,1)(,3,3,,1)(,4,,1)(,5,5,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),2) = ()(,,1)(,2,,1)(,3,3,,1)(,4,3)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),2,1) = ()(,,1)(,2,,1)(,3,3,,1)(,4,3,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),3) = ()(,,1)(,2,,1)(,3,3,,1)(,4,4)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,1)(3^(4,1),3,1) = ()(,,1)(,2,,1)(,3,3,,1)(,4,4,,1)<br /> (0)(1^(2,1),1,1)(2^(3,1),2,2) = ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)<br /> (0)(1^(2,1),1,1)(2^(3,2)) = ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)(,5,5,5,,5)(,6)(,1)(,8,,8)(,9,9,,8)(,10,10,10,,8)(,11,11,11,11)(,12,12,12,12,,12)(,13,12,12,12,,12)(,14,12)<br /> (0)(1^(2,1),1,1)(2^(3,2),2)(3^(4)) = ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)(,5,5,5,,5)(,6)(,,1)<br /> (0)(1^(2,1),1,1)(2^(3,2),2)(3^(4,2),2) = ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)(,5,5,5,,5)(,6,6,6,6,,5)<br /> (0)(1^(2,1),1,1)(2^(3,2),2,2) = ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4)(,5,5,5,,5)(,6,6,6,6,,5)(,7,7,7,7,7,,5)<br /> (0)(1^(2,1),1,1,1) = ()(,,1)(,2,,1)(,3,3,,1)(,4,4,4,,1)<br /> (0)(1^(2,1),1^(2)) = ()(,,1)(,,2)<br /> (0)(1^(2,1),1^(2))(2) = ()(,,1)(,,2)(,2)<br /> (0)(1^(2,1),1^(2))(2,1) = ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,5)<br /> (0)(1^(2,1),1^(2))(2,1^(3,1))(3^(4,3),3^(4)) = ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,5)(,8,8,,8)(,9,9,,9)<br /> (0)(1^(2,1),1^(2))(2,1^(3,1),1) = ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,,5)<br /> (0)(1^(2,1),1^(2))(2,1^(3,1),1^(3)) = ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,,5)(,8,,8)<br /> (0)(1^(2,1),1^(2))(2,2) = ()(,,1)(,,2)(,2)(,1)(,5,,5)(,6,,6)(,6,6)<br /> (0)(1^(2,1),1^(2))(2^(3)) = ()(,,1)(,,2)(,2)(,,1)<br /> (0)(1^(2,1),1^(2))(2^(3,1),1) = ()(,,1)(,,2)(,2,,1)<br /> (0)(1^(2,1),1^(2))(2^(3,1),1,1) = ()(,,1)(,,2)(,2,,1)(,4,4,,1)<br /> (0)(1^(2,1),1^(2))(2^(3,1),1^(3)) = ()(,,1)(,,2)(,2,,1)(,4,,4)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2) = ()(,,1)(,,2)(,2,,1)(,4,,4)(,4,4)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2,1) = ()(,,1)(,,2)(,2,,1)(,4,,4)(,4,4,,1)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2,1^(3)) = ()(,,1)(,,2)(,2,,1)(,4,,4)(,4,4,,1)(,6,6,,6)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2,2) = ()(,,1)(,,2)(,2,,1)(,4,,4)(,4,4,,1)(,6,6,,6)(,6,6,6)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2^(3)) = ()(,,1)(,,2)(,,2)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3) = ()(,,1)(,,2)(,3)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,5)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,1^(4,1),1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,5)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,1^(4,1),1^(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,5)(,8,,8)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,1^(4,1),1^(4))(4^(5,1),4^(5)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,5)(,8,,8)(,8,,8)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,5,,5)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1))(1^(5,1),1^(5)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,5,,5)(,9,,9)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,6,,5)(,9,9,,9)(,10,9,,5)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),1^(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,6,,5)(,9,9,,9)(,10,9,,5)(,11,11,,11)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),2) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,6,,5)(,9,9,,9)(,10,9,9)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),2,2) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,6,,5)(,9,9,,9)(,10,9,9)(,9,9,9,,5)(,12,12,12,,12)(,13,12,12,12)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3,2^(4,1),2^(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,6,,6)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2^(3))(3^(4,1),3^(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8)(,6,,6)<br /> (0)(1^(2,1),1^(2))(2^(3,1),2^(3),2) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,8)<br /> (0)(1^(2,1),1^(2))(2^(3,2)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,8,,8)(,10,6)<br /> (0)(1^(2,1),1^(2))(2^(3,2),2) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,8,,8)(,10,8)(,9,8,,8)<br /> (0)(1^(2,1),1^(2))(2^(3,2),2,2) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,9,9,,8)(,10,10,10,10,,8)<br /> (0)(1^(2,1),1^(2))(2^(3,2),2^(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,9,,9)<br /> (0)(1^(2,1),1^(2))(2^(3,2),2^(3))(3^(4,3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,9,,9)(,10,9,9)(,11,11,11,,11)(,12,11,11,,11)(,13,9)<br /> (0)(1^(2,1),1^(2))(2^(3,2),2^(3))(3^(4,3),3^(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6)(,8,8,,8)(,9,9,,9)(,10,9,9)(,11,11,11,,11)(,12,12,12,,12)<br /> (0)(1^(2,1),1^(2),1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(9)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3,2^(4,1),2^(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,6,,6)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,1),3^(4),3) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,10)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,2)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,,10)(,11,10,,10)(,12,6)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,,10)(,11,10,,10)(,12,10)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,3),3^(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,,10)(,11,11,,11)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3))(3^(4,3),3^(4),3) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6)(,10,10,,10)(,11,11,,11)(,12,11,11,,10)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,6,,6)(,9,6,,5)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,7)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,7,5)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,2) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,7,6)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,2^(4,1),2^(4),1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,7,6,,5)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,2^(4,1),2^(4),1)(4) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3,3) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3^(4,1),3^(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8)(,6,,6)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),1)(3^(4,1),3^(4),1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,5)<br /> (0)(1^(2,1),1^(2),1)(2^(3,1),2^(3),2) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8)<br /> (0)(1^(2,1),1^(2),1)(2^(3,2)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8)(,9,9,9,,9)(,10,9,9,,9)(,11,6)<br /> (0)(1^(2,1),1^(2),1)(2^(3,2),2^(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8)(,9,9,9,,9)(,10,10,10,,10)<br /> (0)(1^(2,1),1^(2),1)(2^(3,2),2^(3),2) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8)(,9,9,9,,9)(,10,10,10,,10)(,11,10,10,10,,9)<br /> (0)(1^(2,1),1^(2),1,1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,8,,5)<br /> (0)(1^(2,1),1^(2),1^(2)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)<br /> (0)(1^(2,1),1^(2),1^(2))(2) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6)<br /> (0)(1^(2,1),1^(2),1^(2))(2,1^(3,1),1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,5)<br /> (0)(1^(2,1),1^(2),1^(2))(2,1^(3,1),1^(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,5)(,10,,10)<br /> (0)(1^(2,1),1^(2),1^(2))(2,1^(3,1),1^(3),1^(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,5)(,10,,10)(,11,10,,5)(,12,12,,12)<br /> (0)(1^(2,1),1^(2),1^(2))(2,2) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,6)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,6,,5)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3,2^(4,1),2^(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,6,,6)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3^(4,1),3^(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,11,11)(,6,,6)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3^(4,3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,11,11,,11)(,12,11,,11)(,13,11)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3^(4,3),3^(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,11,11,,11)(,12,12,,12)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3))(3^(4,3),3^(4),3^(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6)(,11,11,,11)(,12,12,,12)(,13,12,12,,11)(,14,14,14,,14)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6,,5)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,6,,6)(,10,6,,5)(,11,11,,11)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,7)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3,2^(4,1),2^(4),1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,7,6,,5)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3,2^(4,1),2^(4),1^(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,7,6,,5)(,10,10,,10)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3,2^(4,1),2^(4),1^(4))(4) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3,3) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8)(,6,,6)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4))(2^(5,1),2^(5),1^(5)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8)(,6,,6)(,11,6,,5)(,12,12,,12)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4))(2^(5,1),2^(5),1^(5))(5^(6,1),5^(6)) = <br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4))(4^(5,4),4^(5),4^(5)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8)(,10,10,,10)(,11,11,,11)(,12,11,11,,10)(,13,13,13,,13)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4),1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,,5)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),1^(3))(3^(4,1),3^(4),1^(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,,5)(,10,10,,10)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,8)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2,1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,8,,5)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2,1^(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,8,,5)(,10,10,10,,10)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2,2) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,8,,5)(,10,10,10,,10)(,10,10,10,10)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,1),2^(3),2^(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,8,8,,8)<br /> (0)(1^(2,1),1^(2),1^(2))(2^(3,2),2^(3),2^(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,9,8)(,10,10,,10)(,11,11,,11)(,12,11,11,,10)(,13,13,13,,13)<br /> (0)(1^(2,1),1^(2),1^(2),1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,6,,5)(,8,8,,8)(,9,8,,5)<br /> (0)(1^(2,1),1^(2)(2)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)<br /> (0)(1^(2,1),1^(2,1)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(8,5)<br /> (0)(1^(2,1),1^(2,1))(2) = <br /> (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3))(3) = <br /> (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3),2^(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,11,11,,11)(,15,11,11,,10)(,16,16,16,,16)(,17,16,16,,16)(,18,10)(,16,16,16,,16)<br /> (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,11,11,,11)(,15,11,,11)(,16,5)<br /> (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1))(3) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12)<br /> (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1))(3,2^(4,1),2^(4,1)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,11,11,,11)(,16,11,,11)(,17,10)<br /> (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1))(3,3) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15)<br /> (0)(1^(2,1),1^(2,1))(2^(3,1),2^(3,1),2) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,15)<br /> (0)(1^(2,1),1^(2,1))(2^(3,2)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,,15)(,16,15,15,,15)(,17,15)<br /> (0)(1^(2,1),1^(2,1))(2^(3,2),2^(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,,15)(,16,16,16,,16)<br /> (0)(1^(2,1),1^(2,1))(2^(3,2),2^(3,1)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,,15)(,16,16,16,,16)(,17,16,16,,16)(,18,5)<br /> (0)(1^(2,1),1^(2,1))(2^(3,2),2^(3,2)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11)(,15,15,15,,15)(,16,16,16,,16)(,17,16,16,,16)(,18,15)<br /> (0)(1^(2,1),1^(2,1),1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11,,10)<br /> (0)(1^(2,1),1^(2,1),1^(2,1)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,11,,10)(,15,15,15,,15)(,16,15,15,,15)(,17,10)<br /> (0)(1^(2,1)(2)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,,11)<br /> (0)(1^(2,1)(2,1)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,12,11,,11)(,15,10)<br /> (0)(1^(2,1)(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,13)<br /> (0)(1^(2,1)(3,1)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,13,5)<br /> (0)(1^(2,1)(3,3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,14,14)<br /> (0)(1^(2,1)(3^(4))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,14,14,,14)<br /> (0)(1^(2,1)(3^(4,3))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10)(,14,14,,14)(,15,15,,15)(,16,15,,15)(,17,14)<br /> (0)(1^(2,1,1)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,5)(,10,10,,10)(,11,11,,11)(,12,11,,11)(,13,10,10)<br /> (0)(1^(2,1^(3))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)<br /> (0)(1^(2,1^(3,1))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)<br /> (0)(1^(2,1^(3,1)))(1^(3,1),1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,13,13,,13)(,18,13,,13)(,19,13)(,18,13,,13)<br /> (0)(1^(2,1^(3,1)))(2) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,14)<br /> (0)(1^(2,1^(3,1)))(2^(3,1^(4,1))) = <br /> (0)(1^(2,1^(3,1)))(2^(3,1^(4,1)))(3) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,15)<br /> (0)(1^(2,1^(3,1)),1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,15,14,14,,13)<br /> (0)(1^(2,1^(3,1))(2)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,15,14,,14)<br /> (0)(1^(2,1^(3,1))(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13)(,16)<br /> (0)(1^(2,1^(3,1))(3,1,1)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13,13)<br /> (0)(1^(2,1^(3,1))(3,1^(4))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13,13)(,13,13,,13)<br /> (0)(1^(2,1^(3,1))(3,1^(4,1))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,5)(,13,13,,13)(,14,14,,14)(,15,14,,14)(,16,13,13)(,13,13,,13)(,18,13,,13)(,19,5)<br /> (0)(1^(2,1^(3,1))(3,1^(4,1)))(1^(3,1),1) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,5,,5)(,10,,5)(,11,5)(,10,,5)<br /> (0)(1^(2,1^(3,1))(3,1^(4,1)))(2,1^(3,1),1) = <br /> (0)(1^(2,1^(3,1))(3,1^(4,1))(2)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,7,,6)<br /> (0)(1^(2,1^(3,1))(3,1^(4,1))(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,8)<br /> (0)(1^(2,1^(3,1))(3,1^(4,1))(4)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,9)<br /> (0)(1^(2,1^(3,1))(3,3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,9,9)<br /> (0)(1^(2,1^(3,1))(3^(4,3))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,9,9,,9)(,10,9,,9)(,11,9)<br /> (0)(1^(2,1^(3,1))(3^(4,3^(5,3)))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,5)(,9,9,,9)(,10,10,,10)(,11,10,,10)(,12,9)<br /> (0)(1^(2,1^(3,1),1)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)<br /> (0)(1^(2,1^(3,1),1^(3))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)(,9,,9)<br /> (0)(1^(2,1^(3,1),1^(3,1))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)(,9,,9)(,10,,9)(,11,5)<br /> (0)(1^(2,1^(3,1^(4)))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)(,9,,9)(,10,,9)(,11,5)(,5,,5)<br /> (0)(1^(2,1^(3,1^(4,1)))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,5)(,9,,9)(,10,,9)(,11,5)(,5,,5)(,13,,5)(,14,5)<br /> (0)(1^(2,2)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)<br /> (0)(1^(2^(3))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,5,,5)<br /> (0)(1^(2^(3,1))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,5,,5)(,10,,5)(,11,5)<br /> (0)(1^(2^(3,1))(2^(4))) = <br /> (0)(1^(2^(3,1),1)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,6,6,,5)(,10,10,,10)(,11,10,,10)(,12,10,,5)<br /> (0)(1^(2^(3,1),2^(3))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,6,,6)<br /> (0)(1^(2^(3,2))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,6,,6)(,10,,6)(,11,6)<br /> (0)(1^(2^(3,2))(2)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,7,,6)<br /> (0)(1^(2^(3,2))(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,8)<br /> (0)(1^(2^(3,2))(3,1)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,8,5)<br /> (0)(1^(2^(3,2))(3,2)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,8,6)<br /> (0)(1^(2^(3,2))(3,2^(4,2))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,8,6)(,6,,6)(,11,,6)(,12,6)<br /> (0)(1^(2^(3,2))(3,3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6)(,9,9)<br /> (0)(1^(2^(3,2),1)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)<br /> (0)(1^(2^(3,2),1)(3,3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9)<br /> (0)(1^(2^(3,2),1)(3^(4,2),3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,9)<br /> (0)(1^(2^(3,2),1)(3^(4,2),3,3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,9)(,10,10,10,10)<br /> (0)(1^(2^(3,2),1,1)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,9,,5)<br /> (0)(1^(2^(3,2),1^(3))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,,9)<br /> (0)(1^(2^(3,2),1^(3^(4,3),1))) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,6,,5)(,9,9,,9)(,10,9,,9)(,11,9,9,,5)<br /> (0)(1^(2^(3,2),2)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,6)<br /> (0)(1^(2^(3,2),2)(3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,6)(,8)<br /> (0)(1^(2^(3,2),2)(3,2^(4,2),1)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,6)(,8,6,,5)<br /> (0)(1^(2^(3,2),2)(3,2^(4,2),2)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,,6)(,8,,6)(,8,,6)<br /> (0)(1^(2^(3,2),2)(3,3)) = ()(,,1)(,,2)(,3)(,1)(,5,,5)(,6,,6)(,7,7)<br /> (0)(1^(2^(3,2),2)(3^(4))) = ()(,,1)(,,2)(,3)(,,1)<br /> (0)(1^(2^(3,2),2)(3^(4,1),3^(4))) = ()(,,1)(,,2)(,3)(,,2)<br /> (0)(1^(2^(3,2),2)(3^(4,2))) = ()(,,1)(,,2)(,3)(,,2)(,5)(,1)(,7,,7)(,8,,8)(,9,9)(,8,,8)(,11,,8)(,12,8)<br /> (0)(1^(2^(3,2),2)(3^(4,2),1)) = ()(,,1)(,,2)(,3,,1)<br /> (0)(1^(2^(3,2),2)(3^(4,2),2)) = ()(,,1)(,,2)(,3,,2)<br /> (0)(1^(2^(3,2),2)(3^(4,2),3)) = ()(,,1)(,,2)(,3,,2)(,4,4)<br /> (0)(1^(2^(3,2),2)(3^(4,2),3^(4))) = <br /> (0)(1^(2^(3,2),2,1)) = ()(,,1)(,,2)(,3,,2)(,4,4,,1)<br /> (0)(1^(2^(3,2),2,2)) = ()(,,1)(,,2)(,3,,2)(,4,4,,2)<br /> (0)(1^(2^(3,2),2^(3))) = ()(,,1)(,,2)(,,3)<br /> (0)(1^(2^(3^(4)))) = ()(,,1)(,,2)(,,3)(,4)(,1)(,6,,6)(,7,,7)(,8,,8)(,9,,8)(,10,8)(,6,,6)<br /> Limit = ()(,,1)(,,2,2)<br /> [[分类:分析]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=%E8%B6%85%E5%88%9D%E7%AD%89%E5%BA%8F%E5%88%97&diff=3669 2026-08-08T15:03:44Z

<p>0100000000a7：​</p> <hr /> <div>'''超初等序列(Hyper Primitive Sequence System, HPrSS)'''，是一种[[Beklemishev's Worm|Worm]]型序数记号，它是[[初等序列系统|PrSS]]的一种扩展。<br /> <br /> == 定义 ==<br /> <br /> === 合法表达式 ===<br /> 一个合法的 HPrSS 表达式是以 1 开头的正整数序列，即形如<br /> <br /> &lt;math&gt;(a_1,a_2,\cdots,a_n)\quad(n,a_1,a_2,\cdots,a_n\in\N,a_1=1)&lt;/math&gt;<br /> <br /> 的序列。<br /> <br /> 例如：&lt;math&gt;(1,4,6,4)&lt;/math&gt;和&lt;math&gt;(1,1,4,5,1,4)&lt;/math&gt;都是合法的 HPrSS 表达式，而&lt;math&gt;(1,2,\pi)&lt;/math&gt;不是。<br /> <br /> === 结构 ===<br /> HPrSS的合法式可分为'''零表达式'''、'''后继表达式'''和'''极限表达式'''。<br /> <br /> * '''零表达式'''指&lt;math&gt;n=0&lt;/math&gt;的表达式，即空序列；<br /> * '''后继表达式'''指&lt;math&gt;n&gt;0,a_n=1&lt;/math&gt;的表达式，即末项为1的非空序列；<br /> * '''极限表达式'''指&lt;math&gt;n&gt;0,a_n&gt;1&lt;/math&gt;的表达式，末项不为1的非空序列。<br /> <br /> 对于 HPrSS 的一个极限表达式&lt;math&gt;(a_1,a_2,\cdots,a_n)&lt;/math&gt;，定义以下术语：<br /> <br /> ==== 父项 ====<br /> 对于&lt;math&gt;m\in\{1,2,\cdots,n\}&lt;/math&gt;，记&lt;math&gt;p_m=\max\{1\le p_m&lt;m\mid a_{p_m}&lt;a_m\}&lt;/math&gt;，若这样的&lt;math&gt;p_m&lt;/math&gt;存在，则称&lt;math&gt;a_{p_m}&lt;/math&gt;为&lt;math&gt;a_m&lt;/math&gt;的'''父项'''。<br /> <br /> 如果这样的&lt;math&gt;p_m&lt;/math&gt;不存在，我们也可以把&lt;math&gt;a_m&lt;/math&gt;的父项定义为一个虚构的“第0项”，其值为&lt;math&gt;a_0=0&lt;/math&gt;。<br /> <br /> 通俗的说，&lt;math&gt;a_m&lt;/math&gt;的父项是在&lt;math&gt;a_m&lt;/math&gt;左边、最靠右的、且小于&lt;math&gt;a_m&lt;/math&gt;的项。<br /> <br /> 例如，在&lt;math&gt;(1,3,5,4,1,3)&lt;/math&gt;中，4的父项是第一个3，而第二个1没有父项。<br /> <br /> ==== 祖先 ====<br /> 对于&lt;math&gt;m\in\{1,2,\cdots,n\}&lt;/math&gt;，记&lt;math&gt;m_0=m&lt;/math&gt;，&lt;math&gt;m_{i+1}=p_{m_i}&lt;/math&gt;，&lt;math&gt;P_m=\{m_i\mid i\ge 0\}&lt;/math&gt;我们将&lt;math&gt;a_m&lt;/math&gt;的'''祖先'''定义为所有&lt;math&gt;a_p(p\in P_m)&lt;/math&gt;。<br /> <br /> 通俗地说，某一项的祖先是它本身、它的父项、父项的父项、父项的父项的父项……中的某一项。<br /> <br /> 例如，&lt;math&gt;({\color{red}1},{\color{red}4},6,7,{\color{red}6},{\color{red}7})&lt;/math&gt;中，末项7的祖先是所有红色的项。<br /> <br /> ==== 阶差 ====<br /> 对于&lt;math&gt;m\in\{1,2,\cdots,n\}&lt;/math&gt;，若&lt;math&gt;a_m&lt;/math&gt;的父项是&lt;math&gt;a_{p_m}&lt;/math&gt;，则定义&lt;math&gt;a_m&lt;/math&gt;的'''阶差'''为&lt;math&gt;d_m=a_m-a_{p_m}&lt;/math&gt;;若没有父项，则定义&lt;math&gt;a_m&lt;/math&gt;的阶差为&lt;math&gt;d_m=a_m&lt;/math&gt;。<br /> <br /> 由父项的定义可知，阶差一定是正整数。<br /> <br /> ==== 阶差序列 ====<br /> 设&lt;math&gt;a_m&lt;/math&gt;的阶差为&lt;math&gt;d_m&lt;/math&gt;，我们把&lt;math&gt;(d_1,d_2,\cdots,d_n)&lt;/math&gt;称为&lt;math&gt;(a_1,a_2,\cdots,a_n)&lt;/math&gt;的'''阶差序列'''。<br /> <br /> ==== 坏根 ====<br /> 给定极限表达式&lt;math&gt;(a_1,a_2,\cdots,a_n)&lt;/math&gt;，其末项的阶差为&lt;math&gt;d_n&lt;/math&gt;。我们记序列的'''坏根'''为&lt;math&gt;a_r&lt;/math&gt;，其中&lt;math&gt;r&lt;/math&gt;定义如下：<br /> <br /> * 若&lt;math&gt;d_n=1&lt;/math&gt;，则&lt;math&gt;r=p_n&lt;/math&gt;，即序列的坏根定义末项的父项；<br /> <br /> * 若&lt;math&gt;d_n\ge 1&lt;/math&gt;，则&lt;math&gt;r=\max\{k\in P_n|d_k&lt;d_n\}&lt;/math&gt;。通俗地说，序列的坏根为末项的祖先中，最靠右的，且阶差小于末项阶差的项。<br /> <br /> ==== 序列的阶差 ====<br /> 序列的'''阶差'''定义为&lt;math&gt;\delta=a_n-a_r-1&lt;/math&gt;，这一点和 [[长初等序列|LPrSS]] 一致。<br /> <br /> ==== 坏部&amp;好部 ====<br /> 坏部、好部的定义和 PrSS 一致：坏部&lt;math&gt;B=(a_r,a_{r+1},\cdots,a_{n-1})&lt;/math&gt;，好部&lt;math&gt;G=(a_1,a_2,\cdots,a_{r-1})&lt;/math&gt;。<br /> <br /> == 展开 ==<br /> 对于一个合法的 HPrSS 表达式&lt;math&gt;S=(a_1,a_2,\cdots,a_n)&lt;/math&gt;，其展开规则如下：<br /> <br /> * 若&lt;math&gt;S&lt;/math&gt;为零表达式，则&lt;math&gt;S&lt;/math&gt;代表序数0；<br /> * 若&lt;math&gt;S&lt;/math&gt;为后继表达式，则其前驱是'''&lt;math&gt;S'=(a_1,a_2,\cdots,a_{n-1})&lt;/math&gt;'''；<br /> * 若&lt;math&gt;S&lt;/math&gt;为极限表达式，根据前文定义确定坏根、阶差、好部、坏部；记&lt;math&gt;B_t=(a_r+t\delta,a_{r+1}+t\delta,\cdots,a_{n-1}+t\delta)&lt;/math&gt;，它可以看成坏部的每一项加上阶差的t倍，则其基本列的第&lt;math&gt;m&lt;/math&gt;项为&lt;math&gt;S[m]=(G,B,B_1,B_2,\cdots,B_m)&lt;/math&gt;。或者说，&lt;math&gt;S&lt;/math&gt;的展开式为&lt;math&gt;(G,B,B_1,B_2,\cdots)&lt;/math&gt;。<br /> <br /> === 举例 ===<br /> 考虑 HPrSS 表达式&lt;math&gt;(1,4,6,6)&lt;/math&gt;。<br /> <br /> 首先，找出末项6的所有祖先项，用红色表示：&lt;math&gt;({\color{red}1},{\color{red}4},6,{\color{red}6})&lt;/math&gt;。<br /> <br /> 其次，计算出阶差序列，为&lt;math&gt;(1,3,2,2)&lt;/math&gt;。<br /> <br /> 然后，我们从末项的祖先项中，找到最右边的阶差小于2的项。这里4的阶差为3，我们跳过它，故坏根是首项1。<br /> <br /> 根据末项和坏根，我们得到了好部&lt;math&gt;G=()&lt;/math&gt;，坏部&lt;math&gt;B=(1,4,6)&lt;/math&gt;，阶差&lt;math&gt;\delta=6-1-1=4&lt;/math&gt;。<br /> <br /> 根据坏部和阶差，我们可以求出&lt;math&gt;B_1=(5,8,10)&lt;/math&gt;，&lt;math&gt;B_2=(9,12,14)&lt;/math&gt;，等等。<br /> <br /> 最后，我们得到了展开式&lt;math&gt;(1,4,6,6)=(1,4,6,5,8,10,9,12,14,\cdots)&lt;/math&gt;。<br /> <br /> 可以将其和 [[长初等序列#举例|LPrSS 中相同表达式的展开]]进行对比。<br /> <br /> == 与 PSS Hydra 的对应 ==<br /> HPrSS可以和[[PSS Hydra]]存在直接的转换关系，下面介绍互译算法。<br /> <br /> 说明：算法中出现的所有“序列”均指正整数序列，不需要为HPrSS的合法式。<br /> <br /> === HPrSS到PSS Hydra ===<br /> 给定一个HPrSS表达式&lt;math&gt;S=(a_1,a_2,\cdots,a_n)&lt;/math&gt;，设其对应的PSS Hydra表达式为&lt;math&gt;PH(S)&lt;/math&gt;。则：<br /> <br /> * 如果&lt;math&gt;S&lt;/math&gt;为空序列，则&lt;math&gt;PH(S)=0&lt;/math&gt;。<br /> * 否则，记&lt;math&gt;x_1=1&lt;/math&gt;，&lt;math&gt;x_{n+1}=\min\{k&gt;x_n\mid a_k\le a_{x_n}\}&lt;/math&gt;，即&lt;math&gt;a_{x_{n+1}}&lt;/math&gt;是&lt;math&gt;a_{x_n}&lt;/math&gt;右边第一个小于等于&lt;math&gt;a_{x_n}&lt;/math&gt;的项。这样&lt;math&gt;S&lt;/math&gt;就可以写成&lt;math&gt;(a_{x_1},S_1,a_{x_2},S_2,\cdots,a_{x_k},S_k)&lt;/math&gt;，由&lt;math&gt;a_{x_{n+1}}&lt;/math&gt;的定义可知&lt;math&gt;S_i&lt;/math&gt;中的每一项均大于&lt;math&gt;a_{x_n}&lt;/math&gt;。<br /> * 我们有&lt;math&gt;PH(S)=\psi^H_{a_{x_1}}(PH(S_1-a_{x_1}))+\psi^H_{a_{x_2}}(PH(S_2-a_{x_2}))+\cdots+\psi^H_{a_{x_k}}(PH(S_k-a_{x_k}))&lt;/math&gt;，其中&lt;math&gt;S-a&lt;/math&gt;为将&lt;math&gt;S&lt;/math&gt;的每一项都减去&lt;math&gt;a&lt;/math&gt;得到的序列。<br /> <br /> 例如，考虑HPrSS表达式&lt;math&gt;(1,4,7,6,3,5,7)&lt;/math&gt;<br /> <br /> 进行第二步，得到&lt;math&gt;k=1,x_1=1&lt;/math&gt;，故&lt;math&gt;({\color{red}1},4,7,6,3,5,7)=\psi^H_1((3,6,5,2,4,6))&lt;/math&gt;<br /> <br /> 对&lt;math&gt;(3,6,5,2,4,6)&lt;/math&gt;进行第二步，得到&lt;math&gt;k=2,x_1=1,x_2=4&lt;/math&gt;，故&lt;math&gt;({\color{red}3},6,5,{\color{red}2},4,6)=\psi^H_3((3,2))+\psi^H_2((2,4))&lt;/math&gt;<br /> <br /> 分别计算&lt;math&gt;(3,2)&lt;/math&gt;和&lt;math&gt;(2,4)&lt;/math&gt;对应的PSS Hydra，得到&lt;math&gt;(3,2)=\psi^H_3(0)+\psi^H_2(0)&lt;/math&gt;，&lt;math&gt;(2,4)=\psi^H_2(\psi^H_2(0))&lt;/math&gt;<br /> <br /> 综上，我们得到了&lt;math&gt;(1,4,7,6,3,5,7)=\psi^H_1(\psi^H_3(\psi^H_3(0)+\psi^H_2(0))+\psi^H_2(\psi^H_2(\psi^H_2(0)))&lt;/math&gt;<br /> <br /> === PSS Hydra到HPrSS ===<br /> 给定一个PSS Hydra表达式&lt;math&gt;H&lt;/math&gt;，设其对应的HPrSS表达式为&lt;math&gt;LP(H)&lt;/math&gt;。则：<br /> <br /> * 如果&lt;math&gt;H=0&lt;/math&gt;，则&lt;math&gt;LP(H)&lt;/math&gt;为空序列。<br /> * &lt;math&gt;LP(H_1+H_2)=(LP(H_1),LP(H_2))&lt;/math&gt;，其中&lt;math&gt;(S_1,S_2)&lt;/math&gt;为两个序列的拼接。<br /> * &lt;math&gt;LP(\psi^H_x(H))=(x,(LP(H)+x))&lt;/math&gt;。<br /> {{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=%E8%B6%85%E5%88%9D%E7%AD%89%E5%BA%8F%E5%88%97&diff=3627 2026-08-02T06:24:37Z

<p>0100000000a7：​</p> <hr /> <div>'''超初等序列(Hyper Primitive Sequence System, HPrSS)'''，是一种[[Beklemishev's Worm|Worm]]型序数记号，它是[[初等序列系统|PrSS]]的一种扩展。<br /> <br /> == 定义 ==<br /> <br /> === 合法表达式 ===<br /> 一个合法的 HPrSS 表达式是以 1 开头的正整数序列，即形如<br /> <br /> &lt;math&gt;(a_1,a_2,\cdots,a_n)\quad(n,a_1,a_2,\cdots,a_n\in\N,a_1=1)&lt;/math&gt;<br /> <br /> 的序列。<br /> <br /> 例如：&lt;math&gt;(1,4,6,4)&lt;/math&gt;和&lt;math&gt;(1,1,4,5,1,4)&lt;/math&gt;都是合法的 HPrSS 表达式，而&lt;math&gt;(1,2,\pi)&lt;/math&gt;不是。<br /> <br /> === 结构 ===<br /> HPrSS的合法式可分为'''零表达式'''、'''后继表达式'''和'''极限表达式'''。<br /> <br /> * '''零表达式'''指&lt;math&gt;n=0&lt;/math&gt;的表达式，即空序列；<br /> * '''后继表达式'''指&lt;math&gt;n&gt;0,a_n=1&lt;/math&gt;的表达式，即末项为1的非空序列；<br /> * '''极限表达式'''指&lt;math&gt;n&gt;0,a_n&gt;1&lt;/math&gt;的表达式，末项不为1的非空序列。<br /> <br /> 对于 HPrSS 的一个极限表达式&lt;math&gt;(a_1,a_2,\cdots,a_n)&lt;/math&gt;，定义以下术语：<br /> <br /> ==== 父项 ====<br /> 对于&lt;math&gt;m\in\{1,2,\cdots,n\}&lt;/math&gt;，记&lt;math&gt;p_m=\max\{1\le p_m&lt;m\mid a_{p_m}&lt;a_m\}&lt;/math&gt;，若这样的&lt;math&gt;p_m&lt;/math&gt;存在，则称&lt;math&gt;a_{p_m}&lt;/math&gt;为&lt;math&gt;a_m&lt;/math&gt;的'''父项'''。<br /> <br /> 如果这样的&lt;math&gt;p_m&lt;/math&gt;不存在，我们也可以把&lt;math&gt;a_m&lt;/math&gt;的父项定义为一个虚构的“第0项”，其值为&lt;math&gt;a_0=0&lt;/math&gt;。<br /> <br /> 通俗的说，&lt;math&gt;a_m&lt;/math&gt;的父项是在&lt;math&gt;a_m&lt;/math&gt;左边、最靠右的、且小于&lt;math&gt;a_m&lt;/math&gt;的项。<br /> <br /> 例如，在&lt;math&gt;(1,3,5,4,1,3)&lt;/math&gt;中，4的父项是第一个3，而第二个1没有父项。<br /> <br /> ==== 祖先 ====<br /> 对于&lt;math&gt;m\in\{1,2,\cdots,n\}&lt;/math&gt;，记&lt;math&gt;m_0=m&lt;/math&gt;，&lt;math&gt;m_{i+1}=p_{m_i}&lt;/math&gt;，&lt;math&gt;P_m=\{m_i\mid i\ge 0\}&lt;/math&gt;我们将&lt;math&gt;a_m&lt;/math&gt;的'''祖先'''定义为所有&lt;math&gt;a_p(p\in P_m)&lt;/math&gt;。<br /> <br /> 通俗地说，某一项的祖先是它本身、它的父项、父项的父项、父项的父项的父项……中的某一项。<br /> <br /> 例如，&lt;math&gt;({\color{red}1},{\color{red}4},6,7,{\color{red}6},{\color{red}7})&lt;/math&gt;中，末项7的祖先是所有红色的项。<br /> <br /> ==== 阶差 ====<br /> 对于&lt;math&gt;m\in\{1,2,\cdots,n\}&lt;/math&gt;，若&lt;math&gt;a_m&lt;/math&gt;的父项是&lt;math&gt;a_{p_m}&lt;/math&gt;，则定义&lt;math&gt;a_m&lt;/math&gt;的'''阶差'''为&lt;math&gt;d_m=a_m-a_{p_m}&lt;/math&gt;;若没有父项，则定义&lt;math&gt;a_m&lt;/math&gt;的阶差为&lt;math&gt;d_m=a_m&lt;/math&gt;。<br /> <br /> 由父项的定义可知，阶差一定是正整数。<br /> <br /> ==== 阶差序列 ====<br /> 设&lt;math&gt;a_m&lt;/math&gt;的阶差为&lt;math&gt;d_m&lt;/math&gt;，我们把&lt;math&gt;(d_1,d_2,\cdots,d_n)&lt;/math&gt;称为&lt;math&gt;(a_1,a_2,\cdots,a_n)&lt;/math&gt;的'''阶差序列'''。<br /> <br /> ==== 坏根 ====<br /> 给定极限表达式&lt;math&gt;(a_1,a_2,\cdots,a_n)&lt;/math&gt;，其末项的阶差为&lt;math&gt;d_n&lt;/math&gt;。我们记序列的'''坏根'''为&lt;math&gt;a_r&lt;/math&gt;，其中&lt;math&gt;r&lt;/math&gt;定义如下：<br /> <br /> * 若&lt;math&gt;d_n=1&lt;/math&gt;，则&lt;math&gt;r=p_n&lt;/math&gt;，即序列的坏根定义末项的父项；<br /> <br /> * 若&lt;math&gt;d_n\ge 1&lt;/math&gt;，则&lt;math&gt;r=\max\{k\in P_n|d_k&lt;d_n\}&lt;/math&gt;。通俗地说，序列的坏根为末项的祖先中，最靠右的，且阶差小于末项阶差的项。<br /> <br /> ==== 序列的阶差 ====<br /> 序列的'''阶差'''定义为&lt;math&gt;\delta=a_n-a_r-1&lt;/math&gt;，这一点和 [[长初等序列|LPrSS]] 一致。<br /> <br /> ==== 坏部&amp;好部 ====<br /> 坏部、好部的定义和 PrSS 一致：坏部&lt;math&gt;B=(a_r,a_{r+1},\cdots,a_{n-1})&lt;/math&gt;，好部&lt;math&gt;G=(a_1,a_2,\cdots,a_{r-1})&lt;/math&gt;。<br /> <br /> == 展开 ==<br /> 对于一个合法的 HPrSS 表达式&lt;math&gt;S=(a_1,a_2,\cdots,a_n)&lt;/math&gt;，其展开规则如下：<br /> <br /> * 若&lt;math&gt;S&lt;/math&gt;为零表达式，则&lt;math&gt;S&lt;/math&gt;代表序数0；<br /> * 若&lt;math&gt;S&lt;/math&gt;为后继表达式，则其前驱是'''&lt;math&gt;S'=(a_1,a_2,\cdots,a_{n-1})&lt;/math&gt;'''；<br /> * 若&lt;math&gt;S&lt;/math&gt;为极限表达式，根据前文定义确定坏根、阶差、好部、坏部；记&lt;math&gt;B_t=(a_r+t\delta,a_{r+1}+t\delta,\cdots,a_{n-1}+t\delta)&lt;/math&gt;，它可以看成坏部的每一项加上阶差的t倍，则其基本列的第&lt;math&gt;m&lt;/math&gt;项为&lt;math&gt;S[m]=(G,B,B_1,B_2,\cdots,B_m)&lt;/math&gt;。或者说，&lt;math&gt;S&lt;/math&gt;的展开式为&lt;math&gt;(G,B,B_1,B_2,\cdots)&lt;/math&gt;。<br /> <br /> === 举例 ===<br /> 考虑 HPrSS 表达式&lt;math&gt;(1,4,6,6)&lt;/math&gt;。<br /> <br /> 首先，找出末项6的所有祖先项，用红色表示：&lt;math&gt;({\color{red}1},{\color{red}4},6,{\color{red}6})&lt;/math&gt;。<br /> <br /> 其次，计算出阶差序列，为&lt;math&gt;(1,3,2,2)&lt;/math&gt;。<br /> <br /> 然后，我们从末项的祖先项中，找到最右边的阶差小于2的项。这里4的阶差为3，我们跳过它，故坏根是首项1。<br /> <br /> 根据末项和坏根，我们得到了好部&lt;math&gt;G=()&lt;/math&gt;，坏部&lt;math&gt;B=(1,4,6)&lt;/math&gt;，阶差&lt;math&gt;\delta=6-1-1=4&lt;/math&gt;。<br /> <br /> 根据坏部和阶差，我们可以求出&lt;math&gt;B_1=(5,8,10)&lt;/math&gt;，&lt;math&gt;B_2=(9,12,14)&lt;/math&gt;，等等。<br /> <br /> 最后，我们得到了展开式&lt;math&gt;(1,4,6,6)=(1,4,6,5,8,10,9,12,14,\cdots)&lt;/math&gt;。<br /> <br /> 可以将其和 [[长初等序列#举例|LPrSS 中相同表达式的展开]]进行对比。<br /> <br /> == 与 PSS Hydra 的对应 ==<br /> HPrSS可以和[[PSS Hydra]]存在直接的转换关系，下面介绍互译算法。<br /> <br /> 说明：算法中出现的所有“序列”均指正整数序列，不需要为HPrSS的合法式。<br /> <br /> === HPrSS到PSS Hydra ===<br /> 给定一个HPrSS表达式&lt;math&gt;S=(a_1,a_2,\cdots,a_n)&lt;/math&gt;，设其对应的PSS Hydra表达式为&lt;math&gt;PH(S)&lt;/math&gt;。则：<br /> <br /> * 如果&lt;math&gt;S&lt;/math&gt;为空序列，则&lt;math&gt;PH(S)=0&lt;/math&gt;。<br /> * 否则，记&lt;math&gt;x_1=1&lt;/math&gt;，&lt;math&gt;x_{n+1}=\min\{k&gt;x_n\mid a_k\le a_{x_n}\}&lt;/math&gt;，即&lt;math&gt;a_{x_{n+1}}&lt;/math&gt;是&lt;math&gt;a_{x_n}&lt;/math&gt;右边第一个小于等于&lt;math&gt;a_{x_n}&lt;/math&gt;的项。这样&lt;math&gt;S&lt;/math&gt;就可以写成&lt;math&gt;(a_{x_1},S_1,a_{x_2},S_2,\cdots,a_{x_k},S_k)&lt;/math&gt;，由&lt;math&gt;a_{x_{n+1}}&lt;/math&gt;的定义可知&lt;math&gt;S_i&lt;/math&gt;中的每一项均大于&lt;math&gt;a_{x_n}&lt;/math&gt;。<br /> * 我们有&lt;math&gt;PH(S)=\psi^H_{a_{x_1}}(PH(S_1-a_{x_1}))+\psi^H_{a_{x_2}}(PH(S_2-a_{x_2}))+\cdots+\psi^H_{a_{x_k}}(PH(S_k-a_{x_k}))&lt;/math&gt;，其中&lt;math&gt;S-a&lt;/math&gt;为将&lt;math&gt;S&lt;/math&gt;的每一项都减去&lt;math&gt;a&lt;/math&gt;得到的序列。<br /> <br /> 例如，考虑LPrSS表达式&lt;math&gt;(1,4,7,6,3,5,7)&lt;/math&gt;<br /> <br /> 进行第二步，得到&lt;math&gt;k=1,x_1=1&lt;/math&gt;，故&lt;math&gt;({\color{red}1},4,7,6,3,5,7)=\psi^H_1((3,6,5,2,4,6))&lt;/math&gt;<br /> <br /> 对&lt;math&gt;(3,6,5,2,4,6)&lt;/math&gt;进行第二步，得到&lt;math&gt;k=2,x_1=1,x_2=4&lt;/math&gt;，故&lt;math&gt;({\color{red}3},6,5,{\color{red}2},4,6)=\psi^H_3((3,2))+\psi^H_2((2,4))&lt;/math&gt;<br /> <br /> 分别计算&lt;math&gt;(3,2)&lt;/math&gt;和&lt;math&gt;(2,4)&lt;/math&gt;对应的PSS Hydra，得到&lt;math&gt;(3,2)=\psi^H_3(0)+\psi^H_2(0)&lt;/math&gt;，&lt;math&gt;(2,4)=\psi^H_2(\psi^H_2(0))&lt;/math&gt;<br /> <br /> 综上，我们得到了&lt;math&gt;(1,4,7,6,3,5,7)=\psi^H_1(\psi^H_3(\psi^H_3(0)+\psi^H_2(0))+\psi^H_2(\psi^H_2(\psi^H_2(0)))&lt;/math&gt;<br /> <br /> === PSS Hydra到HPrSS ===<br /> 给定一个PSS Hydra表达式&lt;math&gt;H&lt;/math&gt;，设其对应的HPrSS表达式为&lt;math&gt;LP(H)&lt;/math&gt;。则：<br /> <br /> * 如果&lt;math&gt;H=0&lt;/math&gt;，则&lt;math&gt;LP(H)&lt;/math&gt;为空序列。<br /> * &lt;math&gt;LP(H_1+H_2)=(LP(H_1),LP(H_2))&lt;/math&gt;，其中&lt;math&gt;(S_1,S_2)&lt;/math&gt;为两个序列的拼接。<br /> * &lt;math&gt;LP(\psi^H_x(H))=(x,(LP(H)+x))&lt;/math&gt;。<br /> {{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=Test&diff=3479 2026-07-19T13:59:12Z

<p>0100000000a7：​</p> <hr /> <div>此页面为测试页面。任何人都可以随意修改此页面以便测试。<br /> <br /> 我死的好惨呀！我是时间过得真慢QQ，我的聚集地和大群都被踢出去了，其他群也不要了，没有任何一个要我了，还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来<br /> <br /> 孩子们这并不好像，谁叫你还我命来的😂<br /> <br /> === 编写技巧 ===<br /> <br /> * 行内代码块：&lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;code&gt;xxx&lt;/code&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;code&gt;xxx&lt;/code&gt;。<br /> * 在列表里换行：使用 &lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;br&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;br&gt;第一行；&lt;br&gt;第二行。<br /> * 在列表里嵌套列表：无序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ul&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ul&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：&lt;ul&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ul&gt;有序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ol&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ol&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：<br /> &lt;ol&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ol&gt;于是可以&lt;ul&gt; &lt;li&gt;awa&lt;ul&gt; &lt;li&gt;114514&lt;ul&gt; &lt;li&gt;3.1415926&lt;ul&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;789&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;2.71828&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;qwerty&lt;/li&gt; &lt;/ul&gt;<br /> &lt;ol&gt; &lt;li&gt;awa&lt;ol&gt; &lt;li&gt;114514&lt;ol&gt; &lt;li&gt;3.1415926&lt;ol&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;789&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;2.71828&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;qwerty&lt;/li&gt; &lt;/ol&gt;<br /> * 分界线：使用 &lt;code&gt;----&lt;/code&gt;。效果是这样：<br /> <br /> ----<br /> <br /> 这句话有7个字<br /> <br /> &lt;math&gt;\varnothing,\emptyset&lt;/math&gt;，<br /> \(\varnothing,\emptyset\)<br /> LaTeX公式&lt;code&gt;\varnothing,\emptyset&lt;/code&gt;用不同渲染方式的结果<br /> <br /> &lt;math display=&quot;block&quot;&gt;\begin{aligned}<br /> f(x)\;&amp;=(a+b+1)/2-x\\<br /> &amp;=(a+2x-1-a+f(2x-1-a)+1)/2-x\\<br /> &amp;=f(2x-1-a)/2\\<br /> &amp;=f(2x-1-(x-1+f(x-1)))/2\\<br /> &amp;=f(x-f(x-1))/2<br /> \end{aligned}&lt;/math&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> 111<br /> <br /> \( G(64)=\left. \begin{matrix} 3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \cdots \uparrow}3 \\3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \uparrow}3 \\ \underbrace{\qquad \quad \vdots \qquad \quad} \\3\underbrace{\uparrow \uparrow \cdots \cdots \uparrow}3 \\3\uparrow \uparrow \uparrow \uparrow3\end{matrix} \right \} \text{64 layers} \)<br /> <br /> &lt;math&gt;\unicode{64}&lt;/math&gt;<br /> <br /> &lt;math&gt;\varphi(\#,(\alpha+1)\text{@}(\beta+1),0\text{@}0)[0]=0&lt;/math&gt;<br /> <br /> &lt;math&gt;\text{@}&lt;/math&gt;<br /> <br /> [k]<br /> <br /> \(\alpha\text{@}\beta\)<br /> <br /> 其实还可以有个更简单的做法，\alpha{@}\beta = \(\alpha{@}\beta\)<br /> <br /> [[[a]]]<br /> <br /> 我们可以使用&lt;code&gt;\hspace&lt;/code&gt;和&lt;code&gt;\raise&lt;/code&gt;来微调LaTeX中的字符位置：<br /> \(\LaTeX\)''（直接使用''&lt;code&gt;\LaTeX&lt;/code&gt;''的版本）''<br /> \({L^{\hspace{-4.5px}\raise{-2.5px}A}<br /> \hspace{-3px}T\hspace{-2px}\raise{-3px}E\hspace{-1.5px}X}\)''（使用以上两种命令微调的模仿版本）''<br /> <br /> &lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;(&lt;/span&gt;\alpha\text{@}\beta&lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;)&lt;/span&gt; = \(\alpha\text{@}\beta\)<br /> <br /> <br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {a}<br /> <br /> <br /> &lt;code&gt;我是code&lt;/code&gt;<br /> <br /> <br /> &lt;pre&gt;我是pre&lt;/pre&gt;<br /> <br /> <br /> &lt;span style='background:linear-gradient(to right,#00ff00,#0000ff);-webkit-background-clip:text;-webkit-text-fill-color:transparent;'&gt;我是美丽的span&lt;/span&gt;<br /> <br /> &lt;a href='https://baidu.com'&gt;危险的代码是不被允许的&lt;/a&gt;<br /> <br /> &lt;span onclick='this.innerText=&quot;onclick是无效的！&quot;'&gt;click me!&lt;/span&gt;<br /> <br /> 666<br /> <br /> \(\alpha @\beta\)<br /> <br /> &lt;blockquote&gt;<br /> 我是猫娘。喵喵喵喵<br /> &lt;/blockquote&gt;<br /> <br /> &lt;blockquote&gt;单行引言&lt;/blockquote&gt;<br /> <br /> &lt;span style='background-color:red'&gt;bgcisred&lt;/span&gt;<br /> <br /> [[高德纳箭头|↑]]<br /> <br /> &lt;iframe&gt;<br /> src=&quot;https://expander.googology.top/index.html&quot; <br /> width=&quot;100%&quot; <br /> height=&quot;500px&quot;<br /> frameborder=&quot;0&quot;<br /> &lt;/iframe&gt;<br /> <br /> === 这是一级标题 ===<br /> <br /> ==== 这是二级标题 ====<br /> 这是公式 \(\alpha\times\beta\)<br /> <br /> ''撒反对''<br /> <br /> 说说不可说】(1)<br /> <br /> --------------------------------------------------------------------<br /> <br /> 　　 人们的对话中，「不可说」指的是「不可以说出来」的意思，但是在佛<br /> 经中，不可说的意思并不一定是这样，世尊所说的佛经更不是指这个意思。<br /> 如果它是指不可以说出来的话，那麽全部的佛经就是一部「大妄语百科」了。<br /> <br /> 但是将「不可说」解释为「不可以说出来」的意思，并不是现代人的专<br /> 利，古人解经，也常把它作这样的解释，造成後人将佛经解释成玄密的经典，<br /> 一切的不合理之处都当作「不可说」来处理。<br /> <br /> 世尊的确说过许多的不可说，如:《华严经》<br /> 「不可言说不可说，充满一切不可说，不可言说诸劫中，说不可说不可尽，<br /> ....<br /> 於一微细毛端处，有不可说诸普贤，....一毛端处所有刹，其数无量不可<br /> 　说..」在第四十五卷中，世尊一口气说了将近四百个不可说。<br /> <br /> 《地藏菩萨本愿经》【忉利天宫神通品】「尔时，十方无量世界不可<br /> 　说不可说一切诸佛，及大菩萨摩诃萨，皆来集会，赞叹释迦牟尼佛．．」<br /> 这里用了两个不可说。<br /> <br /> 《小般若经》【深功德品】「一切法不可说，须菩提，一切法空相不<br /> 可说．．」<br /> <br /> 其实「不可说」的意义是「数量大到无法用语言形容」的意思，并不<br /> 是指所说的主题「不能说」，如果是不能说，那麽上面这些经典就是「废<br /> 话大全」了。<br /> <br /> 世尊说法四十九年，探讨的主题遍及人类所有的疑问，从来没有一样<br /> 　是「不能说出来」的，不但他老人家自己说，更鼓励所有修行菩萨要为众　<br /> 生说呢。(参见《般若经》)<br /> <br /> 那麽，「不可说」倒底有多大，会大到语言法形容呢？我们试著来找<br /> 找看。<br /> <br /> {| class=&quot;wikitable&quot; border=&quot;0&quot; cellpadding=&quot;1&quot; cellspacing=&quot;1&quot;<br /> ! scope=&quot;col&quot; |<br /> ! scope=&quot;col&quot; |A<br /> ! scope=&quot;col&quot; |B<br /> |-<br /> |0<br /> |1RB<br /> 1LA<br /> &lt;br&gt;1CP<br /> &lt;br&gt;114514<br /> |1LA<br /> |-<br /> |1<br /> |1LB<br /> |1RB<br /> |}<br /> 111<br /> <br /> {| class=&quot;wikitable&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | style=&quot;width: 20%;&quot; | 张三 || style=&quot;width: 80%; word-wrap: break-word;&quot; | 这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> 表格？<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;width: 300px; overflow: hidden; text-overflow: ellipsis&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | 张三<br /> | 这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> &lt;blockquote&gt;这里是一个孤立页面 我不知道它为什么还在这里<br /> <br /> 就当作是gggwiki的一个彩蛋吧（&lt;/blockquote&gt;<br /> <br /> <br /> <br /> <br /> <br /> [https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 果糕]<br /> 果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！<br /> <br /> &lt;div id=&quot;guogao1&quot;&gt;将以下代码放入控制台并回车，有“小惊喜”：&lt;/div&gt;&lt;small&gt;&lt;small&gt;&lt;nowiki&gt;(()=&gt;{document.getElementById(&quot;guogao1&quot;).appendChild((()=&gt;{let a = document.createElement(&quot;div&quot;);a.innerHTML = `&lt;div class=&quot;fixed-btn&quot;&gt;&lt;a onclick=&quot;let b=document.createElement('div');b.innerHTML=\`&lt;div id='guogao' style='transition: transform .5s ease-out;position: absolute;top:45%;left:50%;z-index: 9999999;transform: scale(1);cursor: pointer;-webkit-user-select: none;-moz-user-select: none;-ms-user-select: none;user-select: none;' onclick='this.remove()'&gt;${decodeURI('%F0%9F%98%B0')}&lt;/div&gt;\`;document.body.appendChild(b);setTimeout(() =&gt; {document.getElementById('guogao').style.transform='scale(45)'}, 50)&quot; class=&quot;new&quot; title=&quot;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&quot;&gt;&lt;span class=&quot;btn-text blue&quot;&gt;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&lt;/span&gt;&lt;/a&gt;&lt;/div&gt;`;return a})());return (()=&gt;{console.clear();return decodeURI('%E7%A5%9E%E7%A7%98%E6%8C%89%E9%92%AE%E5%87%BA%E7%8E%B0%EF%BC%81')})()})()<br /> &lt;/nowiki&gt;&lt;/small&gt;&lt;/small&gt;<br /> <br /> 以下是Naruyoko在[https://naruyoko.github.io/ExpantaNum.js/]中给出过的latex<br /> <br /> &lt;div style=&quot;overflow:auto&quot;&gt;<br /> \[<br /> \begin{matrix}\underbrace{\left.\left.\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}\cdots\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}10}\\\underbrace{\left.\left.\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}\cdots\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}10}\\\underbrace{\left.\left.\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}\cdots\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}10}\\\underbrace{\left.\left.\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}\cdots\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}10}\\\left.\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}\left.\left.\left.\left.\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}2\underset{171869969539773881871357}{\underbrace{28767407104742504939274665007259268034875905285622251679055397167730260624040178402089159341052814222\cdots}}.\end{matrix}<br /> \]<br /> &lt;/div&gt;<br /> [[分类:入门]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=Test&diff=3478 2026-07-19T13:58:27Z

<p>0100000000a7：​</p> <hr /> <div>此页面为测试页面。任何人都可以随意修改此页面以便测试。<br /> <br /> 我死的好惨呀！我是时间过得真慢QQ，我的聚集地和大群都被踢出去了，其他群也不要了，没有任何一个要我了，还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来<br /> <br /> 孩子们这并不好像，谁叫你还我命来的😂<br /> <br /> === 编写技巧 ===<br /> <br /> * 行内代码块：&lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;code&gt;xxx&lt;/code&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;code&gt;xxx&lt;/code&gt;。<br /> * 在列表里换行：使用 &lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;br&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;br&gt;第一行；&lt;br&gt;第二行。<br /> * 在列表里嵌套列表：无序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ul&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ul&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：&lt;ul&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ul&gt;有序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ol&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ol&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：<br /> &lt;ol&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ol&gt;于是可以&lt;ul&gt; &lt;li&gt;awa&lt;ul&gt; &lt;li&gt;114514&lt;ul&gt; &lt;li&gt;3.1415926&lt;ul&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;789&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;2.71828&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;qwerty&lt;/li&gt; &lt;/ul&gt;<br /> &lt;ol&gt; &lt;li&gt;awa&lt;ol&gt; &lt;li&gt;114514&lt;ol&gt; &lt;li&gt;3.1415926&lt;ol&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;789&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;2.71828&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;qwerty&lt;/li&gt; &lt;/ol&gt;<br /> * 分界线：使用 &lt;code&gt;----&lt;/code&gt;。效果是这样：<br /> <br /> ----<br /> <br /> 这句话有7个字<br /> <br /> &lt;math&gt;\varnothing,\emptyset&lt;/math&gt;，<br /> \(\varnothing,\emptyset\)<br /> LaTeX公式&lt;code&gt;\varnothing,\emptyset&lt;/code&gt;用不同渲染方式的结果<br /> <br /> &lt;math display=&quot;block&quot;&gt;\begin{aligned}<br /> f(x)\;&amp;=(a+b+1)/2-x\\<br /> &amp;=(a+2x-1-a+f(2x-1-a)+1)/2-x\\<br /> &amp;=f(2x-1-a)/2\\<br /> &amp;=f(2x-1-(x-1+f(x-1)))/2\\<br /> &amp;=f(x-f(x-1))/2<br /> \end{aligned}&lt;/math&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> 111<br /> <br /> \( G(64)=\left. \begin{matrix} 3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \cdots \uparrow}3 \\3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \uparrow}3 \\ \underbrace{\qquad \quad \vdots \qquad \quad} \\3\underbrace{\uparrow \uparrow \cdots \cdots \uparrow}3 \\3\uparrow \uparrow \uparrow \uparrow3\end{matrix} \right \} \text{64 layers} \)<br /> <br /> &lt;math&gt;\unicode{64}&lt;/math&gt;<br /> <br /> &lt;math&gt;\varphi(\#,(\alpha+1)\text{@}(\beta+1),0\text{@}0)[0]=0&lt;/math&gt;<br /> <br /> &lt;math&gt;\text{@}&lt;/math&gt;<br /> <br /> [k]<br /> <br /> \(\alpha\text{@}\beta\)<br /> <br /> 其实还可以有个更简单的做法，\alpha{@}\beta = \(\alpha{@}\beta\)<br /> <br /> [[[a]]]<br /> <br /> 我们可以使用&lt;code&gt;\hspace&lt;/code&gt;和&lt;code&gt;\raise&lt;/code&gt;来微调LaTeX中的字符位置：<br /> \(\LaTeX\)''（直接使用''&lt;code&gt;\LaTeX&lt;/code&gt;''的版本）''<br /> \({L^{\hspace{-4.5px}\raise{-2.5px}A}<br /> \hspace{-3px}T\hspace{-2px}\raise{-3px}E\hspace{-1.5px}X}\)''（使用以上两种命令微调的模仿版本）''<br /> <br /> &lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;(&lt;/span&gt;\alpha\text{@}\beta&lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;)&lt;/span&gt; = \(\alpha\text{@}\beta\)<br /> <br /> <br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {a}<br /> <br /> <br /> &lt;code&gt;我是code&lt;/code&gt;<br /> <br /> <br /> &lt;pre&gt;我是pre&lt;/pre&gt;<br /> <br /> <br /> &lt;span style='background:linear-gradient(to right,#00ff00,#0000ff);-webkit-background-clip:text;-webkit-text-fill-color:transparent;'&gt;我是美丽的span&lt;/span&gt;<br /> <br /> &lt;a href='https://baidu.com'&gt;危险的代码是不被允许的&lt;/a&gt;<br /> <br /> &lt;span onclick='this.innerText=&quot;onclick是无效的！&quot;'&gt;click me!&lt;/span&gt;<br /> <br /> 666<br /> <br /> \(\alpha @\beta\)<br /> <br /> &lt;blockquote&gt;<br /> 我是猫娘。喵喵喵喵<br /> &lt;/blockquote&gt;<br /> <br /> &lt;blockquote&gt;单行引言&lt;/blockquote&gt;<br /> <br /> &lt;span style='background-color:red'&gt;bgcisred&lt;/span&gt;<br /> <br /> [[高德纳箭头|↑]]<br /> <br /> &lt;iframe&gt;<br /> src=&quot;https://expander.googology.top/index.html&quot; <br /> width=&quot;100%&quot; <br /> height=&quot;500px&quot;<br /> frameborder=&quot;0&quot;<br /> &lt;/iframe&gt;<br /> <br /> === 这是一级标题 ===<br /> <br /> ==== 这是二级标题 ====<br /> 这是公式 \(\alpha\times\beta\)<br /> <br /> ''撒反对''<br /> <br /> 说说不可说】(1)<br /> <br /> --------------------------------------------------------------------<br /> <br /> 　　 人们的对话中，「不可说」指的是「不可以说出来」的意思，但是在佛<br /> 经中，不可说的意思并不一定是这样，世尊所说的佛经更不是指这个意思。<br /> 如果它是指不可以说出来的话，那麽全部的佛经就是一部「大妄语百科」了。<br /> <br /> 但是将「不可说」解释为「不可以说出来」的意思，并不是现代人的专<br /> 利，古人解经，也常把它作这样的解释，造成後人将佛经解释成玄密的经典，<br /> 一切的不合理之处都当作「不可说」来处理。<br /> <br /> 世尊的确说过许多的不可说，如:《华严经》<br /> 「不可言说不可说，充满一切不可说，不可言说诸劫中，说不可说不可尽，<br /> ....<br /> 於一微细毛端处，有不可说诸普贤，....一毛端处所有刹，其数无量不可<br /> 　说..」在第四十五卷中，世尊一口气说了将近四百个不可说。<br /> <br /> 《地藏菩萨本愿经》【忉利天宫神通品】「尔时，十方无量世界不可<br /> 　说不可说一切诸佛，及大菩萨摩诃萨，皆来集会，赞叹释迦牟尼佛．．」<br /> 这里用了两个不可说。<br /> <br /> 《小般若经》【深功德品】「一切法不可说，须菩提，一切法空相不<br /> 可说．．」<br /> <br /> 其实「不可说」的意义是「数量大到无法用语言形容」的意思，并不<br /> 是指所说的主题「不能说」，如果是不能说，那麽上面这些经典就是「废<br /> 话大全」了。<br /> <br /> 世尊说法四十九年，探讨的主题遍及人类所有的疑问，从来没有一样<br /> 　是「不能说出来」的，不但他老人家自己说，更鼓励所有修行菩萨要为众　<br /> 生说呢。(参见《般若经》)<br /> <br /> 那麽，「不可说」倒底有多大，会大到语言法形容呢？我们试著来找<br /> 找看。<br /> <br /> {| class=&quot;wikitable&quot; border=&quot;0&quot; cellpadding=&quot;1&quot; cellspacing=&quot;1&quot;<br /> ! scope=&quot;col&quot; |<br /> ! scope=&quot;col&quot; |A<br /> ! scope=&quot;col&quot; |B<br /> |-<br /> |0<br /> |1RB<br /> 1LA<br /> &lt;br&gt;1CP<br /> &lt;br&gt;114514<br /> |1LA<br /> |-<br /> |1<br /> |1LB<br /> |1RB<br /> |}<br /> 111<br /> <br /> {| class=&quot;wikitable&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | style=&quot;width: 20%;&quot; | 张三 || style=&quot;width: 80%; word-wrap: break-word;&quot; | 这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> 表格？<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;width: 300px; overflow: hidden; text-overflow: ellipsis&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | 张三<br /> | 这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> &lt;blockquote&gt;这里是一个孤立页面 我不知道它为什么还在这里<br /> <br /> 就当作是gggwiki的一个彩蛋吧（&lt;/blockquote&gt;<br /> <br /> <br /> <br /> <br /> <br /> [https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 果糕]<br /> 果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！<br /> <br /> &lt;div id=&quot;guogao1&quot;&gt;将以下代码放入控制台并回车，有“小惊喜”：&lt;/div&gt;&lt;small&gt;&lt;small&gt;&lt;nowiki&gt;(()=&gt;{document.getElementById(&quot;guogao1&quot;).appendChild((()=&gt;{let a = document.createElement(&quot;div&quot;);a.innerHTML = `&lt;div class=&quot;fixed-btn&quot;&gt;&lt;a onclick=&quot;let b=document.createElement('div');b.innerHTML=\`&lt;div id='guogao' style='transition: transform .5s ease-out;position: absolute;top:45%;left:50%;z-index: 9999999;transform: scale(1);cursor: pointer;-webkit-user-select: none;-moz-user-select: none;-ms-user-select: none;user-select: none;' onclick='this.remove()'&gt;${decodeURI('%F0%9F%98%B0')}&lt;/div&gt;\`;document.body.appendChild(b);setTimeout(() =&gt; {document.getElementById('guogao').style.transform='scale(45)'}, 50)&quot; class=&quot;new&quot; title=&quot;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&quot;&gt;&lt;span class=&quot;btn-text blue&quot;&gt;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&lt;/span&gt;&lt;/a&gt;&lt;/div&gt;`;return a})());return (()=&gt;{console.clear();return decodeURI('%E7%A5%9E%E7%A7%98%E6%8C%89%E9%92%AE%E5%87%BA%E7%8E%B0%EF%BC%81')})()})()<br /> <br /> <br /> 以下是Naruyoko在[https://naruyoko.github.io/ExpantaNum.js/]中给出过的latex<br /> <br /> &lt;div style=&quot;overflow:auto&quot;&gt;<br /> \[<br /> \begin{matrix}\underbrace{\left.\left.\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}\cdots\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}10}\\\underbrace{\left.\left.\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}\cdots\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}10}\\\underbrace{\left.\left.\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}\cdots\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}10}\\\underbrace{\left.\left.\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}\cdots\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}10}\\\left.\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}\left.\left.\left.\left.\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}2\underset{171869969539773881871357}{\underbrace{28767407104742504939274665007259268034875905285622251679055397167730260624040178402089159341052814222\cdots}}.\end{matrix}<br /> \]<br /> &lt;/div&gt;<br /> &lt;/nowiki&gt;&lt;/small&gt;&lt;/small&gt;<br /> [[分类:入门]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=Test&diff=3477 2026-07-19T13:56:11Z

<p>0100000000a7：​</p> <hr /> <div>此页面为测试页面。任何人都可以随意修改此页面以便测试。<br /> <br /> 我死的好惨呀！我是时间过得真慢QQ，我的聚集地和大群都被踢出去了，其他群也不要了，没有任何一个要我了，还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来<br /> <br /> 孩子们这并不好像，谁叫你还我命来的😂<br /> <br /> === 编写技巧 ===<br /> <br /> * 行内代码块：&lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;code&gt;xxx&lt;/code&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;code&gt;xxx&lt;/code&gt;。<br /> * 在列表里换行：使用 &lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;br&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;br&gt;第一行；&lt;br&gt;第二行。<br /> * 在列表里嵌套列表：无序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ul&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ul&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：&lt;ul&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ul&gt;有序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ol&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ol&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：<br /> &lt;ol&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ol&gt;于是可以&lt;ul&gt; &lt;li&gt;awa&lt;ul&gt; &lt;li&gt;114514&lt;ul&gt; &lt;li&gt;3.1415926&lt;ul&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;789&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;2.71828&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;qwerty&lt;/li&gt; &lt;/ul&gt;<br /> &lt;ol&gt; &lt;li&gt;awa&lt;ol&gt; &lt;li&gt;114514&lt;ol&gt; &lt;li&gt;3.1415926&lt;ol&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;789&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;2.71828&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;qwerty&lt;/li&gt; &lt;/ol&gt;<br /> * 分界线：使用 &lt;code&gt;----&lt;/code&gt;。效果是这样：<br /> <br /> ----<br /> <br /> 这句话有7个字<br /> <br /> &lt;math&gt;\varnothing,\emptyset&lt;/math&gt;，<br /> \(\varnothing,\emptyset\)<br /> LaTeX公式&lt;code&gt;\varnothing,\emptyset&lt;/code&gt;用不同渲染方式的结果<br /> <br /> &lt;math display=&quot;block&quot;&gt;\begin{aligned}<br /> f(x)\;&amp;=(a+b+1)/2-x\\<br /> &amp;=(a+2x-1-a+f(2x-1-a)+1)/2-x\\<br /> &amp;=f(2x-1-a)/2\\<br /> &amp;=f(2x-1-(x-1+f(x-1)))/2\\<br /> &amp;=f(x-f(x-1))/2<br /> \end{aligned}&lt;/math&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> 111<br /> <br /> \( G(64)=\left. \begin{matrix} 3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \cdots \uparrow}3 \\3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \uparrow}3 \\ \underbrace{\qquad \quad \vdots \qquad \quad} \\3\underbrace{\uparrow \uparrow \cdots \cdots \uparrow}3 \\3\uparrow \uparrow \uparrow \uparrow3\end{matrix} \right \} \text{64 layers} \)<br /> <br /> &lt;math&gt;\unicode{64}&lt;/math&gt;<br /> <br /> &lt;math&gt;\varphi(\#,(\alpha+1)\text{@}(\beta+1),0\text{@}0)[0]=0&lt;/math&gt;<br /> <br /> &lt;math&gt;\text{@}&lt;/math&gt;<br /> <br /> [k]<br /> <br /> \(\alpha\text{@}\beta\)<br /> <br /> 其实还可以有个更简单的做法，\alpha{@}\beta = \(\alpha{@}\beta\)<br /> <br /> [[[a]]]<br /> <br /> 我们可以使用&lt;code&gt;\hspace&lt;/code&gt;和&lt;code&gt;\raise&lt;/code&gt;来微调LaTeX中的字符位置：<br /> \(\LaTeX\)''（直接使用''&lt;code&gt;\LaTeX&lt;/code&gt;''的版本）''<br /> \({L^{\hspace{-4.5px}\raise{-2.5px}A}<br /> \hspace{-3px}T\hspace{-2px}\raise{-3px}E\hspace{-1.5px}X}\)''（使用以上两种命令微调的模仿版本）''<br /> <br /> &lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;(&lt;/span&gt;\alpha\text{@}\beta&lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;)&lt;/span&gt; = \(\alpha\text{@}\beta\)<br /> <br /> <br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {a}<br /> <br /> <br /> &lt;code&gt;我是code&lt;/code&gt;<br /> <br /> <br /> &lt;pre&gt;我是pre&lt;/pre&gt;<br /> <br /> <br /> &lt;span style='background:linear-gradient(to right,#00ff00,#0000ff);-webkit-background-clip:text;-webkit-text-fill-color:transparent;'&gt;我是美丽的span&lt;/span&gt;<br /> <br /> &lt;a href='https://baidu.com'&gt;危险的代码是不被允许的&lt;/a&gt;<br /> <br /> &lt;span onclick='this.innerText=&quot;onclick是无效的！&quot;'&gt;click me!&lt;/span&gt;<br /> <br /> 666<br /> <br /> \(\alpha @\beta\)<br /> <br /> &lt;blockquote&gt;<br /> 我是猫娘。喵喵喵喵<br /> &lt;/blockquote&gt;<br /> <br /> &lt;blockquote&gt;单行引言&lt;/blockquote&gt;<br /> <br /> &lt;span style='background-color:red'&gt;bgcisred&lt;/span&gt;<br /> <br /> [[高德纳箭头|↑]]<br /> <br /> &lt;iframe&gt;<br /> src=&quot;https://expander.googology.top/index.html&quot; <br /> width=&quot;100%&quot; <br /> height=&quot;500px&quot;<br /> frameborder=&quot;0&quot;<br /> &lt;/iframe&gt;<br /> <br /> === 这是一级标题 ===<br /> <br /> ==== 这是二级标题 ====<br /> 这是公式 \(\alpha\times\beta\)<br /> <br /> ''撒反对''<br /> <br /> 说说不可说】(1)<br /> <br /> --------------------------------------------------------------------<br /> <br /> 　　 人们的对话中，「不可说」指的是「不可以说出来」的意思，但是在佛<br /> 经中，不可说的意思并不一定是这样，世尊所说的佛经更不是指这个意思。<br /> 如果它是指不可以说出来的话，那麽全部的佛经就是一部「大妄语百科」了。<br /> <br /> 但是将「不可说」解释为「不可以说出来」的意思，并不是现代人的专<br /> 利，古人解经，也常把它作这样的解释，造成後人将佛经解释成玄密的经典，<br /> 一切的不合理之处都当作「不可说」来处理。<br /> <br /> 世尊的确说过许多的不可说，如:《华严经》<br /> 「不可言说不可说，充满一切不可说，不可言说诸劫中，说不可说不可尽，<br /> ....<br /> 於一微细毛端处，有不可说诸普贤，....一毛端处所有刹，其数无量不可<br /> 　说..」在第四十五卷中，世尊一口气说了将近四百个不可说。<br /> <br /> 《地藏菩萨本愿经》【忉利天宫神通品】「尔时，十方无量世界不可<br /> 　说不可说一切诸佛，及大菩萨摩诃萨，皆来集会，赞叹释迦牟尼佛．．」<br /> 这里用了两个不可说。<br /> <br /> 《小般若经》【深功德品】「一切法不可说，须菩提，一切法空相不<br /> 可说．．」<br /> <br /> 其实「不可说」的意义是「数量大到无法用语言形容」的意思，并不<br /> 是指所说的主题「不能说」，如果是不能说，那麽上面这些经典就是「废<br /> 话大全」了。<br /> <br /> 世尊说法四十九年，探讨的主题遍及人类所有的疑问，从来没有一样<br /> 　是「不能说出来」的，不但他老人家自己说，更鼓励所有修行菩萨要为众　<br /> 生说呢。(参见《般若经》)<br /> <br /> 那麽，「不可说」倒底有多大，会大到语言法形容呢？我们试著来找<br /> 找看。<br /> <br /> {| class=&quot;wikitable&quot; border=&quot;0&quot; cellpadding=&quot;1&quot; cellspacing=&quot;1&quot;<br /> ! scope=&quot;col&quot; |<br /> ! scope=&quot;col&quot; |A<br /> ! scope=&quot;col&quot; |B<br /> |-<br /> |0<br /> |1RB<br /> 1LA<br /> &lt;br&gt;1CP<br /> &lt;br&gt;114514<br /> |1LA<br /> |-<br /> |1<br /> |1LB<br /> |1RB<br /> |}<br /> 111<br /> <br /> {| class=&quot;wikitable&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | style=&quot;width: 20%;&quot; | 张三 || style=&quot;width: 80%; word-wrap: break-word;&quot; | 这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> 表格？<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;width: 300px; overflow: hidden; text-overflow: ellipsis&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | 张三<br /> | 这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> &lt;blockquote&gt;这里是一个孤立页面 我不知道它为什么还在这里<br /> <br /> 就当作是gggwiki的一个彩蛋吧（&lt;/blockquote&gt;<br /> <br /> <br /> <br /> <br /> <br /> [https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 果糕]<br /> 果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！<br /> <br /> &lt;div id=&quot;guogao1&quot;&gt;将以下代码放入控制台并回车，有“小惊喜”：&lt;/div&gt;&lt;small&gt;&lt;small&gt;&lt;nowiki&gt;(()=&gt;{document.getElementById(&quot;guogao1&quot;).appendChild((()=&gt;{let a = document.createElement(&quot;div&quot;);a.innerHTML = `&lt;div class=&quot;fixed-btn&quot;&gt;&lt;a onclick=&quot;let b=document.createElement('div');b.innerHTML=\`&lt;div id='guogao' style='transition: transform .5s ease-out;position: absolute;top:45%;left:50%;z-index: 9999999;transform: scale(1);cursor: pointer;-webkit-user-select: none;-moz-user-select: none;-ms-user-select: none;user-select: none;' onclick='this.remove()'&gt;${decodeURI('%F0%9F%98%B0')}&lt;/div&gt;\`;document.body.appendChild(b);setTimeout(() =&gt; {document.getElementById('guogao').style.transform='scale(45)'}, 50)&quot; class=&quot;new&quot; title=&quot;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&quot;&gt;&lt;span class=&quot;btn-text blue&quot;&gt;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&lt;/span&gt;&lt;/a&gt;&lt;/div&gt;`;return a})());return (()=&gt;{console.clear();return decodeURI('%E7%A5%9E%E7%A7%98%E6%8C%89%E9%92%AE%E5%87%BA%E7%8E%B0%EF%BC%81')})()})()<br /> <br /> 以下是Naruyoko在[https://naruyoko.github.io/ExpantaNum.js/]中给出过的latex<br /> \[<br /> \begin{matrix}\underbrace{\left.\left.\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}\cdots\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}10}\\\underbrace{\left.\left.\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}\cdots\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}10}\\\underbrace{\left.\left.\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}\cdots\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}10}\\\underbrace{\left.\left.\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}\cdots\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}10}\\\left.\begin{matrix}\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\\vdots\\\underbrace{\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\cdots\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}10}\\10\end{matrix}\right\}\left.\left.\left.\left.\left.\left.\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}\begin{matrix}1\underbrace{00\cdots00}\\\vdots\\1\underbrace{00\cdots00}\\10\end{matrix}\right\}2\underset{171869969539773881871357}{\underbrace{28767407104742504939274665007259268034875905285622251679055397167730260624040178402089159341052814222\cdots}}.\end{matrix}<br /> \]<br /> <br /> &lt;/nowiki&gt;&lt;/small&gt;&lt;/small&gt;<br /> [[分类:入门]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=Test&diff=3476 2026-07-19T13:54:50Z

<p>0100000000a7：​</p> <hr /> <div>此页面为测试页面。任何人都可以随意修改此页面以便测试。<br /> <br /> 我死的好惨呀！我是时间过得真慢QQ，我的聚集地和大群都被踢出去了，其他群也不要了，没有任何一个要我了，还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来还我命来<br /> <br /> 孩子们这并不好像，谁叫你还我命来的😂<br /> <br /> === 编写技巧 ===<br /> <br /> * 行内代码块：&lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;code&gt;xxx&lt;/code&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;code&gt;xxx&lt;/code&gt;。<br /> * 在列表里换行：使用 &lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;br&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;br&gt;第一行；&lt;br&gt;第二行。<br /> * 在列表里嵌套列表：无序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ul&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ul&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：&lt;ul&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ul&gt;有序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ol&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ol&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：<br /> &lt;ol&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ol&gt;于是可以&lt;ul&gt; &lt;li&gt;awa&lt;ul&gt; &lt;li&gt;114514&lt;ul&gt; &lt;li&gt;3.1415926&lt;ul&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;789&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;2.71828&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;qwerty&lt;/li&gt; &lt;/ul&gt;<br /> &lt;ol&gt; &lt;li&gt;awa&lt;ol&gt; &lt;li&gt;114514&lt;ol&gt; &lt;li&gt;3.1415926&lt;ol&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;789&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;2.71828&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;qwerty&lt;/li&gt; &lt;/ol&gt;<br /> * 分界线：使用 &lt;code&gt;----&lt;/code&gt;。效果是这样：<br /> <br /> ----<br /> <br /> 这句话有7个字<br /> <br /> &lt;math&gt;\varnothing,\emptyset&lt;/math&gt;，<br /> \(\varnothing,\emptyset\)<br /> LaTeX公式&lt;code&gt;\varnothing,\emptyset&lt;/code&gt;用不同渲染方式的结果<br /> <br /> &lt;math display=&quot;block&quot;&gt;\begin{aligned}<br /> f(x)\;&amp;=(a+b+1)/2-x\\<br /> &amp;=(a+2x-1-a+f(2x-1-a)+1)/2-x\\<br /> &amp;=f(2x-1-a)/2\\<br /> &amp;=f(2x-1-(x-1+f(x-1)))/2\\<br /> &amp;=f(x-f(x-1))/2<br /> \end{aligned}&lt;/math&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> 111<br /> <br /> \( G(64)=\left. \begin{matrix} 3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \cdots \uparrow}3 \\3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \uparrow}3 \\ \underbrace{\qquad \quad \vdots \qquad \quad} \\3\underbrace{\uparrow \uparrow \cdots \cdots \uparrow}3 \\3\uparrow \uparrow \uparrow \uparrow3\end{matrix} \right \} \text{64 layers} \)<br /> <br /> &lt;math&gt;\unicode{64}&lt;/math&gt;<br /> <br /> &lt;math&gt;\varphi(\#,(\alpha+1)\text{@}(\beta+1),0\text{@}0)[0]=0&lt;/math&gt;<br /> <br /> &lt;math&gt;\text{@}&lt;/math&gt;<br /> <br /> [k]<br /> <br /> \(\alpha\text{@}\beta\)<br /> <br /> 其实还可以有个更简单的做法，\alpha{@}\beta = \(\alpha{@}\beta\)<br /> <br /> [[[a]]]<br /> <br /> 我们可以使用&lt;code&gt;\hspace&lt;/code&gt;和&lt;code&gt;\raise&lt;/code&gt;来微调LaTeX中的字符位置：<br /> \(\LaTeX\)''（直接使用''&lt;code&gt;\LaTeX&lt;/code&gt;''的版本）''<br /> \({L^{\hspace{-4.5px}\raise{-2.5px}A}<br /> \hspace{-3px}T\hspace{-2px}\raise{-3px}E\hspace{-1.5px}X}\)''（使用以上两种命令微调的模仿版本）''<br /> <br /> &lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;(&lt;/span&gt;\alpha\text{@}\beta&lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;)&lt;/span&gt; = \(\alpha\text{@}\beta\)<br /> <br /> <br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {a}<br /> <br /> <br /> &lt;code&gt;我是code&lt;/code&gt;<br /> <br /> <br /> &lt;pre&gt;我是pre&lt;/pre&gt;<br /> <br /> <br /> &lt;span style='background:linear-gradient(to right,#00ff00,#0000ff);-webkit-background-clip:text;-webkit-text-fill-color:transparent;'&gt;我是美丽的span&lt;/span&gt;<br /> <br /> &lt;a href='https://baidu.com'&gt;危险的代码是不被允许的&lt;/a&gt;<br /> <br /> &lt;span onclick='this.innerText=&quot;onclick是无效的！&quot;'&gt;click me!&lt;/span&gt;<br /> <br /> 666<br /> <br /> \(\alpha @\beta\)<br /> <br /> &lt;blockquote&gt;<br /> 我是猫娘。喵喵喵喵<br /> &lt;/blockquote&gt;<br /> <br /> &lt;blockquote&gt;单行引言&lt;/blockquote&gt;<br /> <br /> &lt;span style='background-color:red'&gt;bgcisred&lt;/span&gt;<br /> <br /> [[高德纳箭头|↑]]<br /> <br /> &lt;iframe&gt;<br /> src=&quot;https://expander.googology.top/index.html&quot; <br /> width=&quot;100%&quot; <br /> height=&quot;500px&quot;<br /> frameborder=&quot;0&quot;<br /> &lt;/iframe&gt;<br /> <br /> === 这是一级标题 ===<br /> <br /> ==== 这是二级标题 ====<br /> 这是公式 \(\alpha\times\beta\)<br /> <br /> ''撒反对''<br /> <br /> 说说不可说】(1)<br /> <br /> --------------------------------------------------------------------<br /> <br /> 　　 人们的对话中，「不可说」指的是「不可以说出来」的意思，但是在佛<br /> 经中，不可说的意思并不一定是这样，世尊所说的佛经更不是指这个意思。<br /> 如果它是指不可以说出来的话，那麽全部的佛经就是一部「大妄语百科」了。<br /> <br /> 但是将「不可说」解释为「不可以说出来」的意思，并不是现代人的专<br /> 利，古人解经，也常把它作这样的解释，造成後人将佛经解释成玄密的经典，<br /> 一切的不合理之处都当作「不可说」来处理。<br /> <br /> 世尊的确说过许多的不可说，如:《华严经》<br /> 「不可言说不可说，充满一切不可说，不可言说诸劫中，说不可说不可尽，<br /> ....<br /> 於一微细毛端处，有不可说诸普贤，....一毛端处所有刹，其数无量不可<br /> 　说..」在第四十五卷中，世尊一口气说了将近四百个不可说。<br /> <br /> 《地藏菩萨本愿经》【忉利天宫神通品】「尔时，十方无量世界不可<br /> 　说不可说一切诸佛，及大菩萨摩诃萨，皆来集会，赞叹释迦牟尼佛．．」<br /> 这里用了两个不可说。<br /> <br /> 《小般若经》【深功德品】「一切法不可说，须菩提，一切法空相不<br /> 可说．．」<br /> <br /> 其实「不可说」的意义是「数量大到无法用语言形容」的意思，并不<br /> 是指所说的主题「不能说」，如果是不能说，那麽上面这些经典就是「废<br /> 话大全」了。<br /> <br /> 世尊说法四十九年，探讨的主题遍及人类所有的疑问，从来没有一样<br /> 　是「不能说出来」的，不但他老人家自己说，更鼓励所有修行菩萨要为众　<br /> 生说呢。(参见《般若经》)<br /> <br /> 那麽，「不可说」倒底有多大，会大到语言法形容呢？我们试著来找<br /> 找看。<br /> <br /> {| class=&quot;wikitable&quot; border=&quot;0&quot; cellpadding=&quot;1&quot; cellspacing=&quot;1&quot;<br /> ! scope=&quot;col&quot; |<br /> ! scope=&quot;col&quot; |A<br /> ! scope=&quot;col&quot; |B<br /> |-<br /> |0<br /> |1RB<br /> 1LA<br /> &lt;br&gt;1CP<br /> &lt;br&gt;114514<br /> |1LA<br /> |-<br /> |1<br /> |1LB<br /> |1RB<br /> |}<br /> 111<br /> <br /> {| class=&quot;wikitable&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | style=&quot;width: 20%;&quot; | 张三 || style=&quot;width: 80%; word-wrap: break-word;&quot; | 这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> 表格？<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;width: 300px; overflow: hidden; text-overflow: ellipsis&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | 张三<br /> | 这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> &lt;blockquote&gt;这里是一个孤立页面 我不知道它为什么还在这里<br /> <br /> 就当作是gggwiki的一个彩蛋吧（&lt;/blockquote&gt;<br /> <br /> <br /> <br /> <br /> <br /> [https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 果糕]<br /> 果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！<br /> <br /> &lt;div id=&quot;guogao1&quot;&gt;将以下代码放入控制台并回车，有“小惊喜”：&lt;/div&gt;&lt;small&gt;&lt;small&gt;&lt;nowiki&gt;(()=&gt;{document.getElementById(&quot;guogao1&quot;).appendChild((()=&gt;{let a = document.createElement(&quot;div&quot;);a.innerHTML = `&lt;div class=&quot;fixed-btn&quot;&gt;&lt;a onclick=&quot;let b=document.createElement('div');b.innerHTML=\`&lt;div id='guogao' style='transition: transform .5s ease-out;position: absolute;top:45%;left:50%;z-index: 9999999;transform: scale(1);cursor: pointer;-webkit-user-select: none;-moz-user-select: none;-ms-user-select: none;user-select: none;' onclick='this.remove()'&gt;${decodeURI('%F0%9F%98%B0')}&lt;/div&gt;\`;document.body.appendChild(b);setTimeout(() =&gt; {document.getElementById('guogao').style.transform='scale(45)'}, 50)&quot; class=&quot;new&quot; title=&quot;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&quot;&gt;&lt;span class=&quot;btn-text blue&quot;&gt;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&lt;/span&gt;&lt;/a&gt;&lt;/div&gt;`;return a})());return (()=&gt;{console.clear();return decodeURI('%E7%A5%9E%E7%A7%98%E6%8C%89%E9%92%AE%E5%87%BA%E7%8E%B0%EF%BC%81')})()})()<br /> <br /> \[<br /> test<br /> \]<br /> <br /> &lt;/nowiki&gt;&lt;/small&gt;&lt;/small&gt;<br /> [[分类:入门]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=Test&diff=3474 2026-07-19T13:24:30Z

<p>0100000000a7：​</p> <hr /> <div>此页面为测试页面。任何人都可以随意修改此页面以便测试。<br /> <br /> === 编写技巧 ===<br /> <br /> * 行内代码块：&lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;code&gt;xxx&lt;/code&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;code&gt;xxx&lt;/code&gt;。<br /> * 在列表里换行：使用 &lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;br&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;br&gt;第一行；&lt;br&gt;第二行。<br /> * 在列表里嵌套列表：无序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ul&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ul&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：&lt;ul&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ul&gt;有序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ol&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ol&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：<br /> &lt;ol&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ol&gt;于是可以&lt;ul&gt; &lt;li&gt;awa&lt;ul&gt; &lt;li&gt;114514&lt;ul&gt; &lt;li&gt;3.1415926&lt;ul&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;789&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;2.71828&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;qwerty&lt;/li&gt; &lt;/ul&gt;<br /> &lt;ol&gt; &lt;li&gt;awa&lt;ol&gt; &lt;li&gt;114514&lt;ol&gt; &lt;li&gt;3.1415926&lt;ol&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;789&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;2.71828&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;qwerty&lt;/li&gt; &lt;/ol&gt;<br /> * 分界线：使用 &lt;code&gt;----&lt;/code&gt;。效果是这样：<br /> <br /> ----<br /> <br /> 这句话有7个字<br /> <br /> &lt;math&gt;\varnothing,\emptyset&lt;/math&gt;，<br /> \(\varnothing,\emptyset\)<br /> LaTeX公式&lt;code&gt;\varnothing,\emptyset&lt;/code&gt;用不同渲染方式的结果<br /> <br /> &lt;math display=&quot;block&quot;&gt;\begin{aligned}<br /> f(x)\;&amp;=(a+b+1)/2-x\\<br /> &amp;=(a+2x-1-a+f(2x-1-a)+1)/2-x\\<br /> &amp;=f(2x-1-a)/2\\<br /> &amp;=f(2x-1-(x-1+f(x-1)))/2\\<br /> &amp;=f(x-f(x-1))/2<br /> \end{aligned}&lt;/math&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> 111<br /> <br /> \( G(64)=\left. \begin{matrix} 3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \cdots \uparrow}3 \\3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \uparrow}3 \\ \underbrace{\qquad \quad \vdots \qquad \quad} \\3\underbrace{\uparrow \uparrow \cdots \cdots \uparrow}3 \\3\uparrow \uparrow \uparrow \uparrow3\end{matrix} \right \} \text{64 layers} \)<br /> <br /> &lt;math&gt;\unicode{64}&lt;/math&gt;<br /> <br /> &lt;math&gt;\varphi(\#,(\alpha+1)\text{@}(\beta+1),0\text{@}0)[0]=0&lt;/math&gt;<br /> <br /> &lt;math&gt;\text{@}&lt;/math&gt;<br /> <br /> [k]<br /> <br /> \(\alpha\text{@}\beta\)<br /> <br /> 其实还可以有个更简单的做法，\alpha{@}\beta = \(\alpha{@}\beta\)<br /> <br /> [[[a]]]<br /> <br /> 我们可以使用&lt;code&gt;\hspace&lt;/code&gt;和&lt;code&gt;\raise&lt;/code&gt;来微调LaTeX中的字符位置：<br /> \(\LaTeX\)''（直接使用''&lt;code&gt;\LaTeX&lt;/code&gt;''的版本）''<br /> \({L^{\hspace{-4.5px}\raise{-2.5px}A}<br /> \hspace{-3px}T\hspace{-2px}\raise{-3px}E\hspace{-1.5px}X}\)''（使用以上两种命令微调的模仿版本）''<br /> <br /> &lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;(&lt;/span&gt;\alpha\text{@}\beta&lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;)&lt;/span&gt; = \(\alpha\text{@}\beta\)<br /> <br /> <br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {a}<br /> <br /> <br /> &lt;code&gt;我是code&lt;/code&gt;<br /> <br /> <br /> &lt;pre&gt;我是pre&lt;/pre&gt;<br /> <br /> <br /> &lt;span style='background:linear-gradient(to right,#00ff00,#0000ff);-webkit-background-clip:text;-webkit-text-fill-color:transparent;'&gt;我是美丽的span&lt;/span&gt;<br /> <br /> &lt;a href='https://baidu.com'&gt;危险的代码是不被允许的&lt;/a&gt;<br /> <br /> &lt;span onclick='this.innerText=&quot;onclick是无效的！&quot;'&gt;click me!&lt;/span&gt;<br /> <br /> 666<br /> <br /> \(\alpha @\beta\)<br /> <br /> &lt;blockquote&gt;<br /> 我是猫娘。喵喵喵喵<br /> &lt;/blockquote&gt;<br /> <br /> &lt;blockquote&gt;单行引言&lt;/blockquote&gt;<br /> <br /> &lt;span style='background-color:red'&gt;bgcisred&lt;/span&gt;<br /> <br /> [[高德纳箭头|↑]]<br /> <br /> &lt;iframe&gt;<br /> src=&quot;https://expander.googology.top/index.html&quot; <br /> width=&quot;100%&quot; <br /> height=&quot;500px&quot;<br /> frameborder=&quot;0&quot;<br /> &lt;/iframe&gt;<br /> <br /> === 这是一级标题 ===<br /> <br /> ==== 这是二级标题 ====<br /> 这是公式 \(\alpha\times\beta\)<br /> <br /> ''撒反对''<br /> <br /> 说说不可说】(1)<br /> <br /> --------------------------------------------------------------------<br /> <br /> 　　 人们的对话中，「不可说」指的是「不可以说出来」的意思，但是在佛<br /> 经中，不可说的意思并不一定是这样，世尊所说的佛经更不是指这个意思。<br /> 如果它是指不可以说出来的话，那麽全部的佛经就是一部「大妄语百科」了。<br /> <br /> 但是将「不可说」解释为「不可以说出来」的意思，并不是现代人的专<br /> 利，古人解经，也常把它作这样的解释，造成後人将佛经解释成玄密的经典，<br /> 一切的不合理之处都当作「不可说」来处理。<br /> <br /> 世尊的确说过许多的不可说，如:《华严经》<br /> 「不可言说不可说，充满一切不可说，不可言说诸劫中，说不可说不可尽，<br /> ....<br /> 於一微细毛端处，有不可说诸普贤，....一毛端处所有刹，其数无量不可<br /> 　说..」在第四十五卷中，世尊一口气说了将近四百个不可说。<br /> <br /> 《地藏菩萨本愿经》【忉利天宫神通品】「尔时，十方无量世界不可<br /> 　说不可说一切诸佛，及大菩萨摩诃萨，皆来集会，赞叹释迦牟尼佛．．」<br /> 这里用了两个不可说。<br /> <br /> 《小般若经》【深功德品】「一切法不可说，须菩提，一切法空相不<br /> 可说．．」<br /> <br /> 其实「不可说」的意义是「数量大到无法用语言形容」的意思，并不<br /> 是指所说的主题「不能说」，如果是不能说，那麽上面这些经典就是「废<br /> 话大全」了。<br /> <br /> 世尊说法四十九年，探讨的主题遍及人类所有的疑问，从来没有一样<br /> 　是「不能说出来」的，不但他老人家自己说，更鼓励所有修行菩萨要为众　<br /> 生说呢。(参见《般若经》)<br /> <br /> 那麽，「不可说」倒底有多大，会大到语言法形容呢？我们试著来找<br /> 找看。<br /> <br /> {| class=&quot;wikitable&quot; border=&quot;0&quot; cellpadding=&quot;1&quot; cellspacing=&quot;1&quot;<br /> ! scope=&quot;col&quot; |<br /> ! scope=&quot;col&quot; |A<br /> ! scope=&quot;col&quot; |B<br /> |-<br /> |0<br /> |1RB<br /> 1LA<br /> &lt;br&gt;1CP<br /> &lt;br&gt;114514<br /> |1LA<br /> |-<br /> |1<br /> |1LB<br /> |1RB<br /> |}<br /> 111<br /> <br /> {| class=&quot;wikitable&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | style=&quot;width: 20%;&quot; | 张三 || style=&quot;width: 80%; word-wrap: break-word;&quot; | 这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> 表格？<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;width: 300px; overflow: hidden; text-overflow: ellipsis&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | 张三<br /> | 这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> &lt;blockquote&gt;这里是一个孤立页面 我不知道它为什么还在这里<br /> <br /> 就当作是gggwiki的一个彩蛋吧（&lt;/blockquote&gt;<br /> <br /> <br /> <br /> <br /> <br /> [https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 果糕]<br /> 果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！<br /> <br /> &lt;div id=&quot;guogao1&quot;&gt;将以下代码放入控制台并回车，有“小惊喜”：&lt;/div&gt;&lt;small&gt;&lt;small&gt;&lt;nowiki&gt;(()=&gt;{document.getElementById(&quot;guogao1&quot;).appendChild((()=&gt;{let a = document.createElement(&quot;div&quot;);a.innerHTML = `&lt;div class=&quot;fixed-btn&quot;&gt;&lt;a onclick=&quot;let b=document.createElement('div');b.innerHTML=\`&lt;div id='guogao' style='transition: transform .5s ease-out;position: absolute;top:45%;left:50%;z-index: 9999999;transform: scale(1);cursor: pointer;-webkit-user-select: none;-moz-user-select: none;-ms-user-select: none;user-select: none;' onclick='this.remove()'&gt;${decodeURI('%F0%9F%98%B0')}&lt;/div&gt;\`;document.body.appendChild(b);setTimeout(() =&gt; {document.getElementById('guogao').style.transform='scale(45)'}, 50)&quot; class=&quot;new&quot; title=&quot;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&quot;&gt;&lt;span class=&quot;btn-text blue&quot;&gt;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&lt;/span&gt;&lt;/a&gt;&lt;/div&gt;`;return a})());return (()=&gt;{console.clear();return decodeURI('%E7%A5%9E%E7%A7%98%E6%8C%89%E9%92%AE%E5%87%BA%E7%8E%B0%EF%BC%81')})()})()<br /> <br /> &lt;/nowiki&gt;&lt;/small&gt;&lt;/small&gt;<br /> [[分类:入门]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=Test&diff=3473 2026-07-19T13:24:04Z

<p>0100000000a7：​</p> <hr /> <div>此页面为测试页面。任何人都可以随意修改此页面以便测试。<br /> <br /> === 编写技巧 ===<br /> <br /> * 行内代码块：&lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;code&gt;xxx&lt;/code&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;code&gt;xxx&lt;/code&gt;。<br /> * 在列表里换行：使用 &lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;br&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;br&gt;第一行；&lt;br&gt;第二行。<br /> * 在列表里嵌套列表：无序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ul&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ul&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：&lt;ul&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ul&gt;有序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ol&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ol&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：<br /> &lt;ol&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ol&gt;于是可以&lt;ul&gt; &lt;li&gt;awa&lt;ul&gt; &lt;li&gt;114514&lt;ul&gt; &lt;li&gt;3.1415926&lt;ul&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;789&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;2.71828&lt;/li&gt; &lt;/ul&gt;&lt;/li&gt; &lt;li&gt;qwerty&lt;/li&gt; &lt;/ul&gt;<br /> &lt;ol&gt; &lt;li&gt;awa&lt;ol&gt; &lt;li&gt;114514&lt;ol&gt; &lt;li&gt;3.1415926&lt;ol&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;789&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;2.71828&lt;/li&gt; &lt;/ol&gt;&lt;/li&gt; &lt;li&gt;qwerty&lt;/li&gt; &lt;/ol&gt;<br /> * 分界线：使用 &lt;code&gt;----&lt;/code&gt;。效果是这样：<br /> <br /> ----<br /> <br /> 这句话有7个字<br /> <br /> &lt;math&gt;\varnothing,\emptyset&lt;/math&gt;，<br /> \(\varnothing,\emptyset\)<br /> LaTeX公式&lt;code&gt;\varnothing,\emptyset&lt;/code&gt;用不同渲染方式的结果<br /> <br /> &lt;math display=&quot;block&quot;&gt;\begin{aligned}<br /> f(x)\;&amp;=(a+b+1)/2-x\\<br /> &amp;=(a+2x-1-a+f(2x-1-a)+1)/2-x\\<br /> &amp;=f(2x-1-a)/2\\<br /> &amp;=f(2x-1-(x-1+f(x-1)))/2\\<br /> &amp;=f(x-f(x-1))/2<br /> \end{aligned}&lt;/math&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> 111<br /> <br /> \( G(64)=\left. \begin{matrix} 3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \cdots \uparrow}3 \\3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \uparrow}3 \\ \underbrace{\qquad \quad \vdots \qquad \quad} \\3\underbrace{\uparrow \uparrow \cdots \cdots \uparrow}3 \\3\uparrow \uparrow \uparrow \uparrow3\end{matrix} \right \} \text{64 layers} \)<br /> <br /> &lt;math&gt;\unicode{64}&lt;/math&gt;<br /> <br /> &lt;math&gt;\varphi(\#,(\alpha+1)\text{@}(\beta+1),0\text{@}0)[0]=0&lt;/math&gt;<br /> <br /> &lt;math&gt;\text{@}&lt;/math&gt;<br /> <br /> [k]<br /> <br /> \(\alpha\text{@}\beta\)<br /> <br /> 其实还可以有个更简单的做法，\(\alpha{@}\beta\)<br /> <br /> [[[a]]]<br /> <br /> 我们可以使用&lt;code&gt;\hspace&lt;/code&gt;和&lt;code&gt;\raise&lt;/code&gt;来微调LaTeX中的字符位置：<br /> \(\LaTeX\)''（直接使用''&lt;code&gt;\LaTeX&lt;/code&gt;''的版本）''<br /> \({L^{\hspace{-4.5px}\raise{-2.5px}A}<br /> \hspace{-3px}T\hspace{-2px}\raise{-3px}E\hspace{-1.5px}X}\)''（使用以上两种命令微调的模仿版本）''<br /> <br /> &lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;(&lt;/span&gt;\alpha\text{@}\beta&lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;)&lt;/span&gt; = \(\alpha\text{@}\beta\)<br /> <br /> <br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {a}<br /> <br /> <br /> &lt;code&gt;我是code&lt;/code&gt;<br /> <br /> <br /> &lt;pre&gt;我是pre&lt;/pre&gt;<br /> <br /> <br /> &lt;span style='background:linear-gradient(to right,#00ff00,#0000ff);-webkit-background-clip:text;-webkit-text-fill-color:transparent;'&gt;我是美丽的span&lt;/span&gt;<br /> <br /> &lt;a href='https://baidu.com'&gt;危险的代码是不被允许的&lt;/a&gt;<br /> <br /> &lt;span onclick='this.innerText=&quot;onclick是无效的！&quot;'&gt;click me!&lt;/span&gt;<br /> <br /> 666<br /> <br /> \(\alpha @\beta\)<br /> <br /> &lt;blockquote&gt;<br /> 我是猫娘。喵喵喵喵<br /> &lt;/blockquote&gt;<br /> <br /> &lt;blockquote&gt;单行引言&lt;/blockquote&gt;<br /> <br /> &lt;span style='background-color:red'&gt;bgcisred&lt;/span&gt;<br /> <br /> [[高德纳箭头|↑]]<br /> <br /> &lt;iframe&gt;<br /> src=&quot;https://expander.googology.top/index.html&quot; <br /> width=&quot;100%&quot; <br /> height=&quot;500px&quot;<br /> frameborder=&quot;0&quot;<br /> &lt;/iframe&gt;<br /> <br /> === 这是一级标题 ===<br /> <br /> ==== 这是二级标题 ====<br /> 这是公式 \(\alpha\times\beta\)<br /> <br /> ''撒反对''<br /> <br /> 说说不可说】(1)<br /> <br /> --------------------------------------------------------------------<br /> <br /> 　　 人们的对话中，「不可说」指的是「不可以说出来」的意思，但是在佛<br /> 经中，不可说的意思并不一定是这样，世尊所说的佛经更不是指这个意思。<br /> 如果它是指不可以说出来的话，那麽全部的佛经就是一部「大妄语百科」了。<br /> <br /> 但是将「不可说」解释为「不可以说出来」的意思，并不是现代人的专<br /> 利，古人解经，也常把它作这样的解释，造成後人将佛经解释成玄密的经典，<br /> 一切的不合理之处都当作「不可说」来处理。<br /> <br /> 世尊的确说过许多的不可说，如:《华严经》<br /> 「不可言说不可说，充满一切不可说，不可言说诸劫中，说不可说不可尽，<br /> ....<br /> 於一微细毛端处，有不可说诸普贤，....一毛端处所有刹，其数无量不可<br /> 　说..」在第四十五卷中，世尊一口气说了将近四百个不可说。<br /> <br /> 《地藏菩萨本愿经》【忉利天宫神通品】「尔时，十方无量世界不可<br /> 　说不可说一切诸佛，及大菩萨摩诃萨，皆来集会，赞叹释迦牟尼佛．．」<br /> 这里用了两个不可说。<br /> <br /> 《小般若经》【深功德品】「一切法不可说，须菩提，一切法空相不<br /> 可说．．」<br /> <br /> 其实「不可说」的意义是「数量大到无法用语言形容」的意思，并不<br /> 是指所说的主题「不能说」，如果是不能说，那麽上面这些经典就是「废<br /> 话大全」了。<br /> <br /> 世尊说法四十九年，探讨的主题遍及人类所有的疑问，从来没有一样<br /> 　是「不能说出来」的，不但他老人家自己说，更鼓励所有修行菩萨要为众　<br /> 生说呢。(参见《般若经》)<br /> <br /> 那麽，「不可说」倒底有多大，会大到语言法形容呢？我们试著来找<br /> 找看。<br /> <br /> {| class=&quot;wikitable&quot; border=&quot;0&quot; cellpadding=&quot;1&quot; cellspacing=&quot;1&quot;<br /> ! scope=&quot;col&quot; |<br /> ! scope=&quot;col&quot; |A<br /> ! scope=&quot;col&quot; |B<br /> |-<br /> |0<br /> |1RB<br /> 1LA<br /> &lt;br&gt;1CP<br /> &lt;br&gt;114514<br /> |1LA<br /> |-<br /> |1<br /> |1LB<br /> |1RB<br /> |}<br /> 111<br /> <br /> {| class=&quot;wikitable&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | style=&quot;width: 20%;&quot; | 张三 || style=&quot;width: 80%; word-wrap: break-word;&quot; | 这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> 表格？<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;width: 300px; overflow: hidden; text-overflow: ellipsis&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | 张三<br /> | 这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> &lt;blockquote&gt;这里是一个孤立页面 我不知道它为什么还在这里<br /> <br /> 就当作是gggwiki的一个彩蛋吧（&lt;/blockquote&gt;<br /> <br /> <br /> <br /> <br /> <br /> [https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 果糕]<br /> 果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！<br /> <br /> &lt;div id=&quot;guogao1&quot;&gt;将以下代码放入控制台并回车，有“小惊喜”：&lt;/div&gt;&lt;small&gt;&lt;small&gt;&lt;nowiki&gt;(()=&gt;{document.getElementById(&quot;guogao1&quot;).appendChild((()=&gt;{let a = document.createElement(&quot;div&quot;);a.innerHTML = `&lt;div class=&quot;fixed-btn&quot;&gt;&lt;a onclick=&quot;let b=document.createElement('div');b.innerHTML=\`&lt;div id='guogao' style='transition: transform .5s ease-out;position: absolute;top:45%;left:50%;z-index: 9999999;transform: scale(1);cursor: pointer;-webkit-user-select: none;-moz-user-select: none;-ms-user-select: none;user-select: none;' onclick='this.remove()'&gt;${decodeURI('%F0%9F%98%B0')}&lt;/div&gt;\`;document.body.appendChild(b);setTimeout(() =&gt; {document.getElementById('guogao').style.transform='scale(45)'}, 50)&quot; class=&quot;new&quot; title=&quot;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&quot;&gt;&lt;span class=&quot;btn-text blue&quot;&gt;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&lt;/span&gt;&lt;/a&gt;&lt;/div&gt;`;return a})());return (()=&gt;{console.clear();return decodeURI('%E7%A5%9E%E7%A7%98%E6%8C%89%E9%92%AE%E5%87%BA%E7%8E%B0%EF%BC%81')})()})()<br /> <br /> &lt;/nowiki&gt;&lt;/small&gt;&lt;/small&gt;<br /> [[分类:入门]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2904 2026-02-28T15:00:28Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月28日，目前可以确定大于以下序列的PPS存在无穷降链：<br /> <br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9,3,0,21,19,3,0,0,21,<br /> <br /> &lt;span style=&quot;color: red&quot;&gt;18,9,3,0&lt;/span&gt;,<br /> <br /> &lt;span style=&quot;color: red&quot;&gt;31,28,9,3,0&lt;/span&gt;,<br /> <br /> &lt;span style=&quot;color: blue&quot;&gt;36,27,18,9,3,0&lt;/span&gt;,<br /> <br /> &lt;span style=&quot;color: blue&quot;&gt;42,38,18,9,3,0&lt;/span&gt;,<br /> <br /> &lt;span style=&quot;color: green&quot;&gt;48,37,27,18,9,3,0&lt;/span&gt;,<br /> <br /> &lt;span style=&quot;color: green&quot;&gt;55,50,27,18,9,3,0&lt;/span&gt;,<br /> <br /> &lt;span style=&quot;color: brown&quot;&gt;62,49,37,27,18,9,3,0&lt;/span&gt;,<br /> <br /> &lt;span style=&quot;color: brown&quot;&gt;70,64,37,27,18,9,3,0&lt;/span&gt;,<br /> <br /> &lt;span style=&quot;color: purple&quot;&gt;78,63,49,37,27,18,9,3,0&lt;/span&gt;,<br /> <br /> &lt;span style=&quot;color: purple&quot;&gt;87,80,49,37,27,18,9,3,0&lt;/span&gt;,...<br /> <br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 根据3165991573的分析，我们可以确定目前PPS的良序极限为ζ₀，但0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10不良序。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2903 2026-02-28T14:58:58Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月28日，目前可以确定大于以下序列的PPS存在无穷降链：<br /> <br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9,3,0,21,19,3,0,0,21,<br /> &lt;span style=&quot;color: red&quot;&gt;18,9,3,0&lt;/span&gt;,<br /> &lt;span style=&quot;color: red&quot;&gt;31,28,9,3,0&lt;/span&gt;,<br /> &lt;span style=&quot;color: blue&quot;&gt;36,27,18,9,3,0&lt;/span&gt;,<br /> &lt;span style=&quot;color: blue&quot;&gt;42,38,18,9,3,0&lt;/span&gt;,<br /> &lt;span style=&quot;color: green&quot;&gt;48,37,27,18,9,3,0&lt;/span&gt;,<br /> &lt;span style=&quot;color: green&quot;&gt;55,50,27,18,9,3,0&lt;/span&gt;,<br /> &lt;span style=&quot;color: brown&quot;&gt;62,49,37,27,18,9,3,0&lt;/span&gt;,<br /> &lt;span style=&quot;color: brown&quot;&gt;70,64,37,27,18,9,3,0&lt;/span&gt;,<br /> &lt;span style=&quot;color: purple&quot;&gt;78,63,49,37,27,18,9,3,0&lt;/span&gt;,<br /> &lt;span style=&quot;color: purple&quot;&gt;87,80,49,37,27,18,9,3,0&lt;/span&gt;,<br /> <br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 根据3165991573的分析，我们可以确定目前PPS的良序极限为ζ₀，但0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10不良序。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2902 2026-02-28T14:43:24Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月28日，目前可以确定大于以下序列的PPS存在无穷降链：<br /> <br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9,3,0,21,19,3,0,0,21,18,9,3,0,31,28,9,3,0,36,27,18,9,3,0,42,38,18,9,3,0,48,37,27,18,9,3,0,55,50,27,18,9,3,0,62,49,37,27,18,9,3,0,70,64,37,27,18,9,3,0,78,63,49,37,27,18,9,3,0,87,80,49,37,27,18,9,3,0,96,79,63,49,37,27,18,9,3,0,106,98,63,49,37,27,18,9,3,0,......<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 根据3165991573的分析，我们可以确定目前PPS的良序极限为ζ₀，但0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10不良序。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2901 2026-02-28T14:41:26Z

<p>0100000000a7：​无穷降链更新</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月28日，目前可以确定大于以下序列的PPS存在无穷降链：<br /> <br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9,3,0,21,19,3,0,0,21,18,9,3,0,31,28,9,3,0,36,27,18,9,3,0,42,38,18,9,3,0,48,37,27,18,9,3,0,55,50,27,18,9,3,0,62,49,37,27,18,9,3,0,70,64,37,27,18,9,3,0,78,63,49,37,27,18,9,3,0,87,80,49,37,27,18,9,3,0,96,79,63,49,37,27,18,9,3,0,106,98,63,49,37,27,18,9,3,0,......<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ PPS良序极限是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 根据3165991573的分析，我们可以确定PPS的良序极限为ζ₀<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2816 2026-02-23T09:16:00Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月23日，目前可以确定大于以下序列的PPS存在无穷降链：<br /> 0,1,&lt;span style=&quot;color:red;&quot;&gt;0,2,2,0,5,2,0,8,8,6,0,12,8,6,0,16,16,15,0,16,16,15,0,15,0,26,26,15,0,26,26,13,6,2,0,15,0,38,38,15,0,38,15,0,45,45,13,8,6,0,0,38,15,0,55,55,13,0,59,58,0,62,58,0,63,53,15,0,0,0,62,55,0,74,74,74,72,55&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0,80,80,0,83,80,0,86,86,84,0,90,86,84,0,94,94,93,0,94,94,93,0,93,0,104,104,93,0,104,104,91,84,80,0,93,0,116,116,93,0,116,93,0,123,123,91,86,84,0,0,116,93,0,133,133,91,0,137,136,0,140,136,0,141,131,93,0,0,0,140,133,0,152,152,152,150,133&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0,158,158,0,161,158,0,164,164,162,0,168,164,162,0,172,172,171,0,172,172,171,0,171,0,182,182,171,0,182,182,169,162,158,0,171,0,194,194,171,0,194,171,0,201,201,169,164,162,0,0,194,171,0,211,211,169,0,215,214,0,218,214,0,219,209,171,0,0,0,218,211,0,230,230,230,228,211&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0,236,236,0,239,236,0,242,242,240,0,246,242,240,0,250,250,249,0,250,250,249,0,249,0,260,260,249,0,260,260,247,240,236,0,249,0,272,272,249,0,272,249,0,279,279,247,242,240,0,0,272,249,0,289,289,247,0,293,292,0,296,292,0,297,287,249,0,0,0,296,289,0,308,308,308,306,289&lt;/span&gt;,...<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2811 2026-02-23T05:03:19Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月23日，目前可以确定大于以下序列的PPS存在无穷降链：<br /> 0,1,&lt;span style=&quot;color:red;&quot;&gt;0,2,2,0,5,2,0,8,8,6,0,12,8,6,0,16,16,15,0,16,16,15,0,15,0,26,26,15,0,26,26,13,6,2,0,15,0,38,38,15,0,38,15,0,45,45,13,8,6,0,0,38,15,0,55,55,13,0,59,59,53,15,0,59,59,53&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0,68,68,0,71,68,0,74,74,72,0,78,74,72,0,82,82,81,0,82,82,81,0,81,0,92,92,81,0,92,92,79,72,68,0,81,0,104,104,81,0,104,81,0,111,111,79,74,72,0,0,104,81,0,121,121,79,0,125,125,119,81,0,125,125,119&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0,134,134,0,137,134,0,140,140,138,0,144,140,138,0,148,148,147,0,148,148,147,0,147,0,158,158,147,0,158,158,145,138,134,0,147,0,170,170,147,0,170,147,0,177,177,145,140,138,0,0,170,147,0,187,187,145,0,191,191,185,147,0,191,191,185&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0,200,200,0,203,200,0,206,206,204,0,210,206,204,0,214,214,213,0,214,214,213,0,213,0,224,224,213,0,224,224,211,204,200,0,213,0,236,236,213,0,236,213,0,243,243,211,206,204,0,0,236,213,0,253,253,211,0,257,257,251,213,0,257,257,251&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0,266,266,0,269,266,0,272,272,270,0,276,272,270,0,280,280,279,0,280,280,279,0,279,0,290,290,279,0,290,290,277,270,266,0,279,0,302,302,279,0,302,279,0,309,309,277,272,270,0,0,302,279,0,319,319,277,0,323,323,317,279,0,323,323,317&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0,332,332,0,335,332,0,338,338,336,0,342,338,336,0,346,346,345,0,346,346,345,0,345,0,356,356,345,0,356,356,343,336,332,0,345,0,368,368,345,0,368,345,0,375,375,343,338,336,0,0,368,345,0,385,385,343,0,389,389,383,345,0,389,389,383&lt;/span&gt;,...<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2810 2026-02-23T01:38:02Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月23日，目前可以确定大于以下序列的PPS存在无穷降链：<br /> 0,1,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;5&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;12&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;51&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;43&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;63&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;70&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;71&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;71&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;109&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;101&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;71&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;121&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;128&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;154&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;154&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;154&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;167&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;159&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;179&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;186&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;225&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;217&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;237&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;244&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;283&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;275&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;295&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;302&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;341&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;333&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,...<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2809 2026-02-23T01:29:18Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月23日，目前可以确定大于0,1,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;5&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;12&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;51&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;43&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;63&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;70&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;71&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;71&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;109&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;101&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;71&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;121&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;128&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;154&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;154&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;154&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;167&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;159&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;179&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;186&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;225&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;217&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;237&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;244&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;283&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;275&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;295&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;302&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;341&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;333&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,...的PPS序列存在无穷降链<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2808 2026-02-23T01:24:49Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月23日，目前PPS的已知良序极限上界为0,1,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;5&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;12&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;51&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;43&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;63&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;70&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;71&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;71&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;109&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;101&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;71&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;121&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;128&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;154&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;154&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;154&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;167&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;159&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;179&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;186&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;225&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;217&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;237&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;244&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;283&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;275&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;295&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;302&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;341&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;333&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,...<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2807 2026-02-23T00:37:44Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月23日，目前PPS的已知良序极限(实际可能更低)为0,1,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;5&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;12&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;51&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;43&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;63&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;70&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span 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style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span 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style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;167&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;159&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;179&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;186&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;225&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;217&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;237&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;244&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;283&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;275&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;295&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;302&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;341&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;333&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,...<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2806 2026-02-23T00:23:49Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月23日，目前PPS的已知良序极限为0,1,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;5&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;12&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;51&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;43&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;63&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;70&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;71&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span 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style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;154&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;154&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;154&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;167&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;159&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;179&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;186&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;225&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;217&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;237&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span 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style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;283&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;275&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;295&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;302&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;341&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;333&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,...<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2805 2026-02-23T00:20:41Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月23日，目前PPS的已知良序极限为0,1,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;5&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;12&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;51&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;43&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;63&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;70&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span 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style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;341&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;333&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;background: linear-gradient(90deg, red, orange, yellow, green, blue, indigo, violet); -webkit-background-clip: text; -webkit-text-fill-color: transparent; color: transparent;&quot;&gt;...&lt;/span&gt;<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2804 2026-02-23T00:14:37Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月23日，目前PPS的已知良序极限为0,1,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;5&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;12&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;51&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;43&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;63&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;70&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;71&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;71&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;109&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;101&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;71&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;121&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;128&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;154&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;154&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;154&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;167&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;159&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;179&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;186&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;225&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;217&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;237&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;244&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;283&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;275&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;295&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;302&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;341&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;333&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2803 2026-02-23T00:12:55Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月22日，目前PPS的已知良序极限为0,1,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;5&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;12&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;16&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;26&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;2&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;38&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;8&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;6&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;51&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;43&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;15&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;45&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;13&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;63&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;70&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;74&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;84&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;71&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;60&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;96&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;71&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;66&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;64&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;109&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;101&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;73&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;103&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;71&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;121&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;118&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;128&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;132&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;142&lt;/span&gt;,&lt;span 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style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;124&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;122&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;167&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;159&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;131&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;161&lt;/span&gt;,&lt;span style=&quot;color:green;&quot;&gt;129&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;179&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;186&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;190&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;200&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;176&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;212&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;182&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;180&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;225&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;217&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;189&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;219&lt;/span&gt;,&lt;span style=&quot;color:purple;&quot;&gt;187&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;237&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;244&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;283&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;275&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:orange;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;295&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;302&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;341&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;333&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:brown;&quot;&gt;303&lt;/span&gt;<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2802 2026-02-23T00:07:58Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月22日，目前PPS的已知良序极限为0,1,0,2,2,0,5,2,0,8,8,6,0,12,8,6,0,16,16,15,0,16,16,15,0,15,0,26,26,15,0,26,26,13,6,2,0,15,0,38,38,15,0,38,15,0,45,45,13,8,6,0,51,43,15,0,0,45,45,13,0,60,60,0,63,60,0,66,66,64,0,70,66,64,0,74,74,73,0,74,74,73,0,73,0,84,84,73,0,84,84,71,64,60,0,73,0,96,96,73,0,96,73,0,103,103,71,66,64,0,109,101,73,0,0,103,103,71,0,118,118,0,121,118,0,124,124,122,0,128,124,122,0,132,132,131,0,132,132,131,0,131,0,142,142,131,0,142,142,129,122,118,0,131,0,154,154,131,0,154,131,0,161,161,129,124,122,0,167,159,131,0,0,161,161,129,0,176,176,0,179,176,0,182,182,180,0,186,182,180,0,190,190,189,0,190,190,189,0,189,0,200,200,189,0,200,200,187,180,176,0,189,0,212,212,189,0,212,189,0,219,219,187,182,180,0,225,217,189,0,0,219,219,187,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;237&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;244&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;248&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;258&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;234&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;270&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;240&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;238&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;283&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;275&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;247&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;277&lt;/span&gt;,&lt;span style=&quot;color:red;&quot;&gt;245&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;295&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;302&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;306&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;316&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;292&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;328&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;303&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;298&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;296&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;341&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;333&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;305&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;0&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;335&lt;/span&gt;,&lt;span style=&quot;color:blue;&quot;&gt;303&lt;/span&gt;,...<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2800 2026-02-22T15:04:15Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月22日，目前PPS的已知良序极限为0,1,0,2,2,0,5,2,0,8,8,6,0,12,8,6,0,16,16,15,0,16,16,15,0,15,0,26,26,15,0,26,26,13,6,2,0,26,13,8,6,0,0,15,0,44,44,15,0,44,15,0,51,51,0,54,54,49,15,&lt;span style=&quot;color:blue&quot;&gt;0,59,59,0,62,59,0,65,65,63,0,69,65,63,0,73,73,72,0,73,73,72,0,72,0,83,83,72,0,83,83,70,63,59,0,83,70,65,63,0,0,72,0,101,101,72,0,101,72,0,108,108,0,111,111,106,72&lt;/span&gt;,&lt;span style=&quot;color:red&quot;&gt;0,116,116,0,119,116,0,122,122,120,0,126,122,120,0,130,130,129,0,130,130,129,0,129,0,140,140,129,0,140,140,127,120,116,0,140,127,122,120,0,0,129,0,158,158,129,0,158,129,0,165,165,0,168,168,163,129&lt;/span&gt;,&lt;span style=&quot;color:green&quot;&gt;0,173,173,0,176,173,0,179,179,177,0,183,179,177,0,187,187,186,0,187,187,186,0,186,0,197,197,186,0,197,197,184,177,173,0,197,184,179,177,0,0,186,0,215,215,186,0,215,186,0,222,222,0,225,225,220,186&lt;/span&gt;,&lt;span style=&quot;color:blue&quot;&gt;0,230,230,0,233,230,0,236,236,234,0,240,236,234,0,244,244,243,0,244,244,243,0,243,0,254,254,243,0,254,254,241,234,230,0,254,241,236,234,0,0,243,0,272,272,243,0,272,243,0,279,279,0,282,282,277,243&lt;/span&gt;,&lt;span style=&quot;color:red&quot;&gt;0,287,287,0,290,287,0,293,293,291,0,297,293,291,0,301,301,300,0,301,301,300,0,300,0,311,311,300,0,311,311,298,291,287,0,311,298,293,291,0,0,300,0,329,329,300,0,329,300,0,336,336,0,339,339,334,300&lt;/span&gt;...<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2799 2026-02-22T15:03:05Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月22日，目前PPS的已知良序极限为0,1,0,2,2,0,5,2,0,8,8,6,0,12,8,6,0,16,16,15,0,16,16,15,0,15,0,26,26,15,0,26,26,13,6,2,0,26,13,8,6,0,0,15,0,44,44,15,0,44,15,0,51,51,0,54,54,49,15,0,59,59,0,62,59,0,65,65,63,0,69,65,63,0,73,73,72,0,73,73,72,0,72,0,83,83,72,0,83,83,70,63,59,0,83,70,65,63,0,0,72,0,101,101,72,0,101,72,0,108,108,0,111,111,106,72,&lt;span style=&quot;color:red&quot;&gt;0,116,116,0,119,116,0,122,122,120,0,126,122,120,0,130,130,129,0,130,130,129,0,129,0,140,140,129,0,140,140,127,120,116,0,140,127,122,120,0,0,129,0,158,158,129,0,158,129,0,165,165,0,168,168,163,129&lt;/span&gt;,&lt;span style=&quot;color:green&quot;&gt;0,173,173,0,176,173,0,179,179,177,0,183,179,177,0,187,187,186,0,187,187,186,0,186,0,197,197,186,0,197,197,184,177,173,0,197,184,179,177,0,0,186,0,215,215,186,0,215,186,0,222,222,0,225,225,220,186&lt;/span&gt;,&lt;span style=&quot;color:blue&quot;&gt;0,230,230,0,233,230,0,236,236,234,0,240,236,234,0,244,244,243,0,244,244,243,0,243,0,254,254,243,0,254,254,241,234,230,0,254,241,236,234,0,0,243,0,272,272,243,0,272,243,0,279,279,0,282,282,277,243&lt;/span&gt;,&lt;span style=&quot;color:red&quot;&gt;0,287,287,0,290,287,0,293,293,291,0,297,293,291,0,301,301,300,0,301,301,300,0,300,0,311,311,300,0,311,311,298,291,287,0,311,298,293,291,0,0,300,0,329,329,300,0,329,300,0,336,336,0,339,339,334,300&lt;/span&gt;...<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2798 2026-02-22T14:52:33Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月22日，目前PPS的已知良序极限为0,1,0,2,2,0,5,2,0,8,8,6,0,12,8,6,0,16,16,15,0,16,16,15,0,15,0,26,26,15,0,26,26,13,6,2,0,26,13,8,6,0,0,15,0,44,44,15,0,44,15,0,51,51,0,54,54,49,15,0,59,59,0,62,59,0,65,65,63,0,69,65,63,0,73,73,72,0,73,73,72,0,72,0,83,83,72,0,83,83,70,63,59,0,83,70,65,63,0,0,72,0,101,101,72,0,101,72,0,108,108,0,111,111,106,72,0,116,116,0,119,116,0,122,122,120,0,126,122,120,0,130,130,129,0,130,130,129,0,129,0,140,140,129,0,140,140,127,120,116,0,140,127,122,120,0,0,129,0,158,158,129,0,158,129,0,165,165,0,168,168,163,129,0,173,173,0,176,173,0,179,179,177,0,183,179,177,0,187,187,186,0,187,187,186,0,186,0,197,197,186,0,197,197,184,177,173,0,197,184,179,177,0,0,186,0,215,215,186,0,215,186,0,222,222,0,225,225,220,186,0,230,230,0,233,230,0,236,236,234,0,240,236,234,0,244,244,243,0,244,244,243,0,243,0,254,254,243,0,254,254,241,234,230,0,254,241,236,234,0,0,243,0,272,272,243,0,272,243,0,279,279,0,282,282,277,243,0,287,287,0,290,287,0,293,293,291,0,297,293,291,0,301,301,300,0,301,301,300,0,300,0,311,311,300,0,311,311,298,291,287,0,311,298,293,291,0,0,300,0,329,329,300,0,329,300,0,336,336,0,339,339,334,300...<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2797 2026-02-22T14:52:23Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月21日，目前PPS的已知良序极限为0,1,0,2,2,0,5,2,0,8,8,6,0,12,8,6,0,16,16,15,0,16,16,15,0,15,0,26,26,15,0,26,26,13,6,2,0,26,13,8,6,0,0,15,0,44,44,15,0,44,15,0,51,51,0,54,54,49,15,0,59,59,0,62,59,0,65,65,63,0,69,65,63,0,73,73,72,0,73,73,72,0,72,0,83,83,72,0,83,83,70,63,59,0,83,70,65,63,0,0,72,0,101,101,72,0,101,72,0,108,108,0,111,111,106,72,0,116,116,0,119,116,0,122,122,120,0,126,122,120,0,130,130,129,0,130,130,129,0,129,0,140,140,129,0,140,140,127,120,116,0,140,127,122,120,0,0,129,0,158,158,129,0,158,129,0,165,165,0,168,168,163,129,0,173,173,0,176,173,0,179,179,177,0,183,179,177,0,187,187,186,0,187,187,186,0,186,0,197,197,186,0,197,197,184,177,173,0,197,184,179,177,0,0,186,0,215,215,186,0,215,186,0,222,222,0,225,225,220,186,0,230,230,0,233,230,0,236,236,234,0,240,236,234,0,244,244,243,0,244,244,243,0,243,0,254,254,243,0,254,254,241,234,230,0,254,241,236,234,0,0,243,0,272,272,243,0,272,243,0,279,279,0,282,282,277,243,0,287,287,0,290,287,0,293,293,291,0,297,293,291,0,301,301,300,0,301,301,300,0,300,0,311,311,300,0,311,311,298,291,287,0,311,298,293,291,0,0,300,0,329,329,300,0,329,300,0,336,336,0,339,339,334,300...<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> === 改版 ===<br /> <br /> ==== PPM 1.2 ====<br /> Parented Predecessor Matrix 1,2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 2 ====<br /> Parented Predecessor Matrix 2<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b，则比较[以这个项为首的判断序列]和[以坏根为首的判断序列]的字典序，如果前者大(只要存在一个)∨(坏根不在末项祖先链上∧这样的项存在)则弱展开，如果后者大∨这样的项不存在则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> 其他项展开：对任意的i&gt;y-L+1，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项<br /> <br /> ==== PPM 3 ====<br /> Parented Predecessor Matrix 3<br /> <br /> 极限表达式：(0)(1,1,1,1,1,...)<br /> <br /> LNZ：末列的最大非零行序号<br /> <br /> 坏根：第(末项的值)列LNZ行的元素，其中末项是末列LNZ行（首项的列标是1、首项是第1项）；如果末列是全0，则表示后继序数<br /> <br /> 记此时末项的列标减末项的值为L，坏根的值为b、列标为c，末项的值为x、列标为y<br /> <br /> 末列展开：{<br /> <br /> 把末列LNZ-1行的祖先链上（设第0行父项固定为前一项）所有列的LNZ行元素提取出来组成判断序列；在判断序列中，如果末项和坏根之间(两边都不含)存在一项，它的值等于b则弱展开，否则强展开。<br /> <br /> 弱展开：LNZ行之前的不变，LNZ行及之后的用坏根列的相同行元素替换<br /> <br /> 强展开：LNZ行之前的不变，LNZ行的值减一，LNZ行之后的行是(坏根列同行元素+展开后末项的值-坏根项的值)<br /> <br /> }<br /> <br /> 末列以右整数个复制单元长度的列展开：强展开时LNZ行元素的值每次复制时增加一个复制单元长度，其他同“其他项展开”<br /> <br /> 其他项展开：对任意的i&gt;y-L，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 基本列[n]为展开到第y+nL-1项{{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=Loader_%E6%95%B0&diff=2795 2026-02-22T09:31:43Z

<p>0100000000a7：​</p> <hr /> <div>'''Loader 数'''是 Ralph Loader 的 C 语言程序 '''Loader.c''' 的输出 &lt;math&gt;D^5(99)&lt;/math&gt;，它在 2001 年的 [[Bignum Bakeoff]] 比赛（用不超过 512 字的代码生成尽可能大的有限整数）中获得第一名。<br /> <br /> 其中 D 函数的强度取决于 Huet-Coquand 构造演算（CoC）的证明论强度，其增长率达到了 &lt;math&gt;{\rm PTO}(Z_\omega)&lt;/math&gt;。迄今为止，它仍然是最强的可计算函数之一。<br /> <br /> === 定义 ===<br /> Loader.c 的源代码&lt;ref&gt;https://github.com/rcls/busy&lt;/ref&gt;如下：&lt;syntaxhighlight lang=&quot;c&quot; line=&quot;1&quot;&gt;<br /> #define R { return<br /> #define P P (<br /> #define L L (<br /> #define T S (v, y, c,<br /> #define C ),<br /> #define X x)<br /> #define F );}<br /> <br /> int r, a;<br /> P y, X<br /> R y - ~y &lt;&lt; x;<br /> }<br /> Z (X<br /> R r = x % 2 ? 0 : 1 + Z (x / 2 F<br /> L X<br /> R x / 2 &gt;&gt; Z (x F<br /> #define U = S(4,13,-4,<br /> T t)<br /> {<br /> int<br /> f = L t C <br /> x = r;<br /> R<br /> f - 2 ?<br /> f &gt; 2 ?<br /> f - v ? t - (f &gt; v) * c : y :<br /> P f, P T L X C <br /> S (v+2, t U y C c, Z (X )))<br /> :<br /> A (T L X C <br /> T Z (X ) F<br /> }<br /> A (y, X<br /> R L y) - 1<br /> ? 5 &lt;&lt; P y, X <br /> : S (4, x, 4, Z (r) F<br /> #define B (x /= 2) % 2 &amp;&amp; (<br /> D (X <br /> {<br /> int<br /> f,<br /> d,<br /> c = 0,<br /> t = 7,<br /> u = 14;<br /> while (x &amp;&amp; D (x - 1 C B 1))<br /> d = L L D (X ) C<br /> f = L r C<br /> x = L r C<br /> c - r || (<br /> L u) || L r) - f ||<br /> B u = S (4, d, 4, r C <br /> t = A (t, d) C<br /> f / 2 &amp; B c = P d, c C <br /> t U t C <br /> u U u) )<br /> C<br /> c &amp;&amp; B<br /> t = P<br /> ~u &amp; 2 | B<br /> u = 1 &lt;&lt; P L c C u) C <br /> P L c C t) C<br /> c = r C<br /> u / 2 &amp; B <br /> c = P t, c C <br /> u U t C <br /> t = 9 );<br /> R a = P P t, P u, P x, c)) C <br /> a F<br /> }<br /> main ()<br /> R D (D (D (D (D (99)))) F<br /> &lt;/syntaxhighlight&gt;此外，Loader 还给出了可读性更高的版本（我们使用中文注释）：&lt;syntaxhighlight lang=&quot;c&quot;&gt;<br /> //Tree、INT、TREE、BitStream 都被定义为 int，只是为了区分用途。<br /> //把宏 DESCEND 直接展开为变量 xx，用于 while 里的递归控制。<br /> typedef int Tree;<br /> typedef int INT;<br /> typedef int TREE;<br /> typedef int BitStream;<br /> #define DESCEND xx<br /> <br /> // 全局临时变量：<br /> // lastRight —— 用于在解码配对结构时暂存“另一半”值；<br /> // accumulate —— 累积所有推导结果（每个结果是(term, type, 剩余比特流, context) 四元组的配对编码）。<br /> Tree lastRight, accumulate;<br /> <br /> <br /> // —— 基础编码：二元配对函数 ——<br /> // 将两个非负整数 yy, xx 编码为一个整数，保证一一对应（双射）。<br /> // 公式：Pair(yy,xx) = (yy − ~yy) &lt;&lt; xx = (2*yy + 1) &lt;&lt; xx<br /> // 这样低位的连续零数目即为 xx，高位奇数部分即为 2*yy+1，方便快速解码。<br /> TREE Pair (TREE yy, TREE xx)<br /> {<br /> return yy - ~yy &lt;&lt; xx;<br /> }<br /> <br /> <br /> // —— 解码：取配对的第二个分量 ——<br /> // 从编码值 xx 中恢复出原始的第二个参数（移位次数）。<br /> // 逻辑：若 xx 为奇数，则移位次数为 0；否则不断除以 2 并累加，直到遇到奇数。<br /> // 计算结果同时写入 lastRight。<br /> TREE Right (TREE xx)<br /> {<br /> return lastRight = xx % 2 ? 0 : 1 + Right (xx / 2);<br /> }<br /> <br /> <br /> // —— 解码：取配对的第一个分量 ——<br /> // 先将编码右移 1 位（去除最低位信息），再右移 Right(xx) 位，得到原始的 yy。<br /> // 上一次调用 Right 时已经把移位计数存入 lastRight，因此这里可直接使用。<br /> TREE Left (TREE xx)<br /> {<br /> return xx / 2 &gt;&gt; Right (xx);<br /> }<br /> <br /> <br /> // —— 宏：提升（Lift） ——<br /> // 将所有自由变量的 De Bruijn 索引统一 +1，维护绑定层级。<br /> // 通过 Subst(vv=4, yy=13, context=-4, term=xx) 实现。<br /> #define Lift(xx) Subst (4, 13, -4, xx)<br /> <br /> <br /> // —— 归一化替换（Subst） ——<br /> // 在 term 中，将索引 vv 的变量替换为术语 yy，并对索引 &gt; vv 的变量减去 context。<br /> // 同时对 λ 抽象 (aux=0)、Π 构造 (aux=1) 和函数应用 (aux=2) 等节点进行递归归一化。<br /> // 参数说明：<br /> // vv : 要替换的变量索引<br /> // yy : 用来替换的术语（已规范化）<br /> // context : 替换后，所有更大索引变量需减去的偏移<br /> // term : 待处理的术语编码<br /> TREE Subst (INT vv, TREE yy, INT context, TREE term)<br /> {<br /> Tree aux = Left (term), // 当前节点类型：0=λ，1=Π，2=应用，&gt;2=变量/常量<br /> xx = lastRight; // 当前节点主体或子配对<br /> <br /> // 按节点类型分支处理<br /> if (aux == 2) {<br /> // 应用节点：先递归替换，再用 Apply 做 β-归约或重构<br /> return Apply (<br /> Subst (vv, yy, context, Left (xx)),<br /> Subst (vv, yy, context, Right (xx))<br /> );<br /> }<br /> else if (aux &gt; 2) {<br /> // 变量或常量：<br /> // 若 aux == vv，则替换为 yy；否则若 aux&gt;vv，就减去偏移 context<br /> return aux == vv<br /> ? yy<br /> : term - (aux &gt; vv ? context : 0);<br /> }<br /> else {<br /> // 抽象节点：aux==0 为 λ，aux==1 为 Π<br /> // 构造新配对 (aux, (子项1', 子项2'))<br /> // 对右子树的 yy 先做 Lift 以调整绑定深度<br /> return Pair (<br /> aux,<br /> Pair (<br /> Subst (vv, yy, context, Left (xx)),<br /> Subst (vv+2, Lift(yy), context, Right (xx))<br /> )<br /> );<br /> }<br /> }<br /> <br /> <br /> // —— 函数应用归一化（Apply） ——<br /> // 若 yy 的操作码 Left(yy)==1（λ 抽象），则对其主体做一次 β-归约：Subst(4, xx, 4, body)。<br /> // 否则重构应用节点 Pair(2, Pair(yy, xx))。<br /> TREE Apply (TREE yy, TREE xx)<br /> {<br /> return Left (yy) == 1<br /> ? Subst (4, xx, 4, Right (lastRight))<br /> : Pair (2, Pair (yy, xx));<br /> }<br /> <br /> <br /> // —— 比特流测试宏 ——<br /> // 把 xx 当作待消费的比特流，每用一次 xx/=2，测试被除后最低位是否为 1。<br /> #define MAYBE (xx /= 2) % 2 &amp;&amp;<br /> <br /> <br /> // —— 主推导过程（Derive） ——<br /> // 将整数 xx 视作一条比特流，按照 Curry–Howard 同构/类型规则生成所有可能的 λ 术语并归一化。<br /> // 输出的(term, type, 剩余比特流, context) 四元组不断累加到全局 accumulate 中。<br /> // 算法概览：<br /> // 1. 递归调用 Derive(xx-1)，保证对所有小于 xx 的比特串也进行推导，确保单调增长。<br /> // 2. 在 while 循环中，依次用 MAYBE 消费一位比特，决定是否执行对应规则：<br /> // - APPLY (函数应用 β-归约)<br /> // - 弱化 (Weaken，将新假设压入上下文，并提升当前项/类型)<br /> // - Π 构造 / λ 引入<br /> // - 变量引入 (VAR(0))<br /> // 3. 每次规则应用后，把当前 term/type/剩余比特流/context 打包配对累积。<br /> TREE Derive (BitStream xx)<br /> {<br /> Tree aux, auxTerm;<br /> Tree context = 0, // 初始空上下文<br /> term = 7, // STAR 常量：Pair(3,0)=7<br /> type = 14; // BOX 常量：Pair(3,1)=14<br /> <br /> // while 条件中先递归 Derive(xx-1)，再根据下一位比特决定是否进入循环体<br /> while (DESCEND &amp;&amp; Derive (xx - 1), MAYBE (1)) {<br /> <br /> // 1) 从子推导中获取一个新项 auxTerm 及其类型 aux<br /> auxTerm = Left (Left (Derive (xx)));<br /> aux = Left (lastRight);<br /> xx = Left (lastRight); // 更新剩余比特流<br /> <br /> // 2) 若当前上下文与子推导上下文相等，则可以尝试 APPLY 或 Weaken<br /> if (context == lastRight) {<br /> // — APPLY：当类型符合 Π(aux, -) 时，对 term 执行函数应用<br /> if (Left (type) == 1 &amp;&amp; Left (lastRight) == aux &amp;&amp; MAYBE (1)) {<br /> type = Subst (4, auxTerm, 4, lastRight);<br /> term = Apply (term, auxTerm);<br /> }<br /> // — 弱化：若 auxType 是 STAR/BOX，可引入新假设<br /> else if ((aux / 2) &amp;&amp; MAYBE (1)) {<br /> context = Pair (auxTerm, context);<br /> term = Lift (term);<br /> type = Lift (type);<br /> }<br /> }<br /> <br /> // 3) Π 构造 或 λ 引入：当上下文非空时，可根据比特选择<br /> if (context &amp;&amp; MAYBE (1)) {<br /> // LHS：若 type 不支持 Π 构造，则强制做 λ 引入，并相应先对 type 做 Π 构造<br /> Tree isLambda = (~type &amp; 2);<br /> if (MAYBE (isLambda)) {<br /> type = Pair (1, Pair (Left (context), type)); // Π(Left(context), type)<br /> }<br /> term = Pair (isLambda | 0, Pair (Left (context), term));<br /> context = lastRight; // 弹出已用的上下文项<br /> }<br /> <br /> // 4) 变量引入：若 type 是 STAR/BOX，可引入 VAR(0)<br /> if ((type / 2) &amp;&amp; MAYBE (1)) {<br /> context = Pair (term, context);<br /> type = Lift (term);<br /> term = Pair (4, 0); // VAR(0)<br /> }<br /> }<br /> <br /> // 将当前四元组打包，并加到 accumulate<br /> return accumulate = Pair (<br /> Pair (term, Pair (type, Pair (xx, context))),<br /> accumulate<br /> );<br /> }<br /> <br /> <br /> // —— 主函数 ——<br /> // 对初值 99 连续调用五次 Derive，以充分“填充” accumulate。<br /> TREE main ()<br /> {<br /> return Derive (Derive (Derive (Derive (Derive (99)))));<br /> }<br /> &lt;/syntaxhighlight&gt;{{默认排序:相关问题}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2758 2026-02-21T10:47:29Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月21日，目前PPS的已知良序极限为0,1,0,2,2,0,5,2,0,8,8,6,0,12,8,6,0,16,16,15,0,16,16,15,0,15,0,26,26,15,0,26,26,13,6,2,0,35,0,26,13,8,6,0,0,15,0,46,46,15,0,46,46,13,6,0,55,55,0,58,58,0,61,61...<br /> <br /> 对PPS无穷降链的寻找可使用[https://github.com/hzyhhzy/AutoGuogaoMachine/tree/master 自动果糕机]进行辅助。<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> {{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=%E8%AE%A8%E8%AE%BA:Test&diff=2740 2026-02-21T09:52:13Z

<p>0100000000a7：​/* 果糕 */ 新章节</p> <hr /> <div>== 果糕 ==<br /> <br /> 果糕 [[用户:0100000000a7|0100000000a7]]（[[用户讨论:0100000000a7|留言]]） 2026年2月21日 (六) 17:52 (CST)</div>

0100000000a7 http://wiki.googology.top/index.php?title=Test&diff=2739 2026-02-21T09:51:47Z

<p>0100000000a7：​撤销0100000000a7（讨论）的修订版本2737</p> <hr /> <div>此页面为测试页面。任何人都可以随意修改此页面以便测试。<br /> <br /> === 编写技巧 ===<br /> <br /> * 行内代码块：&lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;code&gt;xxx&lt;/code&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;code&gt;xxx&lt;/code&gt;。<br /> * 在列表里换行：使用 &lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;br&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;br&gt;第一行；&lt;br&gt;第二行。<br /> * 在列表里嵌套列表：无序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ul&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ul&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：&lt;ul&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ul&gt;有序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ol&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ol&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：<br /> &lt;ol&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ol&gt;<br /> * 分界线：使用 &lt;code&gt;----&lt;/code&gt;。效果是这样：<br /> <br /> ----<br /> <br /> 这句话有7个字<br /> <br /> &lt;math&gt;\varnothing,\emptyset&lt;/math&gt;<br /> <br /> &lt;math display=&quot;block&quot;&gt;\begin{aligned}<br /> f(x)\;&amp;=(a+b+1)/2-x\\<br /> &amp;=(a+2x-1-a+f(2x-1-a)+1)/2-x\\<br /> &amp;=f(2x-1-a)/2\\<br /> &amp;=f(2x-1-(x-1+f(x-1)))/2\\<br /> &amp;=f(x-f(x-1))/2<br /> \end{aligned}&lt;/math&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> 111<br /> <br /> \( G(64)=\left. \begin{matrix} 3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \cdots \uparrow}3 \\3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \uparrow}3 \\ \underbrace{\qquad \quad \vdots \qquad \quad} \\3\underbrace{\uparrow \uparrow \cdots \cdots \uparrow}3 \\3\uparrow \uparrow \uparrow \uparrow3\end{matrix} \right \} \text{64 layers} \)<br /> <br /> &lt;math&gt;\unicode{64}&lt;/math&gt;<br /> <br /> &lt;math&gt;\varphi(\#,(\alpha+1)\text{@}(\beta+1),0\text{@}0)[0]=0&lt;/math&gt;<br /> <br /> &lt;math&gt;\text{@}&lt;/math&gt;<br /> <br /> [k]<br /> <br /> \(\alpha\text{@}\beta\)<br /> <br /> [[[a]]]<br /> <br /> &lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;(&lt;/span&gt;\alpha\text{@}\beta&lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;)&lt;/span&gt; = \(\alpha\text{@}\beta\)<br /> <br /> code<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {a}<br /> <br /> <br /> &lt;code&gt;我是code&lt;/code&gt;<br /> <br /> <br /> &lt;pre&gt;我是pre&lt;/pre&gt;<br /> <br /> <br /> &lt;span style='background:linear-gradient(to right,#00ff00,#0000ff);-webkit-background-clip:text;-webkit-text-fill-color:transparent;'&gt;我是美丽的span&lt;/span&gt;<br /> <br /> &lt;a href='https://baidu.com'&gt;危险的代码是不被允许的&lt;/a&gt;<br /> <br /> &lt;span onclick='this.innerText=&quot;onclick是无效的！&quot;'&gt;click me!&lt;/span&gt;<br /> <br /> 666<br /> <br /> \(\alpha @\beta\)<br /> <br /> &lt;blockquote&gt;<br /> 我是猫娘。喵喵喵喵<br /> &lt;/blockquote&gt;<br /> <br /> &lt;blockquote&gt;单行引言&lt;/blockquote&gt;<br /> <br /> &lt;span style='background-color:red'&gt;bgcisred&lt;/span&gt;<br /> <br /> [[高德纳箭头|↑]]<br /> &lt;iframe <br /> src=&quot;https://expander.googology.top/index.html&quot; <br /> width=&quot;100%&quot; <br /> height=&quot;500px&quot;<br /> frameborder=&quot;0&quot;<br /> &gt;&lt;/iframe&gt;<br /> <br /> === 这是一级标题 ===<br /> <br /> ==== 这是二级标题 ====<br /> 这是公式 \(\alpha\times\beta\)<br /> <br /> ''撒反对''<br /> <br /> 说说不可说】(1)<br /> <br /> --------------------------------------------------------------------<br /> <br /> 　　 人们的对话中，「不可说」指的是「不可以说出来」的意思，但是在佛<br /> 经中，不可说的意思并不一定是这样，世尊所说的佛经更不是指这个意思。<br /> 如果它是指不可以说出来的话，那麽全部的佛经就是一部「大妄语百科」了。<br /> <br /> 但是将「不可说」解释为「不可以说出来」的意思，并不是现代人的专<br /> 利，古人解经，也常把它作这样的解释，造成後人将佛经解释成玄密的经典，<br /> 一切的不合理之处都当作「不可说」来处理。<br /> <br /> 世尊的确说过许多的不可说，如:《华严经》<br /> 「不可言说不可说，充满一切不可说，不可言说诸劫中，说不可说不可尽，<br /> ....<br /> 於一微细毛端处，有不可说诸普贤，....一毛端处所有刹，其数无量不可<br /> 　说..」在第四十五卷中，世尊一口气说了将近四百个不可说。<br /> <br /> 《地藏菩萨本愿经》【忉利天宫神通品】「尔时，十方无量世界不可<br /> 　说不可说一切诸佛，及大菩萨摩诃萨，皆来集会，赞叹释迦牟尼佛．．」<br /> 这里用了两个不可说。<br /> <br /> 《小般若经》【深功德品】「一切法不可说，须菩提，一切法空相不<br /> 可说．．」<br /> <br /> 其实「不可说」的意义是「数量大到无法用语言形容」的意思，并不<br /> 是指所说的主题「不能说」，如果是不能说，那麽上面这些经典就是「废<br /> 话大全」了。<br /> <br /> 世尊说法四十九年，探讨的主题遍及人类所有的疑问，从来没有一样<br /> 　是「不能说出来」的，不但他老人家自己说，更鼓励所有修行菩萨要为众　<br /> 生说呢。(参见《般若经》)<br /> <br /> 那麽，「不可说」倒底有多大，会大到语言法形容呢？我们试著来找<br /> 找看。<br /> <br /> {| class=&quot;wikitable&quot; border=&quot;0&quot; cellpadding=&quot;1&quot; cellspacing=&quot;1&quot;<br /> ! scope=&quot;col&quot; |<br /> ! scope=&quot;col&quot; |A<br /> ! scope=&quot;col&quot; |B<br /> |-<br /> |0<br /> |1RB<br /> 1LA<br /> &lt;br&gt;1CP<br /> &lt;br&gt;114514<br /> |1LA<br /> |-<br /> |1<br /> |1LB<br /> |1RB<br /> |}<br /> 111<br /> <br /> {| class=&quot;wikitable&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | style=&quot;width: 20%;&quot; | 张三 || style=&quot;width: 80%; word-wrap: break-word;&quot; | 这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> 表格？<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;width: 300px; overflow: hidden; text-overflow: ellipsis&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | 张三<br /> | 这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> &lt;blockquote&gt;这里是一个孤立页面 我不知道它为什么还在这里<br /> <br /> 就当作是gggwiki的一个彩蛋吧（&lt;/blockquote&gt;<br /> <br /> <br /> <br /> <br /> <br /> [https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 果糕]<br /> 果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！<br /> <br /> &lt;div id=&quot;guogao1&quot;&gt;将以下代码放入控制台并回车，有“小惊喜”：&lt;/div&gt;&lt;small&gt;&lt;small&gt;&lt;nowiki&gt;(()=&gt;{document.getElementById(&quot;guogao1&quot;).appendChild((()=&gt;{let a = document.createElement(&quot;div&quot;);a.innerHTML = `&lt;div class=&quot;fixed-btn&quot;&gt;&lt;a onclick=&quot;let b=document.createElement('div');b.innerHTML=\`&lt;div id='guogao' style='transition: transform .5s ease-out;position: absolute;top:45%;left:50%;z-index: 9999999;transform: scale(1);cursor: pointer;-webkit-user-select: none;-moz-user-select: none;-ms-user-select: none;user-select: none;' onclick='this.remove()'&gt;${decodeURI('%F0%9F%98%B0')}&lt;/div&gt;\`;document.body.appendChild(b);setTimeout(() =&gt; {document.getElementById('guogao').style.transform='scale(45)'}, 50)&quot; class=&quot;new&quot; title=&quot;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&quot;&gt;&lt;span class=&quot;btn-text blue&quot;&gt;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&lt;/span&gt;&lt;/a&gt;&lt;/div&gt;`;return a})());return (()=&gt;{console.clear();return decodeURI('%E7%A5%9E%E7%A7%98%E6%8C%89%E9%92%AE%E5%87%BA%E7%8E%B0%EF%BC%81')})()})()<br /> <br /> &lt;/nowiki&gt;&lt;/small&gt;&lt;/small&gt;</div>

0100000000a7 http://wiki.googology.top/index.php?title=Test&diff=2737 2026-02-21T09:51:12Z

<p>0100000000a7：​</p> <hr /> <div>此页面为测试页面。任何人都可以随意修改此页面以便测试。<br /> <br /> === 编写技巧 ===<br /> <br /> * 行内代码块：&lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;code&gt;xxx&lt;/code&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;code&gt;xxx&lt;/code&gt;。<br /> * 在列表里换行：使用 &lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;br&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;br&gt;第一行；&lt;br&gt;第二行。<br /> * 在列表里嵌套列表：无序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ul&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ul&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：&lt;ul&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ul&gt;有序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ol&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ol&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：<br /> &lt;ol&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ol&gt;<br /> * 分界线：使用 &lt;code&gt;----&lt;/code&gt;。效果是这样：<br /> <br /> ----<br /> <br /> 这句话有7个字<br /> <br /> &lt;math&gt;\varnothing,\emptyset&lt;/math&gt;<br /> <br /> &lt;math display=&quot;block&quot;&gt;\begin{aligned}<br /> f(x)\;&amp;=(a+b+1)/2-x\\<br /> &amp;=(a+2x-1-a+f(2x-1-a)+1)/2-x\\<br /> &amp;=f(2x-1-a)/2\\<br /> &amp;=f(2x-1-(x-1+f(x-1)))/2\\<br /> &amp;=f(x-f(x-1))/2<br /> \end{aligned}&lt;/math&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> 111<br /> <br /> \( G(64)=\left. \begin{matrix} 3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \cdots \uparrow}3 \\3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \uparrow}3 \\ \underbrace{\qquad \quad \vdots \qquad \quad} \\3\underbrace{\uparrow \uparrow \cdots \cdots \uparrow}3 \\3\uparrow \uparrow \uparrow \uparrow3\end{matrix} \right \} \text{64 layers} \)<br /> <br /> &lt;math&gt;\unicode{64}&lt;/math&gt;<br /> <br /> &lt;math&gt;\varphi(\#,(\alpha+1)\text{\@}(\beta+1),0\text{\@}0)[0]=0&lt;/math&gt;<br /> <br /> &lt;math&gt;\text{\@}&lt;/math&gt;<br /> <br /> [k]<br /> <br /> \(\alpha\text{\@}\beta\)<br /> <br /> [[[a]]]<br /> <br /> &lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;(&lt;/span&gt;\alpha\text{\@}\beta&lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;)&lt;/span&gt; = \(\alpha\text{\@}\beta\)<br /> <br /> code<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {a}<br /> <br /> <br /> &lt;code&gt;我是code&lt;/code&gt;<br /> <br /> <br /> &lt;pre&gt;我是pre&lt;/pre&gt;<br /> <br /> <br /> &lt;span style='background:linear-gradient(to right,#00ff00,#0000ff);-webkit-background-clip:text;-webkit-text-fill-color:transparent;'&gt;我是美丽的span&lt;/span&gt;<br /> <br /> &lt;a href='https://baidu.com'&gt;危险的代码是不被允许的&lt;/a&gt;<br /> <br /> &lt;span onclick='this.innerText=&quot;onclick是无效的！&quot;'&gt;click me!&lt;/span&gt;<br /> <br /> 666<br /> <br /> \(\alpha @\beta\)<br /> <br /> &lt;blockquote&gt;<br /> 我是猫娘。喵喵喵喵<br /> &lt;/blockquote&gt;<br /> <br /> &lt;blockquote&gt;单行引言&lt;/blockquote&gt;<br /> <br /> &lt;span style='background-color:red'&gt;bgcisred&lt;/span&gt;<br /> <br /> [[高德纳箭头|↑]]<br /> &lt;iframe <br /> src=&quot;https://expander.googology.top/index.html&quot; <br /> width=&quot;100%&quot; <br /> height=&quot;500px&quot;<br /> frameborder=&quot;0&quot;<br /> &gt;&lt;/iframe&gt;<br /> <br /> === 这是一级标题 ===<br /> <br /> ==== 这是二级标题 ====<br /> 这是公式 \(\alpha\times\beta\)<br /> <br /> ''撒反对''<br /> <br /> 说说不可说】(1)<br /> <br /> --------------------------------------------------------------------<br /> <br /> 　　 人们的对话中，「不可说」指的是「不可以说出来」的意思，但是在佛<br /> 经中，不可说的意思并不一定是这样，世尊所说的佛经更不是指这个意思。<br /> 如果它是指不可以说出来的话，那麽全部的佛经就是一部「大妄语百科」了。<br /> <br /> 但是将「不可说」解释为「不可以说出来」的意思，并不是现代人的专<br /> 利，古人解经，也常把它作这样的解释，造成後人将佛经解释成玄密的经典，<br /> 一切的不合理之处都当作「不可说」来处理。<br /> <br /> 世尊的确说过许多的不可说，如:《华严经》<br /> 「不可言说不可说，充满一切不可说，不可言说诸劫中，说不可说不可尽，<br /> ....<br /> 於一微细毛端处，有不可说诸普贤，....一毛端处所有刹，其数无量不可<br /> 　说..」在第四十五卷中，世尊一口气说了将近四百个不可说。<br /> <br /> 《地藏菩萨本愿经》【忉利天宫神通品】「尔时，十方无量世界不可<br /> 　说不可说一切诸佛，及大菩萨摩诃萨，皆来集会，赞叹释迦牟尼佛．．」<br /> 这里用了两个不可说。<br /> <br /> 《小般若经》【深功德品】「一切法不可说，须菩提，一切法空相不<br /> 可说．．」<br /> <br /> 其实「不可说」的意义是「数量大到无法用语言形容」的意思，并不<br /> 是指所说的主题「不能说」，如果是不能说，那麽上面这些经典就是「废<br /> 话大全」了。<br /> <br /> 世尊说法四十九年，探讨的主题遍及人类所有的疑问，从来没有一样<br /> 　是「不能说出来」的，不但他老人家自己说，更鼓励所有修行菩萨要为众　<br /> 生说呢。(参见《般若经》)<br /> <br /> 那麽，「不可说」倒底有多大，会大到语言法形容呢？我们试著来找<br /> 找看。<br /> <br /> {| class=&quot;wikitable&quot; border=&quot;0&quot; cellpadding=&quot;1&quot; cellspacing=&quot;1&quot;<br /> ! scope=&quot;col&quot; |<br /> ! scope=&quot;col&quot; |A<br /> ! scope=&quot;col&quot; |B<br /> |-<br /> |0<br /> |1RB<br /> 1LA<br /> &lt;br&gt;1CP<br /> &lt;br&gt;114514<br /> |1LA<br /> |-<br /> |1<br /> |1LB<br /> |1RB<br /> |}<br /> 111<br /> <br /> {| class=&quot;wikitable&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | style=&quot;width: 20%;&quot; | 张三 || style=&quot;width: 80%; word-wrap: break-word;&quot; | 这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> 表格？<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;width: 300px; overflow: hidden; text-overflow: ellipsis&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | 张三<br /> | 这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> &lt;blockquote&gt;这里是一个孤立页面 我不知道它为什么还在这里<br /> <br /> 就当作是gggwiki的一个彩蛋吧（&lt;/blockquote&gt;<br /> <br /> <br /> <br /> <br /> <br /> [https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 果糕]<br /> 果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！<br /> <br /> &lt;div id=&quot;guogao1&quot;&gt;将以下代码放入控制台并回车，有“小惊喜”：&lt;/div&gt;&lt;small&gt;&lt;small&gt;&lt;nowiki&gt;(()=&gt;{document.getElementById(&quot;guogao1&quot;).appendChild((()=&gt;{let a = document.createElement(&quot;div&quot;);a.innerHTML = `&lt;div class=&quot;fixed-btn&quot;&gt;&lt;a onclick=&quot;let b=document.createElement('div');b.innerHTML=\`&lt;div id='guogao' style='transition: transform .5s ease-out;position: absolute;top:45%;left:50%;z-index: 9999999;transform: scale(1);cursor: pointer;-webkit-user-select: none;-moz-user-select: none;-ms-user-select: none;user-select: none;' onclick='this.remove()'&gt;${decodeURI('%F0%9F%98%B0')}&lt;/div&gt;\`;document.body.appendChild(b);setTimeout(() =&gt; {document.getElementById('guogao').style.transform='scale(45)'}, 50)&quot; class=&quot;new&quot; title=&quot;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&quot;&gt;&lt;span class=&quot;btn-text blue&quot;&gt;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&lt;/span&gt;&lt;/a&gt;&lt;/div&gt;`;return a})());return (()=&gt;{console.clear();return decodeURI('%E7%A5%9E%E7%A7%98%E6%8C%89%E9%92%AE%E5%87%BA%E7%8E%B0%EF%BC%81')})()})()<br /> <br /> &lt;/nowiki&gt;&lt;/small&gt;&lt;/small&gt;</div>

0100000000a7 http://wiki.googology.top/index.php?title=Test&diff=2735 2026-02-21T09:48:36Z

<p>0100000000a7：​</p> <hr /> <div>此页面为测试页面。任何人都可以随意修改此页面以便测试。<br /> <br /> === 编写技巧 ===<br /> <br /> * 行内代码块：&lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;code&gt;xxx&lt;/code&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;code&gt;xxx&lt;/code&gt;。<br /> * 在列表里换行：使用 &lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;br&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;br&gt;第一行；&lt;br&gt;第二行。<br /> * 在列表里嵌套列表：无序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ul&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ul&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：&lt;ul&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ul&gt;有序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ol&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ol&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：<br /> &lt;ol&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ol&gt;<br /> * 分界线：使用 &lt;code&gt;----&lt;/code&gt;。效果是这样：<br /> <br /> ----<br /> <br /> 这句话有7个字<br /> <br /> &lt;math&gt;\varnothing,\emptyset&lt;/math&gt;<br /> <br /> &lt;math display=&quot;block&quot;&gt;\begin{aligned}<br /> f(x)\;&amp;=(a+b+1)/2-x\\<br /> &amp;=(a+2x-1-a+f(2x-1-a)+1)/2-x\\<br /> &amp;=f(2x-1-a)/2\\<br /> &amp;=f(2x-1-(x-1+f(x-1)))/2\\<br /> &amp;=f(x-f(x-1))/2<br /> \end{aligned}&lt;/math&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> 111<br /> <br /> \( G(64)=\left. \begin{matrix} 3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \cdots \uparrow}3 \\3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \uparrow}3 \\ \underbrace{\qquad \quad \vdots \qquad \quad} \\3\underbrace{\uparrow \uparrow \cdots \cdots \uparrow}3 \\3\uparrow \uparrow \uparrow \uparrow3\end{matrix} \right \} \text{64 layers} \)<br /> <br /> &lt;math&gt;\unicode{64}&lt;/math&gt;<br /> <br /> &lt;math&gt;\varphi(\#,(\alpha+1)\text{@}(\beta+1),0\text{@}0)[0]=0&lt;/math&gt;<br /> <br /> &lt;math&gt;\text{@}&lt;/math&gt;<br /> <br /> [k]<br /> <br /> \(\alpha\text{@}\beta\)<br /> <br /> [[[a]]]<br /> <br /> &lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;(&lt;/span&gt;\alpha\text{@}\beta&lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;)&lt;/span&gt; = \(\alpha\text{@}\beta\)<br /> <br /> code<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {a}<br /> <br /> <br /> &lt;code&gt;我是code&lt;/code&gt;<br /> <br /> <br /> &lt;pre&gt;我是pre&lt;/pre&gt;<br /> <br /> <br /> &lt;span style='background:linear-gradient(to right,#00ff00,#0000ff);-webkit-background-clip:text;-webkit-text-fill-color:transparent;'&gt;我是美丽的span&lt;/span&gt;<br /> <br /> &lt;a href='https://baidu.com'&gt;危险的代码是不被允许的&lt;/a&gt;<br /> <br /> &lt;span onclick='this.innerText=&quot;onclick是无效的！&quot;'&gt;click me!&lt;/span&gt;<br /> <br /> 666<br /> <br /> \(\alpha @\beta\)<br /> <br /> &lt;blockquote&gt;<br /> 我是猫娘。喵喵喵喵<br /> &lt;/blockquote&gt;<br /> <br /> &lt;blockquote&gt;单行引言&lt;/blockquote&gt;<br /> <br /> &lt;span style='background-color:red'&gt;bgcisred&lt;/span&gt;<br /> <br /> [[高德纳箭头|↑]]<br /> &lt;iframe <br /> src=&quot;https://expander.googology.top/index.html&quot; <br /> width=&quot;100%&quot; <br /> height=&quot;500px&quot;<br /> frameborder=&quot;0&quot;<br /> &gt;&lt;/iframe&gt;<br /> <br /> === 这是一级标题 ===<br /> <br /> ==== 这是二级标题 ====<br /> 这是公式 \(\alpha\times\beta\)<br /> <br /> ''撒反对''<br /> <br /> 说说不可说】(1)<br /> <br /> --------------------------------------------------------------------<br /> <br /> 　　 人们的对话中，「不可说」指的是「不可以说出来」的意思，但是在佛<br /> 经中，不可说的意思并不一定是这样，世尊所说的佛经更不是指这个意思。<br /> 如果它是指不可以说出来的话，那麽全部的佛经就是一部「大妄语百科」了。<br /> <br /> 但是将「不可说」解释为「不可以说出来」的意思，并不是现代人的专<br /> 利，古人解经，也常把它作这样的解释，造成後人将佛经解释成玄密的经典，<br /> 一切的不合理之处都当作「不可说」来处理。<br /> <br /> 世尊的确说过许多的不可说，如:《华严经》<br /> 「不可言说不可说，充满一切不可说，不可言说诸劫中，说不可说不可尽，<br /> ....<br /> 於一微细毛端处，有不可说诸普贤，....一毛端处所有刹，其数无量不可<br /> 　说..」在第四十五卷中，世尊一口气说了将近四百个不可说。<br /> <br /> 《地藏菩萨本愿经》【忉利天宫神通品】「尔时，十方无量世界不可<br /> 　说不可说一切诸佛，及大菩萨摩诃萨，皆来集会，赞叹释迦牟尼佛．．」<br /> 这里用了两个不可说。<br /> <br /> 《小般若经》【深功德品】「一切法不可说，须菩提，一切法空相不<br /> 可说．．」<br /> <br /> 其实「不可说」的意义是「数量大到无法用语言形容」的意思，并不<br /> 是指所说的主题「不能说」，如果是不能说，那麽上面这些经典就是「废<br /> 话大全」了。<br /> <br /> 世尊说法四十九年，探讨的主题遍及人类所有的疑问，从来没有一样<br /> 　是「不能说出来」的，不但他老人家自己说，更鼓励所有修行菩萨要为众　<br /> 生说呢。(参见《般若经》)<br /> <br /> 那麽，「不可说」倒底有多大，会大到语言法形容呢？我们试著来找<br /> 找看。<br /> <br /> {| class=&quot;wikitable&quot; border=&quot;0&quot; cellpadding=&quot;1&quot; cellspacing=&quot;1&quot;<br /> ! scope=&quot;col&quot; |<br /> ! scope=&quot;col&quot; |A<br /> ! scope=&quot;col&quot; |B<br /> |-<br /> |0<br /> |1RB<br /> 1LA<br /> &lt;br&gt;1CP<br /> &lt;br&gt;114514<br /> |1LA<br /> |-<br /> |1<br /> |1LB<br /> |1RB<br /> |}<br /> 111<br /> <br /> {| class=&quot;wikitable&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | style=&quot;width: 20%;&quot; | 张三 || style=&quot;width: 80%; word-wrap: break-word;&quot; | 这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> 表格？<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;width: 300px; overflow: hidden; text-overflow: ellipsis&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | 张三<br /> | 这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> &lt;blockquote&gt;这里是一个孤立页面 我不知道它为什么还在这里<br /> <br /> 就当作是gggwiki的一个彩蛋吧（&lt;/blockquote&gt;<br /> <br /> <br /> <br /> <br /> <br /> [https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 果糕]<br /> 果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！<br /> <br /> &lt;div id=&quot;guogao1&quot;&gt;将以下代码放入控制台并回车，有“小惊喜”：&lt;/div&gt;&lt;small&gt;&lt;small&gt;&lt;nowiki&gt;(()=&gt;{document.getElementById(&quot;guogao1&quot;).appendChild((()=&gt;{let a = document.createElement(&quot;div&quot;);a.innerHTML = `&lt;div class=&quot;fixed-btn&quot;&gt;&lt;a onclick=&quot;let b=document.createElement('div');b.innerHTML=\`&lt;div id='guogao' style='transition: transform .5s ease-out;position: absolute;top:45%;left:50%;z-index: 9999999;transform: scale(1);cursor: pointer;-webkit-user-select: none;-moz-user-select: none;-ms-user-select: none;user-select: none;' onclick='this.remove()'&gt;${decodeURI('%F0%9F%98%B0')}&lt;/div&gt;\`;document.body.appendChild(b);setTimeout(() =&gt; {document.getElementById('guogao').style.transform='scale(45)'}, 50)&quot; class=&quot;new&quot; title=&quot;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&quot;&gt;&lt;span class=&quot;btn-text blue&quot;&gt;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&lt;/span&gt;&lt;/a&gt;&lt;/div&gt;`;return a})());return (()=&gt;{console.clear();return decodeURI('%E7%A5%9E%E7%A7%98%E6%8C%89%E9%92%AE%E5%87%BA%E7%8E%B0%EF%BC%81')})()})()<br /> <br /> &lt;/nowiki&gt;&lt;/small&gt;&lt;/small&gt;</div>

0100000000a7 http://wiki.googology.top/index.php?title=Test&diff=2734 2026-02-21T09:48:02Z

<p>0100000000a7：​</p> <hr /> <div>此页面为测试页面。任何人都可以随意修改此页面以便测试。<br /> <br /> === 编写技巧 ===<br /> <br /> * 行内代码块：&lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;code&gt;xxx&lt;/code&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;code&gt;xxx&lt;/code&gt;。<br /> * 在列表里换行：使用 &lt;syntaxhighlight lang=&quot;text&quot;&gt;&lt;br&gt;&lt;/syntaxhighlight&gt;效果是这样：&lt;br&gt;第一行；&lt;br&gt;第二行。<br /> * 在列表里嵌套列表：无序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ul&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ul&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：&lt;ul&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ul&gt;有序列表使用&lt;syntaxhighlight lang=&quot;text&quot;&gt;<br /> &lt;ol&gt; &lt;li&gt;123&lt;/li&gt; &lt;li&gt;456&lt;/li&gt; &lt;/ol&gt;<br /> &lt;/syntaxhighlight&gt;效果是这样：<br /> &lt;ol&gt;&lt;li&gt;123&lt;/li&gt;&lt;li&gt;456&lt;/li&gt;&lt;/ol&gt;<br /> * 分界线：使用 &lt;code&gt;----&lt;/code&gt;。效果是这样：<br /> <br /> ----<br /> <br /> 这句话有7个字<br /> <br /> &lt;math&gt;\varnothing,\emptyset&lt;/math&gt;<br /> <br /> &lt;math display=&quot;block&quot;&gt;\begin{aligned}<br /> f(x)\,&amp;=(a+b+1)/2-x\\<br /> &amp;=(a+2x-1-a+f(2x-1-a)+1)/2-x\\<br /> &amp;=f(2x-1-a)/2\\<br /> &amp;=f(2x-1-(x-1+f(x-1)))/2\\<br /> &amp;=f(x-f(x-1))/2<br /> \end{aligned}&lt;/math&gt;<br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> <br /> 111<br /> <br /> \( G(64)=\left. \begin{matrix} 3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \cdots \uparrow}3 \\3\underbrace{\uparrow \uparrow \cdots \cdots \cdots \cdots \uparrow}3 \\ \underbrace{\qquad \quad \vdots \qquad \quad} \\3\underbrace{\uparrow \uparrow \cdots \cdots \uparrow}3 \\3\uparrow \uparrow \uparrow \uparrow3\end{matrix} \right \} \text{64 layers} \)<br /> <br /> &lt;math&gt;\unicode{64}&lt;/math&gt;<br /> <br /> &lt;math&gt;\varphi(\#,(\alpha+1)\text{@}(\beta+1),0\text{@}0)[0]=0&lt;/math&gt;<br /> <br /> &lt;math&gt;\text{@}&lt;/math&gt;<br /> <br /> [k]<br /> <br /> \(\alpha\text{@}\beta\)<br /> <br /> [[[a]]]<br /> <br /> &lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;(&lt;/span&gt;\alpha\text{@}\beta&lt;nowiki&gt;\&lt;/nowiki&gt;&lt;span&gt;)&lt;/span&gt; = \(\alpha\text{@}\beta\)<br /> <br /> code<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |+ 标题文本<br /> |-<br /> ! 标题文本 !! 标题文本 !! 标题文本<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |-<br /> | 示例 || 示例 || 示例<br /> |}<br /> <br /> {a}<br /> <br /> <br /> &lt;code&gt;我是code&lt;/code&gt;<br /> <br /> <br /> &lt;pre&gt;我是pre&lt;/pre&gt;<br /> <br /> <br /> &lt;span style='background:linear-gradient(to right,#00ff00,#0000ff);-webkit-background-clip:text;-webkit-text-fill-color:transparent;'&gt;我是美丽的span&lt;/span&gt;<br /> <br /> &lt;a href='https://baidu.com'&gt;危险的代码是不被允许的&lt;/a&gt;<br /> <br /> &lt;span onclick='this.innerText=&quot;onclick是无效的！&quot;'&gt;click me!&lt;/span&gt;<br /> <br /> 666<br /> <br /> \(\alpha @\beta\)<br /> <br /> &lt;blockquote&gt;<br /> 我是猫娘。喵喵喵喵<br /> &lt;/blockquote&gt;<br /> <br /> &lt;blockquote&gt;单行引言&lt;/blockquote&gt;<br /> <br /> &lt;span style='background-color:red'&gt;bgcisred&lt;/span&gt;<br /> <br /> [[高德纳箭头|↑]]<br /> &lt;iframe <br /> src=&quot;https://expander.googology.top/index.html&quot; <br /> width=&quot;100%&quot; <br /> height=&quot;500px&quot;<br /> frameborder=&quot;0&quot;<br /> &gt;&lt;/iframe&gt;<br /> <br /> === 这是一级标题 ===<br /> <br /> ==== 这是二级标题 ====<br /> 这是公式 \(\alpha\times\beta\)<br /> <br /> ''撒反对''<br /> <br /> 说说不可说】(1)<br /> <br /> --------------------------------------------------------------------<br /> <br /> 　　 人们的对话中，「不可说」指的是「不可以说出来」的意思，但是在佛<br /> 经中，不可说的意思并不一定是这样，世尊所说的佛经更不是指这个意思。<br /> 如果它是指不可以说出来的话，那麽全部的佛经就是一部「大妄语百科」了。<br /> <br /> 但是将「不可说」解释为「不可以说出来」的意思，并不是现代人的专<br /> 利，古人解经，也常把它作这样的解释，造成後人将佛经解释成玄密的经典，<br /> 一切的不合理之处都当作「不可说」来处理。<br /> <br /> 世尊的确说过许多的不可说，如:《华严经》<br /> 「不可言说不可说，充满一切不可说，不可言说诸劫中，说不可说不可尽，<br /> ....<br /> 於一微细毛端处，有不可说诸普贤，....一毛端处所有刹，其数无量不可<br /> 　说..」在第四十五卷中，世尊一口气说了将近四百个不可说。<br /> <br /> 《地藏菩萨本愿经》【忉利天宫神通品】「尔时，十方无量世界不可<br /> 　说不可说一切诸佛，及大菩萨摩诃萨，皆来集会，赞叹释迦牟尼佛．．」<br /> 这里用了两个不可说。<br /> <br /> 《小般若经》【深功德品】「一切法不可说，须菩提，一切法空相不<br /> 可说．．」<br /> <br /> 其实「不可说」的意义是「数量大到无法用语言形容」的意思，并不<br /> 是指所说的主题「不能说」，如果是不能说，那麽上面这些经典就是「废<br /> 话大全」了。<br /> <br /> 世尊说法四十九年，探讨的主题遍及人类所有的疑问，从来没有一样<br /> 　是「不能说出来」的，不但他老人家自己说，更鼓励所有修行菩萨要为众　<br /> 生说呢。(参见《般若经》)<br /> <br /> 那麽，「不可说」倒底有多大，会大到语言法形容呢？我们试著来找<br /> 找看。<br /> <br /> {| class=&quot;wikitable&quot; border=&quot;0&quot; cellpadding=&quot;1&quot; cellspacing=&quot;1&quot;<br /> ! scope=&quot;col&quot; |<br /> ! scope=&quot;col&quot; |A<br /> ! scope=&quot;col&quot; |B<br /> |-<br /> |0<br /> |1RB<br /> 1LA<br /> &lt;br&gt;1CP<br /> &lt;br&gt;114514<br /> |1LA<br /> |-<br /> |1<br /> |1LB<br /> |1RB<br /> |}<br /> 111<br /> <br /> {| class=&quot;wikitable&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | style=&quot;width: 20%;&quot; | 张三 || style=&quot;width: 80%; word-wrap: break-word;&quot; | 这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> 表格？<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;width: 300px; overflow: hidden; text-overflow: ellipsis&quot;<br /> ! 用户名<br /> ! 简介<br /> |-<br /> | 张三<br /> | 这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。这是一个非常长的简介文本，会自动换行以适应列宽。<br /> |}<br /> <br /> &lt;blockquote&gt;这里是一个孤立页面 我不知道它为什么还在这里<br /> <br /> 就当作是gggwiki的一个彩蛋吧（&lt;/blockquote&gt;<br /> <br /> <br /> <br /> <br /> <br /> [https://2023largenumber.fandom.com/zh/wiki/%F0%9F%98%B0#articleComments/ 果糕]<br /> 果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！果糕糕糕！<br /> 果糕糕糕！<br /> <br /> &lt;div id=&quot;guogao1&quot;&gt;将以下代码放入控制台并回车，有“小惊喜”：&lt;/div&gt;&lt;small&gt;&lt;small&gt;&lt;nowiki&gt;(()=&gt;{document.getElementById(&quot;guogao1&quot;).appendChild((()=&gt;{let a = document.createElement(&quot;div&quot;);a.innerHTML = `&lt;div class=&quot;fixed-btn&quot;&gt;&lt;a onclick=&quot;let b=document.createElement('div');b.innerHTML=\`&lt;div id='guogao' style='transition: transform .5s ease-out;position: absolute;top:45%;left:50%;z-index: 9999999;transform: scale(1);cursor: pointer;-webkit-user-select: none;-moz-user-select: none;-ms-user-select: none;user-select: none;' onclick='this.remove()'&gt;${decodeURI('%F0%9F%98%B0')}&lt;/div&gt;\`;document.body.appendChild(b);setTimeout(() =&gt; {document.getElementById('guogao').style.transform='scale(45)'}, 50)&quot; class=&quot;new&quot; title=&quot;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&quot;&gt;&lt;span class=&quot;btn-text blue&quot;&gt;${decodeURI('%E5%B0%8F%E6%83%8A%E5%96%9C')}&lt;/span&gt;&lt;/a&gt;&lt;/div&gt;`;return a})());return (()=&gt;{console.clear();return decodeURI('%E7%A5%9E%E7%A7%98%E6%8C%89%E9%92%AE%E5%87%BA%E7%8E%B0%EF%BC%81')})()})()<br /> <br /> &lt;/nowiki&gt;&lt;/small&gt;&lt;/small&gt;</div>

0100000000a7 http://wiki.googology.top/index.php?title=%E5%BA%8F%E6%95%B0%E8%B6%85%E8%BF%90%E7%AE%97&diff=2733 2026-02-21T09:43:06Z

<p>0100000000a7：​</p> <hr /> <div>序数超运算是对序数使用[[超运算序列|超运算]]的尝试。它虽然是最直观、新人最容易想到的模式，但已经被长期的[[googology]]实践所证明是低效、难以扩展的。<br /> <br /> == 原定义 ==<br /> 首先，我们仿照[[高德纳箭头]]在自然数上的定义和[[序数#序数的运算|序数运算]]的定义，给出序数使用高德纳箭头的定义：<br /> <br /> # &lt;math&gt;\alpha\uparrow^1\beta=\alpha^{\beta}&lt;/math&gt;<br /> # &lt;math&gt;\alpha\uparrow^c1=\alpha&lt;/math&gt;<br /> # &lt;math&gt;\alpha\uparrow^{c+1}(\beta+1)=\alpha\uparrow^c(\alpha\uparrow^{c+1}\beta)&lt;/math&gt;<br /> # &lt;math&gt;\alpha\uparrow^c\lambda=\sup\{\alpha\uparrow^c\beta|\beta&lt;\lambda\}&lt;/math&gt;<br /> <br /> 其中&lt;math&gt;\alpha,\beta&lt;/math&gt;是任意序数，c是自然数，&lt;math&gt;\lambda&lt;/math&gt;是非0极限序数。<br /> <br /> 这样一来，就有&lt;math&gt;\omega\uparrow^2(\omega+1)=\omega^{\omega\uparrow^2\omega}=\sup\{\omega^{\omega\uparrow^2n}|n&lt;\omega\}=\sup\{\omega\uparrow^2n|n&lt;\omega\}=\omega\uparrow^2\omega&lt;/math&gt;.进一步，对任意&lt;math&gt;\beta\geq\omega&lt;/math&gt;，都有&lt;math&gt;\omega\uparrow^2\beta=\omega\uparrow^2\omega&lt;/math&gt;.再进一步，对任意的&lt;math&gt;c\geq2,\beta\geq\omega&lt;/math&gt;,都有&lt;math&gt;\omega\uparrow^c\beta=\omega\uparrow^2\omega&lt;/math&gt;.<br /> <br /> 这显然不是我们所期待的。<br /> <br /> == 左结合法 ==<br /> 第一种试图解决问题的方案是左结合法。它借鉴了[[下箭号表示法|下箭头表示法]]，给出序数使用下箭头的定义：<br /> <br /> # &lt;math&gt;\alpha\downarrow^1\beta=\alpha^{\beta}&lt;/math&gt;<br /> # &lt;math&gt;\alpha\downarrow^c1=\alpha&lt;/math&gt;<br /> # &lt;math&gt;\alpha\downarrow^{c+1}(\beta+1)=(\alpha\downarrow^{c+1}\beta)\downarrow\alpha&lt;/math&gt;<br /> # &lt;math&gt;\alpha\downarrow^c\lambda=\sup\{\alpha\downarrow^c\beta|\beta&lt;\lambda\}&lt;/math&gt;<br /> <br /> 其中&lt;math&gt;\alpha,\beta&lt;/math&gt;是任意序数，c是自然数，&lt;math&gt;\lambda&lt;/math&gt;是非0极限序数。<br /> <br /> 于是有：<br /> <br /> &lt;math&gt;\omega\downarrow^22=\omega^\omega <br /> &lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^23=\omega^{\omega^2}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^2\omega=\omega^{\omega^\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^2\omega)\downarrow^22=\omega^{\omega^{\omega^\omega}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^33=\omega^{\omega^{\omega^{\omega^\omega}}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^34=\omega^{\omega^{\omega^{\omega^{\omega^{\omega^\omega}}}}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^3\omega=\varepsilon_0&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^3\omega)\downarrow^22=\varepsilon_0^{\varepsilon_0}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^3\omega)\downarrow^2\omega=\varepsilon_0^{\varepsilon_0^\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^3\omega)\downarrow^32=\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^3\omega)\downarrow^33=\varepsilon_0^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^43=\varepsilon_1&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^44=\varepsilon_2&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^4\omega=\varepsilon_\omega&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^4\omega)\downarrow^3\omega=\varepsilon_{\omega+1}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^4\omega)\downarrow^42=\varepsilon_{\varepsilon_\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^4\omega)\downarrow^43=\varepsilon_{\varepsilon_\omega2}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^53=\varepsilon_{\varepsilon_\omega\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^54=\varepsilon_{\varepsilon_{\varepsilon_\omega\omega}\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^5\omega=\zeta_0&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^6\omega=\zeta_\omega&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^7\omega=\varphi(3,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^{1+2n}\omega=\varphi(n,0)&lt;/math&gt;<br /> <br /> 把下箭头用到序数上，其极限为&lt;math&gt;\varphi(\omega,0)&lt;/math&gt;，也符合箭头运算的强度。<br /> <br /> 但是，左结合的下箭头行为和高德纳箭头差异还是不小，而且两个箭头对应一个&lt;math&gt;\varphi(n,0)&lt;/math&gt;还是不太符合我们的预期。<br /> <br /> == 攀爬法 ==<br /> 第二种试图解决问题的方案是攀爬法。攀爬法提供了一种更强的推广。我们知道，&lt;math&gt;\varepsilon_1&lt;/math&gt;的基本列是&lt;math&gt;\{\varepsilon_0+1,\omega^{\varepsilon_0+1},\omega^{\omega^{\varepsilon_0+1}},\omega^{\omega^{\omega^{\varepsilon_0+1}}},\cdots\}&lt;/math&gt;，我们可以将其表示为&lt;math&gt;\{\omega^{\omega^{\omega^{\cdots}}}+1,\omega^{\omega^{\omega^{\cdots}}+1},\omega^{\omega^{\omega^{\cdots}+1}},\cdots\}&lt;/math&gt;.在这里我们把&lt;math&gt;\omega&lt;/math&gt;的指数塔固定在&lt;math&gt;\omega&lt;/math&gt;。在这样的基本列中，+1像在指数塔攀爬一样，攀爬法也因此而得名。在基本列的尽头，+1攀爬到了指数塔的顶端，与原来在顶端的1相加变为2。因此我们得到&lt;math&gt;\varepsilon_1=\underbrace{\omega^{\omega^{\cdots^{2}}}}_{\omega+1 \text{ layers}}&lt;/math&gt;.进一步的，按照攀爬法我们有&lt;math&gt;\varepsilon_{\omega}=\underbrace{\omega^{\omega^{\cdots^{\omega}}}}_{\omega+1 \text{ layers}}&lt;/math&gt;,我们将其记为&lt;math&gt;\omega\uparrow\uparrow(\omega+1)=\varepsilon_{\omega}&lt;/math&gt;.<br /> <br /> 进一步有：<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega+2)=\varepsilon_{\omega^{\omega}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega\times2)=\varepsilon_{\varepsilon_0}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega^2)=\zeta_0&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega^3)=\eta_0&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega^{\omega})=\varphi(\omega,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow\omega\uparrow\uparrow\omega=\varphi(\varphi(1,0),0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^34=\varphi(\varphi(\varphi(1,0),0),0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3\omega=\varphi(1,0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega+1)=\varphi(1,0,1)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega^2)=\varphi(1,1,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3\omega\uparrow^3\omega=\varphi(1,\varphi(1,0,0),0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^44=\varphi(1,\varphi(1,\varphi(1,0,0),0),0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^4\omega=\varphi(2,0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^5\omega=\varphi(3,0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^{\omega}\omega=\varphi(\omega,0,0)&lt;/math&gt;<br /> <br /> 由此我们得到了攀爬法序数超运算的极限是&lt;math&gt;\varphi(\omega,0,0)&lt;/math&gt;.<br /> <br /> 但是现在已经证明了，攀爬法是非良序的。因此这一做法得到的推广是不可靠的。<br /> <br /> == +1法 ==<br /> 第三中试图解决问题的方案是+1法。<br /> <br /> 它基于一种特别朴素的想法，即：如果&lt;math&gt;\omega\uparrow^c\alpha=\alpha&lt;/math&gt;,则修改其值为&lt;math&gt;\omega\uparrow^c(\alpha+1)&lt;/math&gt;.显然，这一改变真正起到效果的是指数上的变化。关于+1法序数超运算，我们有：<br /> <br /> 例如：ω^^(ω+1)如果展开为ω^ω^^ω就会遇到不动点，因此触发上述的+1规则。<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega+1)=\omega^{\omega\uparrow\uparrow\omega+1}=\omega^{\varepsilon_0+1}&lt;/math&gt;<br /> <br /> 然后，以此类推：<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega+2)=\omega^{\omega^{\varepsilon_0+1}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega2)=\varepsilon_1&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega3)=\varepsilon_2&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega^2)=\varepsilon_{\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^33=\omega\uparrow\uparrow\omega\uparrow\uparrow\omega=\varepsilon_{\varepsilon_0}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3\omega=\zeta_0&lt;/math&gt;<br /> <br /> 到ζ_0后，+1法的展开方式将会比较复杂，并产生一些奇特的基础序列。继续分析：<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega+1)=\omega\uparrow\uparrow(\omega\uparrow^3\omega+1)<br /> =\omega\uparrow(\omega\uparrow\uparrow(\omega\uparrow^3\omega)+1)<br /> =\omega\uparrow(\omega\uparrow^3\omega+1)<br /> =\omega^{\zeta_0+1}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega\uparrow^3\omega+\omega)=\varepsilon_{\zeta_0+1}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega\uparrow^3\omega*2)=\varepsilon_{\zeta_02}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega+2)=\omega\uparrow\uparrow(\omega\uparrow^3(\omega+1))=\varepsilon_{\omega^{\zeta_0+1}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega+3)=\varepsilon_{\varepsilon_{\omega^{\zeta_0+1}}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega2)=\zeta_1&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^43=\zeta_{\zeta_0}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^4\omega=\eta_0&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^4(\omega+1)=\omega\uparrow^3(\omega\uparrow^4\omega+1)<br /> =\omega\uparrow\omega\uparrow\uparrow\omega\uparrow^3(\omega\uparrow^4\omega+1)<br /> =\omega\uparrow(\omega\uparrow^4\omega+1)<br /> =\omega^{\eta_0+1}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^4(\omega+2)=\omega\uparrow^3(\omega\uparrow^4(\omega+1))=\zeta_{\omega^{\eta_0+1}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^4(\omega2)=\eta_1&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^5\omega=\varphi(4,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^{\omega}\omega=\varphi(\omega,0)&lt;/math&gt;<br /> <br /> 于是我们得到其极限为&lt;math&gt;\varphi(\omega,0)&lt;/math&gt;。它的优点是它和&lt;math&gt;\varphi&lt;/math&gt;函数行为完全一致。但缺点也是这个。这导致了&lt;math&gt;\omega\uparrow\uparrow(\omega+1)=(\omega\uparrow\uparrow\omega)\times\omega&lt;/math&gt;这种奇异的结果，某种意义上丢失了超运算自己的特性。因此可以说，+1法序数超运算被&lt;math&gt;\varphi&lt;/math&gt;函数上位替代了。+1法序数超运算还可以继续拓展，在某些版本中，其增长率与类似的Veblen 函数及Feferman序数折叠函数类似，例如：<br /> <br /> &lt;math&gt;\omega\{\omega\}(\omega2)=\varphi(\omega,1)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\omega+1\}\omega=\varphi(\omega+1,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\omega\uparrow\uparrow\omega\}\omega=\varphi(\varepsilon_0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega\}3=\omega\{\omega\{\omega\}\omega\}\omega=\varphi(\varphi(\omega,0),0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega\}\omega=\Gamma_0&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega+1\}\omega=\varphi(1,1,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega2\}\omega=\varphi(2,0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega^2\}\omega=\varphi(1,0,0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega^\omega\}\omega=\psi(\Omega^{\Omega^\omega})&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega^\Omega\}\omega=\psi(\Omega^{\Omega^\Omega})&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega\uparrow\uparrow\omega\}\omega=\psi(\Omega_2)&lt;/math&gt;<br /> <br /> 但如此的拓展达到同样序数的难度要明显大于一般的[[序数坍缩函数]]。有些版本引入了更为强大的结构，但已经失去了超运算的特性，其强度主要为引入的更高级序数结构，建议使用以更高级核心的序数记号替代之。<br /> <br /> == 总结 ==<br /> 到目前为止，序数超运算不是不良定义，就是不理想的。我们不建议在任何地方使用高于&lt;math&gt;\varepsilon_0&lt;/math&gt;的序数超运算和更高级别的运算。如果要使用，必须仅仅将它作为形式上的符号，并且明确地说明其具体含义。事实上，我们完全可以使用[[Veblen 函数]]这样的更加强大且清晰的[[序数记号]]来替代它。<br /> [[分类:记号]]<br /> [[分类:入门]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=%E5%BA%8F%E6%95%B0%E8%B6%85%E8%BF%90%E7%AE%97&diff=2732 2026-02-21T09:42:43Z

<p>0100000000a7：​</p> <hr /> <div>序数超运算是对序数使用[[超运算序列|超运算]]的尝试。它虽然是最直观、新人最容易想到的模式，但已经被长期的[[googology]]实践所证明是低效、难以扩展的。<br /> <br /> == 原定义 ==<br /> 首先，我们仿照[[高德纳箭头]]在自然数上的定义和[[序数#序数的运算|序数运算]]的定义，给出序数使用高德纳箭头的定义：<br /> <br /> # &lt;math&gt;\alpha\uparrow^1\beta=\alpha^{\beta}&lt;/math&gt;<br /> # &lt;math&gt;\alpha\uparrow^c1=\alpha&lt;/math&gt;<br /> # &lt;math&gt;\alpha\uparrow^{c+1}(\beta+1)=\alpha\uparrow^c(\alpha\uparrow^{c+1}\beta)&lt;/math&gt;<br /> # &lt;math&gt;\alpha\uparrow^c\lambda=\sup\{\alpha\uparrow^c\beta|\beta&lt;\lambda\}&lt;/math&gt;<br /> <br /> 其中&lt;math&gt;\alpha,\beta&lt;/math&gt;是任意序数，c是自然数，&lt;math&gt;\lambda&lt;/math&gt;是非0极限序数。<br /> <br /> 这样一来，就有&lt;math&gt;\omega\uparrow^2(\omega+1)=\omega^{\omega\uparrow^2\omega}=\sup\{\omega^{\omega\uparrow^2n}|n&lt;\omega\}=\sup\{\omega\uparrow^2n|n&lt;\omega\}=\omega\uparrow^2\omega&lt;/math&gt;.进一步，对任意&lt;math&gt;\beta\geq\omega&lt;/math&gt;，都有&lt;math&gt;\omega\uparrow^2\beta=\omega\uparrow^2\omega&lt;/math&gt;.再进一步，对任意的&lt;math&gt;c\geq2,\beta\geq\omega&lt;/math&gt;,都有&lt;math&gt;\omega\uparrow^c\beta=\omega\uparrow^2\omega&lt;/math&gt;.<br /> <br /> 这显然不是我们所期待的。<br /> <br /> == 左结合法 ==<br /> 第一种试图解决问题的方案是左结合法。它借鉴了[[下箭号表示法|下箭头表示法]]，给出序数使用下箭头的定义：<br /> <br /> # &lt;math&gt;\alpha\downarrow^1\beta=\alpha^{\beta}&lt;/math&gt;<br /> # &lt;math&gt;\alpha\downarrow^c1=\alpha&lt;/math&gt;<br /> # &lt;math&gt;\alpha\downarrow^{c+1}(\beta+1)=(\alpha\downarrow^{c+1}\beta)\downarrow\alpha&lt;/math&gt;<br /> # &lt;math&gt;\alpha\downarrow^c\lambda=sup\{\alpha\downarrow^c\beta|\beta&lt;\lambda\}&lt;/math&gt;<br /> <br /> 其中&lt;math&gt;\alpha,\beta&lt;/math&gt;是任意序数，c是自然数，&lt;math&gt;\lambda&lt;/math&gt;是非0极限序数。<br /> <br /> 于是有：<br /> <br /> &lt;math&gt;\omega\downarrow^22=\omega^\omega <br /> &lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^23=\omega^{\omega^2}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^2\omega=\omega^{\omega^\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^2\omega)\downarrow^22=\omega^{\omega^{\omega^\omega}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^33=\omega^{\omega^{\omega^{\omega^\omega}}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^34=\omega^{\omega^{\omega^{\omega^{\omega^{\omega^\omega}}}}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^3\omega=\varepsilon_0&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^3\omega)\downarrow^22=\varepsilon_0^{\varepsilon_0}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^3\omega)\downarrow^2\omega=\varepsilon_0^{\varepsilon_0^\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^3\omega)\downarrow^32=\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^3\omega)\downarrow^33=\varepsilon_0^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^43=\varepsilon_1&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^44=\varepsilon_2&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^4\omega=\varepsilon_\omega&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^4\omega)\downarrow^3\omega=\varepsilon_{\omega+1}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^4\omega)\downarrow^42=\varepsilon_{\varepsilon_\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^4\omega)\downarrow^43=\varepsilon_{\varepsilon_\omega2}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^53=\varepsilon_{\varepsilon_\omega\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^54=\varepsilon_{\varepsilon_{\varepsilon_\omega\omega}\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^5\omega=\zeta_0&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^6\omega=\zeta_\omega&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^7\omega=\varphi(3,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^{1+2n}\omega=\varphi(n,0)&lt;/math&gt;<br /> <br /> 把下箭头用到序数上，其极限为&lt;math&gt;\varphi(\omega,0)&lt;/math&gt;，也符合箭头运算的强度。<br /> <br /> 但是，左结合的下箭头行为和高德纳箭头差异还是不小，而且两个箭头对应一个&lt;math&gt;\varphi(n,0)&lt;/math&gt;还是不太符合我们的预期。<br /> <br /> == 攀爬法 ==<br /> 第二种试图解决问题的方案是攀爬法。攀爬法提供了一种更强的推广。我们知道，&lt;math&gt;\varepsilon_1&lt;/math&gt;的基本列是&lt;math&gt;\{\varepsilon_0+1,\omega^{\varepsilon_0+1},\omega^{\omega^{\varepsilon_0+1}},\omega^{\omega^{\omega^{\varepsilon_0+1}}},\cdots\}&lt;/math&gt;，我们可以将其表示为&lt;math&gt;\{\omega^{\omega^{\omega^{\cdots}}}+1,\omega^{\omega^{\omega^{\cdots}}+1},\omega^{\omega^{\omega^{\cdots}+1}},\cdots\}&lt;/math&gt;.在这里我们把&lt;math&gt;\omega&lt;/math&gt;的指数塔固定在&lt;math&gt;\omega&lt;/math&gt;。在这样的基本列中，+1像在指数塔攀爬一样，攀爬法也因此而得名。在基本列的尽头，+1攀爬到了指数塔的顶端，与原来在顶端的1相加变为2。因此我们得到&lt;math&gt;\varepsilon_1=\underbrace{\omega^{\omega^{\cdots^{2}}}}_{\omega+1 \text{ layers}}&lt;/math&gt;.进一步的，按照攀爬法我们有&lt;math&gt;\varepsilon_{\omega}=\underbrace{\omega^{\omega^{\cdots^{\omega}}}}_{\omega+1 \text{ layers}}&lt;/math&gt;,我们将其记为&lt;math&gt;\omega\uparrow\uparrow(\omega+1)=\varepsilon_{\omega}&lt;/math&gt;.<br /> <br /> 进一步有：<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega+2)=\varepsilon_{\omega^{\omega}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega\times2)=\varepsilon_{\varepsilon_0}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega^2)=\zeta_0&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega^3)=\eta_0&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega^{\omega})=\varphi(\omega,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow\omega\uparrow\uparrow\omega=\varphi(\varphi(1,0),0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^34=\varphi(\varphi(\varphi(1,0),0),0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3\omega=\varphi(1,0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega+1)=\varphi(1,0,1)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega^2)=\varphi(1,1,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3\omega\uparrow^3\omega=\varphi(1,\varphi(1,0,0),0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^44=\varphi(1,\varphi(1,\varphi(1,0,0),0),0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^4\omega=\varphi(2,0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^5\omega=\varphi(3,0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^{\omega}\omega=\varphi(\omega,0,0)&lt;/math&gt;<br /> <br /> 由此我们得到了攀爬法序数超运算的极限是&lt;math&gt;\varphi(\omega,0,0)&lt;/math&gt;.<br /> <br /> 但是现在已经证明了，攀爬法是非良序的。因此这一做法得到的推广是不可靠的。<br /> <br /> == +1法 ==<br /> 第三中试图解决问题的方案是+1法。<br /> <br /> 它基于一种特别朴素的想法，即：如果&lt;math&gt;\omega\uparrow^c\alpha=\alpha&lt;/math&gt;,则修改其值为&lt;math&gt;\omega\uparrow^c(\alpha+1)&lt;/math&gt;.显然，这一改变真正起到效果的是指数上的变化。关于+1法序数超运算，我们有：<br /> <br /> 例如：ω^^(ω+1)如果展开为ω^ω^^ω就会遇到不动点，因此触发上述的+1规则。<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega+1)=\omega^{\omega\uparrow\uparrow\omega+1}=\omega^{\varepsilon_0+1}&lt;/math&gt;<br /> <br /> 然后，以此类推：<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega+2)=\omega^{\omega^{\varepsilon_0+1}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega2)=\varepsilon_1&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega3)=\varepsilon_2&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega^2)=\varepsilon_{\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^33=\omega\uparrow\uparrow\omega\uparrow\uparrow\omega=\varepsilon_{\varepsilon_0}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3\omega=\zeta_0&lt;/math&gt;<br /> <br /> 到ζ_0后，+1法的展开方式将会比较复杂，并产生一些奇特的基础序列。继续分析：<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega+1)=\omega\uparrow\uparrow(\omega\uparrow^3\omega+1)<br /> =\omega\uparrow(\omega\uparrow\uparrow(\omega\uparrow^3\omega)+1)<br /> =\omega\uparrow(\omega\uparrow^3\omega+1)<br /> =\omega^{\zeta_0+1}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega\uparrow^3\omega+\omega)=\varepsilon_{\zeta_0+1}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega\uparrow^3\omega*2)=\varepsilon_{\zeta_02}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega+2)=\omega\uparrow\uparrow(\omega\uparrow^3(\omega+1))=\varepsilon_{\omega^{\zeta_0+1}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega+3)=\varepsilon_{\varepsilon_{\omega^{\zeta_0+1}}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega2)=\zeta_1&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^43=\zeta_{\zeta_0}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^4\omega=\eta_0&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^4(\omega+1)=\omega\uparrow^3(\omega\uparrow^4\omega+1)<br /> =\omega\uparrow\omega\uparrow\uparrow\omega\uparrow^3(\omega\uparrow^4\omega+1)<br /> =\omega\uparrow(\omega\uparrow^4\omega+1)<br /> =\omega^{\eta_0+1}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^4(\omega+2)=\omega\uparrow^3(\omega\uparrow^4(\omega+1))=\zeta_{\omega^{\eta_0+1}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^4(\omega2)=\eta_1&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^5\omega=\varphi(4,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^{\omega}\omega=\varphi(\omega,0)&lt;/math&gt;<br /> <br /> 于是我们得到其极限为&lt;math&gt;\varphi(\omega,0)&lt;/math&gt;。它的优点是它和&lt;math&gt;\varphi&lt;/math&gt;函数行为完全一致。但缺点也是这个。这导致了&lt;math&gt;\omega\uparrow\uparrow(\omega+1)=(\omega\uparrow\uparrow\omega)\times\omega&lt;/math&gt;这种奇异的结果，某种意义上丢失了超运算自己的特性。因此可以说，+1法序数超运算被&lt;math&gt;\varphi&lt;/math&gt;函数上位替代了。+1法序数超运算还可以继续拓展，在某些版本中，其增长率与类似的Veblen 函数及Feferman序数折叠函数类似，例如：<br /> <br /> &lt;math&gt;\omega\{\omega\}(\omega2)=\varphi(\omega,1)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\omega+1\}\omega=\varphi(\omega+1,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\omega\uparrow\uparrow\omega\}\omega=\varphi(\varepsilon_0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega\}3=\omega\{\omega\{\omega\}\omega\}\omega=\varphi(\varphi(\omega,0),0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega\}\omega=\Gamma_0&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega+1\}\omega=\varphi(1,1,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega2\}\omega=\varphi(2,0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega^2\}\omega=\varphi(1,0,0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega^\omega\}\omega=\psi(\Omega^{\Omega^\omega})&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega^\Omega\}\omega=\psi(\Omega^{\Omega^\Omega})&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega\uparrow\uparrow\omega\}\omega=\psi(\Omega_2)&lt;/math&gt;<br /> <br /> 但如此的拓展达到同样序数的难度要明显大于一般的[[序数坍缩函数]]。有些版本引入了更为强大的结构，但已经失去了超运算的特性，其强度主要为引入的更高级序数结构，建议使用以更高级核心的序数记号替代之。<br /> <br /> == 总结 ==<br /> 到目前为止，序数超运算不是不良定义，就是不理想的。我们不建议在任何地方使用高于&lt;math&gt;\varepsilon_0&lt;/math&gt;的序数超运算和更高级别的运算。如果要使用，必须仅仅将它作为形式上的符号，并且明确地说明其具体含义。事实上，我们完全可以使用[[Veblen 函数]]这样的更加强大且清晰的[[序数记号]]来替代它。<br /> [[分类:记号]]<br /> [[分类:入门]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2731 2026-02-21T09:30:34Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月21日，目前PPS的已知良序极限为0,1,0,2,2,0,5,2,0,8,8,6,0,12,8,6,0,16,16,15,0,16,16,15,0,15,0,26,26,15,0,26,26,13,6,2,0,35,0,26,13,8,6,0,0,15,0,46,46,15,0,46,46,13,6,0,55,55,0,58,58,0,61,61...<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> {{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2724 2026-02-21T08:55:49Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月21日，目前PPS的已知良序极限为0,1,0,2,2,0,5,2,0,8,8,6,0,12,8,6,0,16,16,15,0,16,16,15,0,15,0,26,26,15,0,26,26,13,7,0,35,32,13,6,2,0,36,13,8,6,0,0,0,13,7,0,51,15,0,54,54,15,0,54,54,13,6,0,63,63,0,66,66...<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> {{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=%E5%BA%8F%E6%95%B0%E8%B6%85%E8%BF%90%E7%AE%97&diff=2715 2026-02-21T05:59:19Z

<p>0100000000a7：​修复部分公式排版</p> <hr /> <div>序数超运算是对序数使用[[超运算序列|超运算]]的尝试。它虽然是最直观、新人最容易想到的模式，但已经被长期的[[googology]]实践所证明是低效、难以扩展的。<br /> <br /> == 原定义 ==<br /> 首先，我们仿照[[高德纳箭头]]在自然数上的定义和[[序数#序数的运算|序数运算]]的定义，给出序数使用高德纳箭头的定义：<br /> <br /> # &lt;math&gt;\alpha\uparrow^1\beta=\alpha^{\beta}&lt;/math&gt;<br /> # &lt;math&gt;\alpha\uparrow^c1=\alpha&lt;/math&gt;<br /> # &lt;math&gt;\alpha\uparrow^{c+1}(\beta+1)=\alpha\uparrow^c(\alpha\uparrow^{c+1}\beta)&lt;/math&gt;<br /> # &lt;math&gt;\alpha\uparrow^c\lambda=\sup\{\alpha\uparrow^c\beta|\beta&lt;\lambda\}&lt;/math&gt;<br /> <br /> 其中&lt;math&gt;\alpha,\beta&lt;/math&gt;是任意序数，c是自然数，&lt;math&gt;\lambda&lt;/math&gt;是非0极限序数。<br /> <br /> 这样一来，就有&lt;math&gt;\omega\uparrow^2(\omega+1)=\omega^{\omega\uparrow^2\omega}=sup\{\omega^{\omega\uparrow^2n}|n&lt;\omega\}=sup\{\omega\uparrow^2n|n&lt;\omega\}=\omega\uparrow^2\omega&lt;/math&gt;.进一步，对任意&lt;math&gt;\beta\geq\omega&lt;/math&gt;，都有&lt;math&gt;\omega\uparrow^2\beta=\omega\uparrow^2\omega&lt;/math&gt;.再进一步，对任意的&lt;math&gt;c\geq2,\beta\geq\omega&lt;/math&gt;,都有&lt;math&gt;\omega\uparrow^c\beta=\omega\uparrow^2\omega&lt;/math&gt;.<br /> <br /> 这显然不是我们所期待的。<br /> <br /> == 左结合法 ==<br /> 第一种试图解决问题的方案是左结合法。它借鉴了[[下箭号表示法|下箭头表示法]]，给出序数使用下箭头的定义：<br /> <br /> # &lt;math&gt;\alpha\downarrow^1\beta=\alpha^{\beta}&lt;/math&gt;<br /> # &lt;math&gt;\alpha\downarrow^c1=\alpha&lt;/math&gt;<br /> # &lt;math&gt;\alpha\downarrow^{c+1}(\beta+1)=(\alpha\downarrow^{c+1}\beta)\downarrow\alpha&lt;/math&gt;<br /> # &lt;math&gt;\alpha\downarrow^c\lambda=sup\{\alpha\downarrow^c\beta|\beta&lt;\lambda\}&lt;/math&gt;<br /> <br /> 其中&lt;math&gt;\alpha,\beta&lt;/math&gt;是任意序数，c是自然数，&lt;math&gt;\lambda&lt;/math&gt;是非0极限序数。<br /> <br /> 于是有：<br /> <br /> &lt;math&gt;\omega\downarrow^22=\omega^\omega <br /> &lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^23=\omega^{\omega^2}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^2\omega=\omega^{\omega^\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^2\omega)\downarrow^22=\omega^{\omega^{\omega^\omega}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^33=\omega^{\omega^{\omega^{\omega^\omega}}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^34=\omega^{\omega^{\omega^{\omega^{\omega^{\omega^\omega}}}}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^3\omega=\varepsilon_0&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^3\omega)\downarrow^22=\varepsilon_0^{\varepsilon_0}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^3\omega)\downarrow^2\omega=\varepsilon_0^{\varepsilon_0^\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^3\omega)\downarrow^32=\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^3\omega)\downarrow^33=\varepsilon_0^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^43=\varepsilon_1&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^44=\varepsilon_2&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^4\omega=\varepsilon_\omega&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^4\omega)\downarrow^3\omega=\varepsilon_{\omega+1}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^4\omega)\downarrow^42=\varepsilon_{\varepsilon_\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;(\omega\downarrow^4\omega)\downarrow^43=\varepsilon_{\varepsilon_\omega2}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^53=\varepsilon_{\varepsilon_\omega\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^54=\varepsilon_{\varepsilon_{\varepsilon_\omega\omega}\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^5\omega=\zeta_0&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^6\omega=\zeta_\omega&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^7\omega=\varphi(3,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\downarrow^{1+2n}\omega=\varphi(n,0)&lt;/math&gt;<br /> <br /> 把下箭头用到序数上，其极限为&lt;math&gt;\varphi(\omega,0)&lt;/math&gt;，也符合箭头运算的强度。<br /> <br /> 但是，左结合的下箭头行为和高德纳箭头差异还是不小，而且两个箭头对应一个&lt;math&gt;\varphi(n,0)&lt;/math&gt;还是不太符合我们的预期。<br /> <br /> == 攀爬法 ==<br /> 第二种试图解决问题的方案是攀爬法。攀爬法提供了一种更强的推广。我们知道，&lt;math&gt;\varepsilon_1&lt;/math&gt;的基本列是&lt;math&gt;\{\omega^{\varepsilon_0+1},\omega^{\omega^{\varepsilon_0+1}},\omega^{\omega^{\omega^{\varepsilon_0+1}}},\cdots\}&lt;/math&gt;，我们可以将其表示为&lt;math&gt;\{\omega^{\omega^{\omega^{\cdots}}}+1,\omega^{\omega^{\omega^{\cdots}}+1},\omega^{\omega^{\omega^{\cdots}+1}},\cdots\}&lt;/math&gt;.在这里我们把&lt;math&gt;\omega&lt;/math&gt;的指数塔固定在&lt;math&gt;\omega&lt;/math&gt;。在这样的基本列中，+1像在指数塔攀爬一样，攀爬法也因此而得名。在基本列的尽头，+1攀爬到了指数塔的顶端，与原来在顶端的1相加变为2。因此我们得到&lt;math&gt;\varepsilon_1=\underbrace{\omega^{\omega^{\cdots^{2}}}}_{\omega+1 \text{ layers}}&lt;/math&gt;.进一步的，按照攀爬法我们有&lt;math&gt;\varepsilon_{\omega}=\underbrace{\omega^{\omega^{\cdots^{\omega}}}}_{\omega+1 \text{ layers}}&lt;/math&gt;,我们将其记为&lt;math&gt;\omega\uparrow\uparrow(\omega+1)=\varepsilon_{\omega}&lt;/math&gt;.<br /> <br /> 进一步有：<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega+2)=\varepsilon_{\omega^{\omega}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega\times2)=\varepsilon_{\varepsilon_0}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega^2)=\zeta_0&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega^3)=\eta_0&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega^{\omega})=\varphi(\omega,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow\omega\uparrow\uparrow\omega=\varphi(\varphi(1,0),0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^34=\varphi(\varphi(\varphi(1,0),0),0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3\omega=\varphi(1,0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega+1)=\varphi(1,0,1)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega^2)=\varphi(1,1,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3\omega\uparrow^3\omega=\varphi(1,\varphi(1,0,0),0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^44=\varphi(1,\varphi(1,\varphi(1,0,0),0),0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^4\omega=\varphi(2,0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^5\omega=\varphi(3,0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^{\omega}\omega=\varphi(\omega,0,0)&lt;/math&gt;<br /> <br /> 由此我们得到了攀爬法序数超运算的极限是&lt;math&gt;\varphi(\omega,0,0)&lt;/math&gt;.<br /> <br /> 但是现在已经证明了，攀爬法是非良序的。因此这一做法得到的推广是不可靠的。<br /> <br /> == +1法 ==<br /> 第三中试图解决问题的方案是+1法。<br /> <br /> 它基于一种特别朴素的想法，即：如果&lt;math&gt;\omega\uparrow^c\alpha=\alpha&lt;/math&gt;,则修改其值为&lt;math&gt;\omega\uparrow^c(\alpha+1)&lt;/math&gt;.显然，这一改变真正起到效果的是指数上的变化。关于+1法序数超运算，我们有：<br /> <br /> 例如：ω^^(ω+1)如果展开为ω^ω^^ω就会遇到不动点，因此触发上述的+1规则。<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega+1)=\omega^{\omega\uparrow\uparrow\omega+1}=\omega^{\varepsilon_0+1}&lt;/math&gt;<br /> <br /> 然后，以此类推：<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega+2)=\omega^{\omega^{\varepsilon_0+1}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega2)=\varepsilon_1&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega3)=\varepsilon_2&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega^2)=\varepsilon_{\omega}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^33=\omega\uparrow\uparrow\omega\uparrow\uparrow\omega=\varepsilon_{\varepsilon_0}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3\omega=\zeta_0&lt;/math&gt;<br /> <br /> 到ζ_0后，+1法的展开方式将会比较复杂，并产生一些奇特的基础序列。继续分析：<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega+1)=\omega\uparrow\uparrow(\omega\uparrow^3\omega+1)<br /> =\omega\uparrow(\omega\uparrow\uparrow(\omega\uparrow^3\omega)+1)<br /> =\omega\uparrow(\omega\uparrow^3\omega+1)<br /> =\omega^{\zeta_0+1}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega\uparrow^3\omega+\omega)=\varepsilon_{\zeta_0+1}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow\uparrow(\omega\uparrow^3\omega*2)=\varepsilon_{\zeta_02}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega+2)=\omega\uparrow\uparrow(\omega\uparrow^3(\omega+1))=\varepsilon_{\omega^{\zeta_0+1}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega+3)=\varepsilon_{\varepsilon_{\omega^{\zeta_0+1}}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^3(\omega2)=\zeta_1&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^43=\zeta_{\zeta_0}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^4\omega=\eta_0&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^4(\omega+1)=\omega\uparrow^3(\omega\uparrow^4\omega+1)<br /> =\omega\uparrow\omega\uparrow\uparrow\omega\uparrow^3(\omega\uparrow^4\omega+1)<br /> =\omega\uparrow(\omega\uparrow^4\omega+1)<br /> =\omega^{\eta_0+1}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^4(\omega+2)=\omega\uparrow^3(\omega\uparrow^4(\omega+1))=\zeta_{\omega^{\eta_0+1}}&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^4(\omega2)=\eta_1&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^5\omega=\varphi(4,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\uparrow^{\omega}\omega=\varphi(\omega,0)&lt;/math&gt;<br /> <br /> 于是我们得到其极限为&lt;math&gt;\varphi(\omega,0)&lt;/math&gt;。它的优点是它和&lt;math&gt;\varphi&lt;/math&gt;函数行为完全一致。但缺点也是这个。这导致了&lt;math&gt;\omega\uparrow\uparrow(\omega+1)=(\omega\uparrow\uparrow\omega)\times\omega&lt;/math&gt;这种奇异的结果，某种意义上丢失了超运算自己的特性。因此可以说，+1法序数超运算被&lt;math&gt;\varphi&lt;/math&gt;函数上位替代了。+1法序数超运算还可以继续拓展，在某些版本中，其增长率与类似的Veblen 函数及Feferman序数折叠函数类似，例如：<br /> <br /> &lt;math&gt;\omega\{\omega\}(\omega2)=\varphi(\omega,1)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\omega+1\}\omega=\varphi(\omega+1,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\omega\uparrow\uparrow\omega\}\omega=\varphi(\varepsilon_0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega\}3=\omega\{\omega\{\omega\}\omega\}\omega=\varphi(\varphi(\omega,0),0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega\}\omega=\Gamma_0&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega+1\}\omega=\varphi(1,1,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega2\}\omega=\varphi(2,0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega^2\}\omega=\varphi(1,0,0,0)&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega^\omega\}\omega=\psi(\Omega^{\Omega^\omega})&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega^\Omega\}\omega=\psi(\Omega^{\Omega^\Omega})&lt;/math&gt;<br /> <br /> &lt;math&gt;\omega\{\Omega\uparrow\uparrow\omega\}\omega=\psi(\Omega_2)&lt;/math&gt;<br /> <br /> 但如此的拓展达到同样序数的难度要明显大于一般的[[序数坍缩函数]]。有些版本引入了更为强大的结构，但已经失去了超运算的特性，其强度主要为引入的更高级序数结构，建议使用以更高级核心的序数记号替代之。<br /> <br /> == 总结 ==<br /> 到目前为止，序数超运算不是不良定义，就是不理想的。我们不建议在任何地方使用高于&lt;math&gt;\varepsilon_0&lt;/math&gt;的序数超运算和更高级别的运算。如果要使用，必须仅仅将它作为形式上的符号，并且明确地说明其具体含义。事实上，我们完全可以使用[[Veblen 函数]]这样的更加强大且清晰的[[序数记号]]来替代它。<br /> [[分类:记号]]<br /> [[分类:入门]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2714 2026-02-21T05:52:39Z

<p>0100000000a7：​</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月21日，目前PPS的已知良序极限为0,1,0,2,2,0,5,2,0,8,8,6,0,12,8,6,0,16,16,15,0,16,16,15,0,15,0,26,26,15,0,26,26,13,8,6,0,15,0,38,38,15,0,38,38,13,6,1,0,38,15,0,51,51,6,2,0,0,8,6,0,60,60,59,0,60,60,59,0,59,0,70,70,59,0,70,70,0,6,0,79,8,6,0,83,83,82,0,83,83,82,0,82,0,93,93,82,0,93,93,80,8,6,0,82,0,105,105,82,0,105,105,80,6,0,114,114,0,117,117,...<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> {{默认排序:序数记号}}<br /> [[分类:记号]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PrSS_%E7%9A%84%E8%89%AF%E5%BA%8F%E6%80%A7&diff=2687 2026-02-20T09:37:33Z

<p>0100000000a7：​0100000000a7移动页面PrSS 的良序性至PrSS的良序性：​恢复</p> <hr /> <div>#重定向 [[PrSS的良序性]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PrSS%E7%9A%84%E8%89%AF%E5%BA%8F%E6%80%A7&diff=2686 2026-02-20T09:37:33Z

<p>0100000000a7：​0100000000a7移动页面PrSS 的良序性至PrSS的良序性：​恢复</p> <hr /> <div>=== PrSS 没有无穷降链 ===<br /> 首先我们将 [[初等序列系统|PrSS]] 的每个合法表达式 &lt;math&gt;S&lt;/math&gt; 对应于一个不超过 &lt;math&gt;\varepsilon_0&lt;/math&gt; 的[[序数]] &lt;math&gt;F(S)&lt;/math&gt;。然后我们证明 PrSS 表达式展开时，其对应的序数严格递减。于是就可以依据 &lt;math&gt;\varepsilon_0&lt;/math&gt; 的[[良序|良序性]]说明 PrSS 没有无穷降链。<br /> <br /> '''第一步'''：将 PrSS 的每个合法表达式对应于一个不超过 &lt;math&gt;\varepsilon_0&lt;/math&gt; 的序数。<br /> <br /> 对 PrSS 表达式的长度归纳定义。<br /> <br /> 任取 PrSS 合法表达式 &lt;math&gt;S=(a_1,a_2,\cdots,a_n)&lt;/math&gt;。<br /> <br /> 若 &lt;math&gt;n=0&lt;/math&gt;，则 &lt;math&gt;F(S)=0&lt;\varepsilon_0&lt;/math&gt;。<br /> <br /> 若 &lt;math&gt;n&gt;0&lt;/math&gt;，分两种情况讨论：<br /> <br /> * 若 &lt;math&gt;\forall i\in\{2,3,\cdots,n\},a_i\neq 0&lt;/math&gt;，则取 &lt;math&gt;T=(a_2-1,a_3-1,\cdots,a_n-1)&lt;/math&gt;。&lt;br&gt;不难验证，&lt;math&gt;T&lt;/math&gt; 是合法的 PrSS 表达式，且 &lt;math&gt;T&lt;/math&gt; 的长度比 &lt;math&gt;S&lt;/math&gt; 的长度短。令 &lt;math&gt;F(S)=\omega^{F(T)}&lt;/math&gt;。&lt;br&gt;因为 &lt;math&gt;F(T)&lt;\varepsilon_0&lt;/math&gt;，所以 &lt;math&gt;F(S)&lt;\varepsilon_0&lt;/math&gt;。<br /> * 否则，设 &lt;math&gt;S&lt;/math&gt; 中有 &lt;math&gt;r&lt;/math&gt; 项为零，且 &lt;math&gt;a_{k_1}=a_{k_2}=\cdots=a_{k_r}=0&lt;/math&gt;，其中 &lt;math&gt;1=k_1&lt;k_2&lt;k_3&lt;\cdots&lt;k_r&lt;k_{r+1}=n+1&lt;/math&gt;。&lt;br&gt;取 &lt;math&gt;S_i=(a_{k_i},a_{k_i+1},\cdots,a_{k_{i+1}-1}),\quad i=1,2,\cdots,r&lt;/math&gt;，不难验证 &lt;math&gt;S_1,S_2,\cdots,S_r&lt;/math&gt; 都是合法的 PrSS 表达式，且它们的长度都比 &lt;math&gt;S&lt;/math&gt; 短。&lt;br&gt;令 &lt;math&gt;F(S)=F(S_1)+F(S_2)+\cdots+F(S_r)&lt;/math&gt;。&lt;br&gt;因为 &lt;math&gt;F(S_1),F(S_2),\cdots,F(S_r)&lt;\varepsilon_0&lt;/math&gt;，所以 &lt;math&gt;F(S)&lt;\varepsilon_0&lt;/math&gt;。<br /> <br /> '''第二步'''：证明 PrSS 表达式展开时，其对应的序数严格递减。<br /> <br /> 对 PrSS 表达式的长度归纳证明。<br /> <br /> 任取 PrSS 表达式 &lt;math&gt;S=(a_1,a_2,\cdots,a_n)&lt;/math&gt;。<br /> <br /> 若 &lt;math&gt;n=0&lt;/math&gt;，则 &lt;math&gt;S&lt;/math&gt; 无法展开。下面讨论 &lt;math&gt;n&gt;0&lt;/math&gt; 的情况。<br /> <br /> 若 &lt;math&gt;a_n=0&lt;/math&gt;，则 &lt;math&gt;S&lt;/math&gt; 的展开式（前驱表达式）是 &lt;math&gt;T=(a_1,a_2,\cdots,a_{n-1})&lt;/math&gt;。分为两种情况讨论：<br /> <br /> * 若 &lt;math&gt;\forall i\in\{2,3,\cdots,n\},a_i\neq 0&lt;/math&gt;，则 &lt;math&gt;S=(0)&lt;/math&gt;，&lt;math&gt;F(S)=1&lt;/math&gt;，&lt;math&gt;T=()&lt;/math&gt;，&lt;math&gt;F(T)=0&lt;/math&gt;，&lt;math&gt;F(T)&lt;F(S)&lt;/math&gt;。<br /> * 否则，设 &lt;math&gt;S&lt;/math&gt; 中有 &lt;math&gt;r&lt;/math&gt; 项为零，且 &lt;math&gt;a_{k_1}=a_{k_2}=\cdots=a_{k_r}=0&lt;/math&gt;，其中 &lt;math&gt;1=k_1&lt;k_2&lt;k_3&lt;\cdots&lt;k_r=n&lt;k_{r+1}=n+1&lt;/math&gt;。&lt;br&gt;取 &lt;math&gt;S_i=(a_{k_i},a_{k_i+1},\cdots,a_{k_{i+1}-1}),\quad i=1,2,\cdots,r&lt;/math&gt;，则 &lt;math&gt;F(S)=F(S_1)+F(S_2)+\cdots+F(S_r)&lt;/math&gt;。&lt;br&gt;注意到 &lt;math&gt;S_r=(0)&lt;/math&gt;，&lt;math&gt;F(S_r)=1&lt;/math&gt;，所以 &lt;math&gt;F(T)=F(S_1)+F(S_2)+\cdots+F(S_{r-1})&lt;/math&gt;，所以 &lt;math&gt;F(S)=F(T)+1&gt;F(T)&lt;/math&gt;。<br /> <br /> 若 &lt;math&gt;a_n\neq 0&lt;/math&gt;，分为三种情况讨论：<br /> <br /> * 若 &lt;math&gt;S&lt;/math&gt; 中有不止一项是零。&lt;br&gt;设 &lt;math&gt;S&lt;/math&gt; 中有 &lt;math&gt;r&gt;1&lt;/math&gt; 项为零，且 &lt;math&gt;a_{k_1}=a_{k_2}=\cdots=a_{k_r}=0&lt;/math&gt;，其中 &lt;math&gt;1=k_1&lt;k_2&lt;k_3&lt;\cdots&lt;k_r&lt;k_{r+1}=n+1&lt;/math&gt;。&lt;br&gt;取 &lt;math&gt;S_i=(a_{k_i},a_{k_i+1},\cdots,a_{k_{i+1}-1}),\quad i=1,2,\cdots,r&lt;/math&gt;，则 &lt;math&gt;F(S)=F(S_1)+F(S_2)+\cdots+F(S_r)&lt;/math&gt;。&lt;br&gt;设 &lt;math&gt;S&lt;/math&gt; 的坏根为 &lt;math&gt;a_x&lt;/math&gt;。不难看出，&lt;math&gt;x\ge k_r&lt;/math&gt;。&lt;br&gt;设 &lt;math&gt;S_r&lt;/math&gt; 的基本列的第 &lt;math&gt;p&lt;/math&gt; 项是 &lt;math&gt;V_p&lt;/math&gt;。由 PrSS 展开规则，&lt;math&gt;S&lt;/math&gt; 的基本列的第 &lt;math&gt;p&lt;/math&gt; 项是 &lt;math&gt;U_p=(S_1,S_2,\cdots,S_{r-1},V_p)&lt;/math&gt;。&lt;br&gt;因为 &lt;math&gt;S_r&lt;/math&gt; 的长度比 &lt;math&gt;S&lt;/math&gt; 短，根据归纳假设，有 &lt;math&gt;F(V_p)&lt;F(S_r)&lt;/math&gt;。&lt;br&gt;设 &lt;math&gt;V_p=(b_1,b_2,\cdots,b_m)&lt;/math&gt; 中有 &lt;math&gt;s&lt;/math&gt; 项为零，且 &lt;math&gt;b_{l_1}=b_{l_2}=\cdots=b_{l_s}=0&lt;/math&gt;，其中 &lt;math&gt;1=l_1&lt;l_2&lt;l_3&lt;\cdots&lt;l_s&lt;l_{s+1}=m+1&lt;/math&gt;。&lt;br&gt;取 &lt;math&gt;T_i=(b_{l_i},b_{l_i+1},\cdots,b_{l_{i+1}-1}),\quad i=1,2,\cdots,s&lt;/math&gt;，则 &lt;math&gt;F(V_p)=F(T_1)+F(T_2)+\cdots+F(T_s)&lt;/math&gt;。&lt;br&gt;所以 &lt;math display=&quot;block&quot;&gt;\begin{aligned}F(U_s)\,&amp;=F(S_1)+F(S_2)+\cdots+F(S_{r-1})+F(T_1)+F(T_2)+\cdots+F(T_s)\\&amp;=F(S_1)+F(S_2)+\cdots+F(S_{r-1})+(F(T_1)+F(T_2)+\cdots+F(T_s))\\&amp;=F(S_1)+F(S_2)+\cdots+F(S_{r-1})+F(V_s)\\&amp;&lt;F(S_1)+F(S_2)+\cdots+F(S_{r-1})+F(S_r)\\&amp;=F(S)\end{aligned}&lt;/math&gt;<br /> * 若 &lt;math&gt;S&lt;/math&gt; 中仅有首项为零，且末项为 &lt;math&gt;a_n=1&lt;/math&gt;。&lt;br&gt;令 &lt;math&gt;T_1=(a_1,a_2,\cdots,a_{n-1})&lt;/math&gt;。由 PrSS 展开规则，不难看出 &lt;math&gt;S&lt;/math&gt; 的基本列的第 &lt;math&gt;p&lt;/math&gt; 项是 &lt;math&gt;U_p=(T_1,T_1,\cdots,T_1)&lt;/math&gt;，其中有 &lt;math&gt;p&lt;/math&gt; 个 &lt;math&gt;T_1&lt;/math&gt;。&lt;br&gt;显然 &lt;math&gt;n\ge 2&lt;/math&gt;，所以 &lt;math&gt;F(T_1)&gt;0&lt;/math&gt;。&lt;br&gt;那么 &lt;math&gt;F(U_p)=F(T_1)+F(T_1)+\cdots+F(T_1)=F(T_1)\times p&lt;F(T_1)\times\omega&lt;/math&gt;。&lt;br&gt;令 &lt;math&gt;T_2=(a_2-1,a_3-1,\cdots,a_n-1)&lt;/math&gt;，则 &lt;math&gt;F(S)=\omega^{F(T_2)}&lt;/math&gt;。&lt;br&gt;令 &lt;math&gt;T_3=(a_2-1,a_3-1,\cdots,a_{n-1}-1)&lt;/math&gt;，则 &lt;math&gt;F(T_1)=\omega^{F(T_3)}&lt;/math&gt;。&lt;br&gt;因为 &lt;math&gt;a_n-1=0&lt;/math&gt;，所以 &lt;math&gt;F(T_2)=F(T_3)+1&lt;/math&gt;，所以 &lt;math&gt;F(S)=\omega^{F(T_2)}=\omega^{F(T_3)+1}=\omega^{F(T_3)}\times\omega=F(T_1)\times\omega&gt;F(U_p)&lt;/math&gt;。<br /> * 若 &lt;math&gt;S&lt;/math&gt; 中仅有首项为零，且末项为 &lt;math&gt;a_n\neq 1&lt;/math&gt;。&lt;br&gt;令 &lt;math&gt;T=(a_2-1,a_3-1,\cdots,a_n-1)&lt;/math&gt;，因为 &lt;math&gt;a_n-1\neq 0&lt;/math&gt;，所以 &lt;math&gt;T&lt;/math&gt; 是极限表达式。&lt;br&gt;设 &lt;math&gt;T&lt;/math&gt; 的基本列的第 &lt;math&gt;k&lt;/math&gt; 项是 &lt;math&gt;T_k=(b_1,b_2,\cdots,b_{m_k})&lt;/math&gt;，则由 PrSS 展开规则可以看出 &lt;math&gt;S&lt;/math&gt; 的基本列的第 &lt;math&gt;k&lt;/math&gt; 项是 &lt;math&gt;S_k=(0,b_1+1,b_2+1,\cdots,b_{m_k}+1)&lt;/math&gt;。&lt;br&gt;根据归纳假设有 &lt;math&gt;F(T_k)&lt;F(T)&lt;/math&gt;，所以 &lt;math&gt;F(S_k)=\omega^{F(T_k)}&lt;\omega^{F(T)}=F(S)&lt;/math&gt;。<br /> <br /> 证毕。<br /> <br /> 以上，我们证明了 PrSS 表达式的展开过程不会无限进行，即不存在无穷降链。<br /> <br /> 至此，PrSS 已经是一个合格的序数记号了。但我们不止于此，我们要给出判断 PrSS 表达式是否标准的方法，并证明 PrSS 标准式的序是字典序。<br /> <br /> === PrSS 标准表达式 ===<br /> PrSS 的极限基本列是 &lt;math&gt;(),(0),(0,1),(0,1,2),\cdots&lt;/math&gt;。PrSS 的极限基本列的第 &lt;math&gt;n&lt;/math&gt; 项是 &lt;math&gt;L_n=(0,1,2,\cdots,n-1)&lt;/math&gt;。<br /> <br /> '''定义'''（PrSS 标准表达式）<br /> <br /> 一个 PrSS 表达式 &lt;math&gt;S&lt;/math&gt; 是 '''PrSS 标准表达式'''（简称 '''PrSS 标准式'''），当且仅当存在 &lt;math&gt;n&lt;/math&gt; 使得极限基本列的第 &lt;math&gt;n&lt;/math&gt; 项 &lt;math&gt;L_n&lt;/math&gt; 可以经过若干次展开得到 &lt;math&gt;S&lt;/math&gt;。<br /> <br /> 简单地说，标准式就是能从极限基本列展开得到的表达式。对于大部分的序数记号，存在合法但不标准的表达式。这些不标准的合法表达式往往也能对应于一个序数（例如上一节的映射 &lt;math&gt;F&lt;/math&gt; 不要求表达式是标准的），但这将导致不同的合法表达式对应于同一个序数。对应于同一个序数的不同合法表达式，例如 &lt;math&gt;(0,1)&lt;/math&gt; 和 &lt;math&gt;(0,0,1)&lt;/math&gt; 都是对应于 &lt;math&gt;\omega&lt;/math&gt; 的表达式，彼此之间无法展开成对方。这意味着合法表达式集不是全序，更不是良序。不同的标准表达式则不会对应于同一个序数，标准表达式集确实是良序的。<br /> <br /> 在这一节，我们将给出 PrSS 标准式的必要条件。该条件实际上也是充分的，不过充分性将在下一节证明。在此之前，我们先来定义字典序的概念。<br /> <br /> '''定义'''（字典序）<br /> <br /> 设 &lt;math&gt;A&lt;/math&gt; 是一个全序集，其上的全序是 &lt;math&gt;\le&lt;/math&gt;。考虑两个数列 &lt;math&gt;S=(a_1,a_2,\cdots,a_n)&lt;/math&gt; 和 &lt;math&gt;T=(b_1,b_2,\cdots,b_m)&lt;/math&gt;，其中 &lt;math&gt;a_1,a_2,\cdots,a_n,b_1,b_2,\cdots,b_m\in A&lt;/math&gt;。在字典序下，&lt;math&gt;S\le T&lt;/math&gt; 当且仅当以下两条中的一条成立：<br /> * 存在 &lt;math&gt;0\le k&lt;\min\{n,m\}&lt;/math&gt; 使得对任意 &lt;math&gt;i\in\{1,2,\cdots,k\}&lt;/math&gt; 有 &lt;math&gt;a_i=b_i&lt;/math&gt;，但 &lt;math&gt;a_{k+1}&lt;b_{k+1}&lt;/math&gt;；<br /> * 对任意 &lt;math&gt;i\in\{1,2,\cdots,\min\{n,m\}\}&lt;/math&gt; 有 &lt;math&gt;a_i=b_i&lt;/math&gt;，且 &lt;math&gt;n\le m&lt;/math&gt;。<br /> <br /> 不难看出，对任意两个由 &lt;math&gt;A&lt;/math&gt; 中元素组成的有限数列 &lt;math&gt;S,T&lt;/math&gt;，总有 &lt;math&gt;S\le T\lor T\le S&lt;/math&gt;。也就是说，字典序是全序。<br /> <br /> '''引理'''<br /> <br /> PrSS 表达式展开时，字典序变小。<br /> <br /> '''证明'''<br /> <br /> 设 &lt;math&gt;S=(a_1,a_2,\cdots,a_n)&lt;/math&gt; 是 PrSS 表达式。<br /> <br /> 如果 &lt;math&gt;a_n=0&lt;/math&gt;，则 &lt;math&gt;S&lt;/math&gt; 的展开式为 &lt;math&gt;T=(a_1,a_2,\cdots,a_{n-1})&lt;/math&gt;。根据定义，对任意 &lt;math&gt;i\in\{1,2,\cdots,n-1\}&lt;/math&gt; 有 &lt;math&gt;a_i=a_i&lt;/math&gt;，且 &lt;math&gt;n-1&lt;m&lt;/math&gt;，所以 &lt;math&gt;T&lt;S&lt;/math&gt;。<br /> <br /> 如果 &lt;math&gt;a_n\neq 0&lt;/math&gt;，且展开式 &lt;math&gt;T&lt;/math&gt; 是 &lt;math&gt;S&lt;/math&gt; 的基本列的第 &lt;math&gt;0&lt;/math&gt; 项，则 &lt;math&gt;T&lt;/math&gt; 相当于删去 &lt;math&gt;S&lt;/math&gt; 的末项，所以 &lt;math&gt;T&lt;S&lt;/math&gt;。<br /> <br /> 如果 &lt;math&gt;a_n\neq 0&lt;/math&gt;，且展开式 &lt;math&gt;T&lt;/math&gt; 是 &lt;math&gt;S&lt;/math&gt; 的基本列的第 &lt;math&gt;k&gt;0&lt;/math&gt; 项，则 &lt;math&gt;T&lt;/math&gt; 相当于删去 &lt;math&gt;S&lt;/math&gt; 的末项，并复制若干次坏部。因为坏部的第一项（坏根）小于末项，所以 &lt;math&gt;T&lt;S&lt;/math&gt;。<br /> <br /> 证毕。<br /> <br /> 现在可以给出 PrSS 标准式的必要条件了。<br /> <br /> '''临时定义'''（PrSS 规范式）<br /> <br /> 对表达式 &lt;math&gt;S=(a_1,a_2,\cdots,a_n)&lt;/math&gt; 的长度 &lt;math&gt;n&lt;/math&gt; 归纳定义。<br /> <br /> 若 &lt;math&gt;n=0&lt;/math&gt;，则 &lt;math&gt;S=()&lt;/math&gt; 是 PrSS 规范式。<br /> <br /> 若 &lt;math&gt;n&gt;0&lt;/math&gt; 且 &lt;math&gt;S&lt;/math&gt; 中仅有首项是零，则 &lt;math&gt;S&lt;/math&gt; 是 PrSS 规范式当且仅当 &lt;math&gt;(a_2-1,a_3-1,\cdots,a_n-1)&lt;/math&gt; 是 PrSS 规范式。<br /> <br /> 若 &lt;math&gt;n&gt;0&lt;/math&gt; 且 &lt;math&gt;S&lt;/math&gt; 中有 &lt;math&gt;r&gt;1&lt;/math&gt; 项是零，设 &lt;math&gt;a_{k_1}=a_{k_2}=\cdots=a_{k_r}=0&lt;/math&gt;，其中 &lt;math&gt;1=k_1&lt;k_2&lt;\cdots&lt;k_r&lt;k_{r+1}=n+1&lt;/math&gt;，令 &lt;math&gt;S_i=(a_{k_i},a_{k_i+1},\cdots,a_{k_{i+1}-1})&lt;/math&gt;。则 &lt;math&gt;S&lt;/math&gt; 是 PrSS 规范式当且仅当 &lt;math&gt;S_1,S_2,\cdots,S_r&lt;/math&gt; 都是 PrSS 规范式且按字典序 &lt;math&gt;S_1\ge S_2\ge\cdots\ge S_r&lt;/math&gt;。<br /> <br /> PrSS 规范式是本文临时定义的，并不是通用术语。PrSS 规范式实际上等价于 PrSS 标准式。<br /> <br /> '''定理'''<br /> <br /> PrSS 标准式都是 PrSS 规范式。<br /> <br /> '''证明'''<br /> <br /> 不难看出 PrSS 极限基本列都是 PrSS 规范式，因此只需证明 PrSS 规范式的展开式也是 PrSS 规范式即可。<br /> <br /> 对规范表达式 &lt;math&gt;S=(a_1,a_2,\cdots,a_n)&lt;/math&gt; 的长度 &lt;math&gt;n&lt;/math&gt; 归纳证明。<br /> <br /> &lt;math&gt;n=0,1&lt;/math&gt; 的情况是平凡的，下面讨论 &lt;math&gt;n&gt;1&lt;/math&gt; 的情况。<br /> <br /> 若 &lt;math&gt;S&lt;/math&gt; 中有 &lt;math&gt;r&gt;1&lt;/math&gt; 项是零，设 &lt;math&gt;a_{k_1}=a_{k_2}=\cdots=a_{k_r}=0&lt;/math&gt;，其中 &lt;math&gt;1=k_1&lt;k_2&lt;\cdots&lt;k_r&lt;k_{r+1}=n+1&lt;/math&gt;，令 &lt;math&gt;S_i=(a_{k_i},a_{k_i+1},\cdots,a_{k_{i+1}-1})&lt;/math&gt;。则 &lt;math&gt;S&lt;/math&gt; 的展开相当于 &lt;math&gt;S_r&lt;/math&gt; 的展开。根据归纳假设，&lt;math&gt;S_r&lt;/math&gt; 的展开式是规范的。因为 &lt;math&gt;S_r&lt;/math&gt; 展开后字典序会变小（引理），所以 &lt;math&gt;S&lt;/math&gt; 展开后，各部分的字典序依然递减，所以 &lt;math&gt;S&lt;/math&gt; 的展开式是规范的。注意这里要讨论 &lt;math&gt;S_r&lt;/math&gt; 的展开式有不止一个零的情况，不过这个讨论并不难，感兴趣的读者可以自行讨论。<br /> <br /> 若 &lt;math&gt;S&lt;/math&gt; 中仅有一项是零，且 &lt;math&gt;a_n=1&lt;/math&gt;。令 &lt;math&gt;T_1=(a_2-1,a_3-1,\cdots,a_n-1)&lt;/math&gt;。因为 &lt;math&gt;S&lt;/math&gt; 是规范表达式，根据规范表达式的定义，&lt;math&gt;T_1&lt;/math&gt; 也是规范表达式。从规范表达式的定义中不难看出，去掉 &lt;math&gt;T_1&lt;/math&gt; 末尾的 &lt;math&gt;a_n-1=0&lt;/math&gt; 后依然是规范的，即 &lt;math&gt;T_2=(a_2-1,a_3-1,\cdots,a_{n-1}-1)&lt;/math&gt; 规范。所以 &lt;math&gt;T=(a_1,a_2,\cdots,a_{n-1})&lt;/math&gt; 规范。注意到 &lt;math&gt;S&lt;/math&gt; 的展开式形如 &lt;math&gt;(T,T,\cdots,T)&lt;/math&gt;，所以 &lt;math&gt;S&lt;/math&gt; 的展开式是规范的。<br /> <br /> 若 &lt;math&gt;S&lt;/math&gt; 中仅有一项是零，且 &lt;math&gt;a_n\neq 1&lt;/math&gt;。令 &lt;math&gt;T=(a_2-1,a_3-1,\cdots,a_n-1)&lt;/math&gt;。因为 &lt;math&gt;S&lt;/math&gt; 规范，所以 &lt;math&gt;T&lt;/math&gt; 规范。根据归纳假设，&lt;math&gt;T&lt;/math&gt; 的展开式是规范的。设 &lt;math&gt;S&lt;/math&gt; 的一个展开式是 &lt;math&gt;(b_1,b_2,\cdots,b_m)&lt;/math&gt;，则由 PrSS 展开规则可知 &lt;math&gt;(b_2-1,b_3-1,\cdots,b_m-1)&lt;/math&gt; 是 &lt;math&gt;T&lt;/math&gt; 的展开式，是规范的，所以 &lt;math&gt;S&lt;/math&gt; 的展开式也是规范的。<br /> <br /> 证毕。<br /> <br /> 在第一节证明 PrSS 没有无穷降链时，我们使用了序数的良序性。如果想不依赖序数就证明 PrSS 没有无穷降链，参见知乎用户 www620 的证明&lt;ref&gt;https://zhuanlan.zhihu.com/p/13871622947&lt;/ref&gt;。这个证明依赖本节的两个结论：PrSS 表达式展开时字典序变小、PrSS 标准式都是规范式。注意到本节的两个结论不依赖第一节，所以没有循环论证的问题。<br /> <br /> === PrSS 标准式集的良序性 ===<br /> 上一节我们证明了 PrSS 合法表达式在展开过程中字典序变小，并由此得到了 PrSS 标准式的必要条件。这一节，我们证明字典序变小反过来也意味着可以展开得到，并由此得到 PrSS 标准式的充分条件。<br /> <br /> '''定理'''<br /> <br /> 设 &lt;math&gt;S,T&lt;/math&gt; 是 PrSS 规范式，且按字典序 &lt;math&gt;S&lt;T&lt;/math&gt;，则 &lt;math&gt;S&lt;/math&gt; 经过若干次展开可以得到 &lt;math&gt;T&lt;/math&gt;。<br /> <br /> 注意上一节的引理对任意 PrSS 合法式均成立，而这个定理要求 &lt;math&gt;S,T&lt;/math&gt; 都是规范式。<br /> <br /> '''证明'''<br /> <br /> 定义一种特殊的展开函数 &lt;math&gt;E&lt;/math&gt;：设 PrSS 表达式 &lt;math&gt;U&lt;/math&gt; 的基本列为 &lt;math&gt;U_0,U_1,U_2,\cdots&lt;/math&gt;。若存在 &lt;math&gt;i&lt;/math&gt; 使得按字典序 &lt;math&gt;U_i\ge S&lt;/math&gt;，则取 &lt;math&gt;k=\min\{i\mid U_i\ge S\}&lt;/math&gt; 并定义 &lt;math&gt;E(U)=U_k&lt;/math&gt;。如果对任意 &lt;math&gt;i&lt;/math&gt; 都有按字典序 &lt;math&gt;U_i&lt;S&lt;/math&gt;，则取 &lt;math&gt;E(U)=U&lt;/math&gt;。如果 &lt;math&gt;U&lt;/math&gt; 是后缀表达式，则取 &lt;math&gt;U_0=U_1=\cdots&lt;/math&gt; 为 &lt;math&gt;U&lt;/math&gt; 的前驱表达式。特殊地，如果 &lt;math&gt;U&lt;/math&gt; 是零表达式，则 &lt;math&gt;E(U)=U&lt;/math&gt;。<br /> <br /> 从 &lt;math&gt;E&lt;/math&gt; 的定义不难看出，如果按字典序 &lt;math&gt;U\ge S&lt;/math&gt;，则按字典序 &lt;math&gt;E(U)\ge S&lt;/math&gt;。令 &lt;math&gt;T_0=T&lt;/math&gt;，&lt;math&gt;T_{n+1}=E(T_n)&lt;/math&gt;。因为按字典序 &lt;math&gt;T&gt;S&lt;/math&gt;，所以对任意 &lt;math&gt;i&lt;/math&gt; 都有按字典序 &lt;math&gt;T_i\ge S&lt;/math&gt;。<br /> <br /> 而第一节已经证明 PrSS 不存在无穷降链，所以存在 &lt;math&gt;k&lt;/math&gt; 使得 &lt;math&gt;T_k=T_{k+1}=\cdots&lt;/math&gt;。讨论一下不难得到，这时有两种可能：<br /> <br /> * &lt;math&gt;T_k=S&lt;/math&gt;。<br /> * 按字典序 &lt;math&gt;T_k&gt;S&lt;/math&gt;，但 &lt;math&gt;T_k&lt;/math&gt; 的基本列的每一项都按字典序小于 &lt;math&gt;S&lt;/math&gt;。进一步讨论还可以看出，这种情况下 &lt;math&gt;T_k&lt;/math&gt; 一定是极限表达式。<br /> <br /> 前一种情况命题已经成立，只需要用反证法证明后一种情况不存在即可。<br /> <br /> 若存在，设 &lt;math&gt;T_k&lt;/math&gt; 的好部是 &lt;math&gt;G&lt;/math&gt;，坏部是 &lt;math&gt;B&lt;/math&gt;，末项是 &lt;math&gt;L&lt;/math&gt;，坏根是 &lt;math&gt;L-1&lt;/math&gt;，则 &lt;math&gt;T_k=(G,B,L)&lt;/math&gt;，而 &lt;math&gt;T_k&lt;/math&gt; 的展开式形如 &lt;math&gt;(G,B,B,\cdots)&lt;/math&gt;。<br /> <br /> 如果 &lt;math&gt;S&lt;/math&gt; 按字典序小于 &lt;math&gt;T_k&lt;/math&gt; 而大于 &lt;math&gt;(G,B,B,\cdots)&lt;/math&gt;，那么 &lt;math&gt;S&lt;/math&gt; 一定以 &lt;math&gt;(G,B)&lt;/math&gt; 开头。设 &lt;math&gt;S=(G,B,X)&lt;/math&gt;，那么 &lt;math&gt;X&lt;/math&gt; 的首项等于坏根 &lt;math&gt;L-1&lt;/math&gt;，而 &lt;math&gt;X&lt;/math&gt; 按字典序大于 &lt;math&gt;(B,B,\cdots)&lt;/math&gt;。<br /> <br /> 这与 &lt;math&gt;S&lt;/math&gt; 是规范表达式相矛盾。这个矛盾可以更明确地写出来，但会占据大量篇幅且可能不会提供新的见解，所以在此略。也许以后我会补充。<br /> <br /> 证毕。<br /> <br /> 至此，我们已经证明了，规范表达式集上由展开定义的序，等价于字典序。<br /> <br /> '''定理'''<br /> <br /> PrSS 规范式都是 PrSS 标准式。<br /> <br /> '''证明'''<br /> <br /> 设 &lt;math&gt;S&lt;/math&gt; 是 PrSS 规范式。存在 &lt;math&gt;n&lt;/math&gt; 使得 &lt;math&gt;T=(0,1,2,\cdots,n-1)&lt;/math&gt; 按字典序大于 &lt;math&gt;S&lt;/math&gt;。根据上一个定理，&lt;math&gt;T&lt;/math&gt; 可以展开成 &lt;math&gt;S&lt;/math&gt;，所以 &lt;math&gt;S&lt;/math&gt; 是 PrSS 标准式。<br /> <br /> 证毕。<br /> <br /> 至此，我们证明了 PrSS 没有无穷降链、PrSS 标准式集的序是字典序，而字典序是全序，所以 PrSS 标准式集上的序是良序。<br /> <br /> 但我们不止于此。下一节，我们要证明 PrSS 标准式集[[良序|序同构]]于 &lt;math&gt;\varepsilon_0&lt;/math&gt;。<br /> <br /> === PrSS 标准式集的序型 ===<br /> 为了证明 PrSS 标准式集[[良序|序同构]]于 &lt;math&gt;\varepsilon_0&lt;/math&gt;，我们要证明第一节定义的保序映射 &lt;math&gt;F&lt;/math&gt; 是 PrSS 标准式集和 &lt;math&gt;\varepsilon_0&lt;/math&gt; 之间的双射，结合 PrSS 标准式集的全序性，就能说明 &lt;math&gt;F&lt;/math&gt; 是 PrSS 标准式集和 &lt;math&gt;\varepsilon_0&lt;/math&gt; 之间的序同构。<br /> <br /> '''定理'''<br /> <br /> &lt;math&gt;F&lt;/math&gt;是 PrSS 标准式集与&lt;math&gt;\varepsilon_0&lt;/math&gt;之间的保序双射。<br /> <br /> '''证明'''<br /> <br /> 对于小于&lt;math&gt;\varepsilon_0&lt;/math&gt;的序数&lt;math&gt;\alpha&lt;/math&gt;，定义&lt;math&gt;Seq(\alpha)=(a_1,a_2,\cdots,a_k)&lt;/math&gt;是这样的自然数序列：<br /> <br /> * &lt;math&gt;Seq(0)=()&lt;/math&gt;为空序列<br /> * &lt;math&gt;\alpha&gt;0&lt;/math&gt;时，设它的康托范式为&lt;math&gt;\alpha=\omega^{\alpha_1}+\omega^{\alpha_2}+\omega^{\alpha_3}+\cdots +\omega^{\alpha_n}&lt;/math&gt;，则&lt;math&gt;Seq(\alpha)=T(S'(\alpha_1),S'(\alpha_2),\cdots,S'(\alpha_n))&lt;/math&gt;，其中&lt;math&gt;T&lt;/math&gt;为序列的拼合，而如果&lt;math&gt;Seq(\alpha)=(a_1,a_2,\cdots,a_k)&lt;/math&gt;，&lt;math&gt;S'(\alpha)&lt;/math&gt;定义为&lt;math&gt;(0,a_1+1,a_2+1,\cdots,a_k+1)&lt;/math&gt;<br /> <br /> 我们给出几个引理：<br /> <br /> '''引理1''' 如果&lt;math&gt;\varepsilon_0&gt;\alpha\geq\beta&lt;/math&gt;，则按字典序&lt;math&gt;Seq(\alpha)\geq{Seq(\beta)}&lt;/math&gt;<br /> <br /> '''引理2''' &lt;math&gt;Seq(\alpha)&lt;/math&gt;是 PrSS 的规范式。<br /> <br /> '''引理3''' &lt;math&gt;F(Seq(\alpha))=\alpha&lt;/math&gt;<br /> <br /> '''引理4''' &lt;math&gt;Seq(F(S))=S&lt;/math&gt;，其中&lt;math&gt;S&lt;/math&gt;为 PrSS 规范式<br /> <br /> '''引理1的证明''' 取出所有有序对&lt;math&gt;(\alpha,\beta)&lt;/math&gt;使&lt;math&gt;\varepsilon_0&gt;\alpha&gt;\beta&lt;/math&gt;但按字典序&lt;math&gt;Seq(\alpha)\leq{Seq(\beta)}&lt;/math&gt;，取出其中&lt;math&gt;\alpha&lt;/math&gt;最小的一组。写出它们的康托范式：<br /> <br /> &lt;math&gt;\alpha=\omega^{\alpha_1}+\omega^{\alpha_2}+\omega^{\alpha_3}+\cdots +\omega^{\alpha_p}&lt;/math&gt;<br /> <br /> &lt;math&gt;\beta=\omega^{\beta_1}+\omega^{\beta_2}+\omega^{\beta_3}+\cdots +\omega^{\beta_q}&lt;/math&gt;<br /> <br /> 则以下两点成立其一：<br /> # 存在某个&lt;math&gt;i\leq{min\{p,q\}}&lt;/math&gt;使&lt;math&gt;\alpha_i&gt;\beta_i&lt;/math&gt;<br /> # &lt;math&gt;q&lt;p&lt;/math&gt;，且对于所有&lt;math&gt;i\leq{q}&lt;/math&gt;有&lt;math&gt;\alpha_i=\beta_i&lt;/math&gt;<br /> <br /> 对于前者，由于&lt;math&gt;\alpha_i&lt;\alpha&lt;/math&gt;，根据&lt;math&gt;\alpha&lt;/math&gt;的最小性，字典序下&lt;math&gt;Seq(\alpha_i)&gt;Seq(\beta_i)&lt;/math&gt;，根据定义，字典序下&lt;math&gt;Seq(\alpha)&gt;Seq(\beta)&lt;/math&gt;，矛盾。<br /> <br /> 对于后者，易知&lt;math&gt;Seq(\beta_i)&lt;/math&gt;是&lt;math&gt;Seq(\alpha_i)&lt;/math&gt;删去后面数项得到的子序列。故字典序下&lt;math&gt;Seq(\alpha)&gt;Seq(\beta)&lt;/math&gt;，矛盾。<br /> <br /> 因此，这样的有序对&lt;math&gt;(\alpha,\beta)&lt;/math&gt;不存在，所以如果&lt;math&gt;\varepsilon_0&gt;\alpha\geq\beta&lt;/math&gt;，则按字典序&lt;math&gt;Seq(\alpha)\geq{Seq(\beta)}&lt;/math&gt;<br /> <br /> 又如果&lt;math&gt;\varepsilon_0&gt;\alpha=\beta&lt;/math&gt;，则按字典序&lt;math&gt;Seq(\alpha)=Seq(\beta)&lt;/math&gt;。于是引理1得证。<br /> <br /> '''引理2的证明''' 设&lt;math&gt;\alpha&lt;\varepsilon_0&lt;/math&gt;是最小使得&lt;math&gt;Seq(\alpha)&lt;/math&gt;不是 PrSS 的规范式的序数。设它的康托范式为&lt;math&gt;\alpha=\omega^{\alpha_1}+\omega^{\alpha_2}+\omega^{\alpha_3}+\cdots +\omega^{\alpha_n}&lt;/math&gt;。<br /> <br /> (1) 若&lt;math&gt;n=1&lt;/math&gt;，&lt;math&gt;\alpha=\omega^{\alpha_1}&lt;/math&gt;，&lt;math&gt;Seq(\alpha)=S'(\alpha_1)&lt;/math&gt;。根据定义，&lt;math&gt;Seq(\alpha)&lt;/math&gt;是 PrSS 的规范式当且仅当&lt;math&gt;Seq(\alpha_1)&lt;/math&gt;是 PrSS 的规范式，而&lt;math&gt;\alpha_1&lt;\alpha&lt;/math&gt;，根据最小性，&lt;math&gt;Seq(\alpha_1)&lt;/math&gt;是 PrSS 的规范式，故&lt;math&gt;Seq(\alpha)&lt;/math&gt;也是 PrSS 的规范式，矛盾。<br /> <br /> (2) 若&lt;math&gt;n&gt;1&lt;/math&gt;，&lt;math&gt;\alpha=\omega^{\alpha_1}+\omega^{\alpha_2}+\omega^{\alpha_3}+\cdots +\omega^{\alpha_n}&lt;/math&gt;，&lt;math&gt;Seq(\alpha)=T(S'(\alpha_1),S'(\alpha_2),\cdots,S'(\alpha_n))&lt;/math&gt;。根据定义，&lt;math&gt;Seq(\alpha)&lt;/math&gt;是 PrSS 的规范式当且仅当每个&lt;math&gt;Seq(\alpha_k)&lt;/math&gt;均是 PrSS 的规范式且&lt;math&gt;Seq(\alpha_k)&lt;/math&gt;的字典序不增，&lt;math&gt;k=1,2,\cdots,n&lt;/math&gt;。前者是显然的(类似于上文的(1)部分)，而后者由&lt;math&gt;\alpha_1\geq\alpha_2\geq\cdots\alpha_n&lt;/math&gt;和引理1保证。于是&lt;math&gt;Seq(\alpha)&lt;/math&gt;是 PrSS 的规范式，矛盾。<br /> <br /> 故这样的&lt;math&gt;\alpha&lt;\varepsilon_0&lt;/math&gt;不存在。引理2得证。<br /> <br /> '''引理3的证明''' 设&lt;math&gt;\alpha&lt;\varepsilon_0&lt;/math&gt;是最小的不满足&lt;math&gt;F(Seq(\alpha))=\alpha&lt;/math&gt;的序数。它的康托范式为&lt;math&gt;\alpha=\omega^{\alpha_1}+\omega^{\alpha_2}+\omega^{\alpha_3}+\cdots +\omega^{\alpha_n}&lt;/math&gt;。<br /> <br /> 则有&lt;math&gt;Seq(\alpha)=T(S'(\alpha_1),S'(\alpha_2),\cdots,S'(\alpha_n))&lt;/math&gt;。根据定义，&lt;math&gt;F(T(S'(\alpha_1),S'(\alpha_2),\cdots,S'(\alpha_n)))=F(S'(\alpha_1))+F(S'(\alpha_2))+\cdots+F(S'(\alpha_n))=\omega^{F(Seq(\alpha_1))}+\omega^{F(Seq(\alpha_2))}+\cdots+\omega^{F(Seq(\alpha_n))}&lt;/math&gt;，而&lt;math&gt;\alpha_k&lt;\alpha&lt;/math&gt;，&lt;math&gt;k=1,2,\cdots,n&lt;/math&gt;，根据最小性，&lt;math&gt;F(Seq(\alpha_k))=\alpha_k&lt;/math&gt;，故&lt;math&gt;F(T(S'(\alpha_1),S'(\alpha_2),\cdots,S'(\alpha_n)))=\omega^{\alpha_1}+\omega^{\alpha_2}+\omega^{\alpha_3}+\cdots +\omega^{\alpha_n}=\alpha&lt;/math&gt;。矛盾。<br /> <br /> 故这样的&lt;math&gt;\alpha&lt;\varepsilon_0&lt;/math&gt;不存在。引理3得证。<br /> <br /> '''引理4的证明''' 若对于某个 PrSS 规范式&lt;math&gt;S&lt;/math&gt;有&lt;math&gt;Seq(F(S))&gt;S&lt;/math&gt;，则由引理1得&lt;math&gt;F(Seq(F(S))&gt;F(S)&lt;/math&gt;，由引理3得&lt;math&gt;F(S)&gt;F(S)&lt;/math&gt;，矛盾。同理，&lt;math&gt;Seq(F(S))&lt;S&lt;/math&gt;则&lt;math&gt;F(S)&lt;F(S)&lt;/math&gt;，矛盾。故&lt;math&gt;Seq(F(S))=S&lt;/math&gt;。<br /> <br /> '''定理的证明''' 由引理1~4，&lt;math&gt;F&lt;/math&gt;有逆映射&lt;math&gt;Seq&lt;/math&gt;，且&lt;math&gt;Seq&lt;/math&gt;保序。于是&lt;math&gt;Seq&lt;/math&gt;(和其逆&lt;math&gt;F&lt;/math&gt;)是 PrSS 标准式集与&lt;math&gt;\varepsilon_0&lt;/math&gt;之间的序同构。<br /> <br /> 证毕。&lt;references /&gt;<br /> [[分类:集合论相关]]</div>

0100000000a7 http://wiki.googology.top/index.php?title=%E8%AE%B0%E5%8F%B7%E5%B1%95%E5%BC%80%E5%99%A8&diff=2685 2026-02-20T08:11:49Z

<p>0100000000a7：​</p> <hr /> <div>[https://hypcos.github.io/notation-explorer/ NE]包含了许多常见记号的展开器。&lt;br /&gt;<br /> 以下网址也包含了一些记号的展开器，各有不同，请依据实际情况使用：<br /> <br /> [https://0y.googology.top 0-Y展开器(带山脉图)，i0-Y(测试性)]&lt;br /&gt;<br /> [https://solarzone1010.github.io/ SSO内的BMS分析仪，cOCF及HSPN展开器，TONF及GON浏览器等]&lt;br /&gt;<br /> [https://gyafun.jp/ln/basmat.cgi Bashicu矩阵计算器]&lt;br /&gt;<br /> [https://waffle3z.github.io/notations/ BMS、Y序列、HPrSS、LPrSS、BrSS浏览器等]&lt;br /&gt;<br /> [https://fghdisplayer.onrender.com/ LVO内韦伯伦函数的FGH及基本列展开]&lt;br /&gt;<br /> [https://naruyoko.github.io/googology/ Y和ω-Y序列的展开和山脉图绘制、BMS的展开过程演示等]&lt;br /&gt;<br /> [https://koteitan.github.io/BeklemishevsWorms/ worm序列辅助展开程序]<br /> [https://gomen520.github.io/ X-Y展开程序]</div>

0100000000a7 http://wiki.googology.top/index.php?title=PPS&diff=2670 2026-02-20T06:37:52Z

<p>0100000000a7：​添加对良序极限的说明</p> <hr /> <div>'''Parented Predecessor Sequence(PPS)'''是由3184创造的一个序列记号，其父项定位方式是[[项定位方式#2.标记父项位置|标记父项位置]]。<br /> <br /> PPS有着较为简单的定义，但分析它却极为复杂和困难。<br /> <br /> 2025年8月，PPS2被发现[[无穷降链]]。<br /> <br /> 2025年12月10日，PPS1被发现无穷降链。所有PPS衍生物亦未能幸免。<br /> <br /> 截止到2026年2月20日，目前PPS的已知良序极限为0,1,0,2,2,0,5,2,0,8,8,6,0,12,8,6,0,16,16,15,0,16,16,15,0,15,0,26,26,15,0,26,26,13,8,6,0,15,0,38,38,15,0,38,38,13,6,2,0,8,6,0,51,51,50,0,51,51,50,0,50,0,61,61,50,0,61,61,0,6,0,70,8,6,0,74,74,73,0,74,74,73,0,73,0,84,84,73,0,84,84,71,8,6,0,73,0,96,96,73,0,96,96,71,6,0,105,105,0,108,108,0,111,111,0,114,114,0,117,117,...<br /> <br /> 后续phyrion在圣诞节前连夜修改了10+个版本，亦未能避免无穷降链，不过受部分启发提出了[[PRRS]]。<br /> <br /> 前排提示：PPS的行为极其复杂，是标准的“果糕“记号<br /> <br /> === 定义 ===<br /> 以下为PPS1的定义。PPS2和PPS3的问题较为明显且未能修改PPS1的不足之处，因此不在此给出定义。<br /> <br /> PPS是形如0,1,0,3这样用逗号分隔的序列（序列首项是第1项）<br /> <br /> 极限表达式：0,1,2,3,4,5,......<br /> <br /> 记末项的值为x，坏根为第x项，坏根的值为b，末项是序列中的第y项，并令L=y-x<br /> <br /> 展开：<br /> <br /> 1.如果末项是0，则它是后继序数<br /> <br /> 2.末项之前的部分保持不变<br /> <br /> 3.替换末项：如果末项和坏根之间(两边都不含)存在一项，它的值等于b，那么将末项的值换成b；否则将末项的值减1<br /> <br /> 4.递归生成其他项(第i+L项的值由第i项确定)：对任意的i&gt;x，如果第i项的值大于等于x，那么第i+L项的值等于第i项的值+L，否则第i+L项的值等于第i项的值<br /> <br /> 5.基本列[n]为展开到第y+n*L-1项<br /> === 分析 ===<br /> 另见[[PPS分析]]<br /> <br /> PPS的分析是极为困难的，即便是一些分析力很强的googologist，如mtl、zcmx，都曾在PPS上折戟。<br /> <br /> === 地府段 ===<br /> PPS有部分从表达式上看差距不大，但分析却极为困难且需要大量篇幅的段落，它们被称为地府段，简称地府。<br /> <br /> ==== 第一部分：0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10 ====<br /> [[文件:pcf 25-07-22.jpg|缩略图|2025年7月22日，来自PCF]]<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10是地府的第一层。<br /> <br /> 它们分别对应序数&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\varepsilon_0+1}\times 2}}}&lt;/math&gt;<br /> <br /> 和&lt;math&gt;\varepsilon_{\omega^{\omega^{\omega^{\omega^{\varepsilon_{\varepsilon_0}+1}}}}}&lt;/math&gt;。<br /> <br /> 几位扽西力较强的gggist合力也用了近五天才把它扽出来。在分析表格中，它们占用了超过两百行。<br /> <br /> ==== 第二部分：0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10 ====<br /> 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,9 ~ 0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10是地府的第二层。这之间还有不计其数的地府第一层的结构。分析它更是难上加难，'''四百行'''扽西也仅仅只能在第二层地府中踏出小而无力的一步。<br /> <br /> 截至目前，我们仍未得知0,1,0,2,0,4,4,3,0,4,3,0,11,10,0,0,10,0,17,10对应哪个序数，不过根据Phyrion的猜测，它有可能&lt;math&gt;\ge \zeta_0&lt;/math&gt;。<br /> <br /> {{默认排序:序数记号}}<br /> [[分类:记号]]</div>

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