http://wiki.googology.top/api.php?action=feedcontributions&feedformat=atom&user=Alice 2026-06-07T21:40:50Z 用户贡献 MediaWiki 1.43.1 http://wiki.googology.top/index.php?title=DSM&diff=3091 2026-05-23T15:21:49Z

<p>Alice：​</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''magma'''：展开的两种模式，影响展开结果。<br /> <br /> '''试展开'''：指以 strong magma 展开 1 次。<br /> <br /> '''最终展开'''：指以 weak magma 展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> strong magma 与 weak magma 的小展开一致。<br /> <br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> # 若为 strong magma 展开，则若某一项与坏项位于同一行，且其下方一项的祖先项包含坏项的下方一项，则本项为上升项。如果本项与坏项都位于第 0 行，本条件视为成立。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> # 若某一项的父项是坏项或填充项，则本项是填充项。<br /> # 若为 strong magma 展开，则若某一项下方一项的祖先项包含坏项的下方一项，则本项为填充项。如果本项与坏项都位于第 0 行，本条件视为成立。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 若为 weak magma 展开，将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> # 若为 strong magma 展开，将所有填充项（位于第 j 列）的下方一项分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。若填充项位于第 0 行，则被复制的项为一个父项为左侧相邻一列的虚拟项。<br /> <br /> 事实上，完全展开与 1-Y 的展开过程是很相似的。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为'''后继矩阵'''，删除最右列并不进行展开，得到的矩阵为其前驱。否则为'''极限矩阵'''，取其父项矩阵。<br /> <br /> 从右到左找到每一个检测项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(5) = Y(1,3,9,25,26)。<br /> <br /> 据分析，DSM 在 Y(1,3,9,25,26,3) 前方出现了极大的弱化。这可能意味着对类 Y 序列的记号简单增加 Sudden 会遇到与 BSM 等记号类似的问题，而无法真正增加强度。<br /> <br /> 0 ~ Y(1,3,7) : [[DSM分析Part1]]<br /> <br /> Y(1,3,7) ~ Y(1,3,9) : [[DSM分析Part2]]<br /> <br /> Y(1,3,9) ~ Y(1,3,9,25) : [[DSM分析Part3]]{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=3090 2026-05-23T15:19:31Z

<p>Alice：​</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''magma'''：展开的两种模式，影响展开结果。<br /> <br /> '''试展开'''：指以 strong magma 展开 1 次。<br /> <br /> '''最终展开'''：指以 weak magma 展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> strong magma 与 weak magma 的小展开一致。<br /> <br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> # 若为 strong magma 展开，则若某一项与坏项位于同一行，且其下方一项的祖先项包含坏项的下方一项，则本项为上升项。如果本项与坏项都位于第 0 行，本条件视为成立。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> # 若某一项的父项是坏项或填充项，则本项是填充项。<br /> # 若为 strong magma 展开，则若某一项下方一项的祖先项包含坏项的下方一项，则本项为填充项。如果本项与坏项都位于第 0 行，本条件视为成立。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 若为 weak magma 展开，将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> # 若为 strong magma 展开，将所有填充项（位于第 j 列）的下方一项分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。若填充项位于第 0 行，则被复制的项为一个父项为左侧相邻一列的虚拟项。<br /> <br /> 事实上，完全展开与 1-Y 的展开过程是很相似的。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为'''后继矩阵'''，删除最右列并不进行展开，得到的矩阵为其前驱。否则为'''极限矩阵'''，取其父项矩阵。<br /> <br /> 从右到左找到每一个检测项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2,1) = Y(1,3,9,25)。<br /> <br /> 据分析，DSM 在 Y(1,3,9,25,26,3) 前方出现了极大的弱化。这可能意味着对类 Y 序列的记号简单增加 Sudden 会遇到与 BSM 等记号类似的问题，而无法真正增加强度。<br /> <br /> 0 ~ Y(1,3,7) : [[DSM分析Part1]]<br /> <br /> Y(1,3,7) ~ Y(1,3,9) : [[DSM分析Part2]]<br /> <br /> Y(1,3,9) ~ Y(1,3,9,25) : [[DSM分析Part3]]{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=3089 2026-05-23T15:19:15Z

<p>Alice：​</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''magma'''：展开的两种模式，影响展开结果。<br /> <br /> '''试展开'''：指以 strong magma 展开 1 次。<br /> <br /> '''最终展开'''：指以 weak magma 展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> strong magma 与 weak magma 的小展开一致。<br /> <br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> # 若为 strong magma 展开，则若某一项与坏项位于同一行，且其下方一项的祖先项包含坏项的下方一项，则本项为上升项。如果本项与坏项都位于第 0 行，本条件视为成立。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> # 若某一项的父项是坏项或填充项，则本项是填充项。<br /> # 若为 strong magma 展开，则若某一项下方一项的祖先项包含坏项的下方一项，则本项为填充项。如果本项与坏项都位于第 0 行，本条件视为成立。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 若为 weak magma 展开，将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> # 若为 strong magma 展开，将所有填充项（位于第 j 列）的下方一项分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。若填充项位于第 0 行，则被复制的项为一个父项为左侧相邻一列的虚拟项。<br /> <br /> 事实上，完全展开与 1-Y 的展开过程是很相似的。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为'''后继矩阵'''，删除最右列并不进行展开，得到的矩阵为其前驱。否则为'''极限矩阵'''，取其父项矩阵。<br /> <br /> 从右到左找到每一个检测项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2,1) = Y(1,3,9,25)。<br /> <br /> 据分析，DSM 在 Y(1,3,9,25,26,3) 前方出现了极大的弱化。这可能意味着对类 Y 序列的记号简单增加 Sudden 会遇到与 BSM 等记号类似的问题而无法真正增加强度。<br /> <br /> 0 ~ Y(1,3,7) : [[DSM分析Part1]]<br /> <br /> Y(1,3,7) ~ Y(1,3,9) : [[DSM分析Part2]]<br /> <br /> Y(1,3,9) ~ Y(1,3,9,25) : [[DSM分析Part3]]{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=3079 2026-05-22T23:14:57Z

<p>Alice：​</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''magma'''：展开的两种模式，影响展开结果。<br /> <br /> '''试展开'''：指以 strong magma 展开 1 次。<br /> <br /> '''最终展开'''：指以 weak magma 展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> strong magma 与 weak magma 的小展开一致。<br /> <br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> # 若为 strong magma 展开，则若某一项与坏项位于同一行，且其下方一项的祖先项包含坏项的下方一项，则本项为上升项。如果本项与坏项都位于第 0 行，本条件视为成立。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> # 若某一项的父项是坏项或填充项，则本项是填充项。<br /> # 若为 strong magma 展开，则若某一项下方一项的祖先项包含坏项的下方一项，则本项为填充项。如果本项与坏项都位于第 0 行，本条件视为成立。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 若为 weak magma 展开，将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> # 若为 strong magma 展开，将所有填充项（位于第 j 列）的下方一项分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。若填充项位于第 0 行，则被复制的项为一个父项为左侧相邻一列的虚拟项。<br /> <br /> 事实上，完全展开与 1-Y 的展开过程是很相似的。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为'''后继矩阵'''，删除最右列并不进行展开，得到的矩阵为其前驱。否则为'''极限矩阵'''，取其父项矩阵。<br /> <br /> 从右到左找到每一个检测项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2,1) = Y(1,3,9,25)。<br /> <br /> 0 ~ Y(1,3,7) : [[DSM分析Part1]]<br /> <br /> Y(1,3,7) ~ Y(1,3,9) : [[DSM分析Part2]]<br /> <br /> Y(1,3,9) ~ Y(1,3,9,25) : [[DSM分析Part3]]{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part3&diff=3078 2026-05-22T23:14:17Z

<p>Alice：​</p> <hr /> <div>本分析由 test_alpha0 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == Y(1,3,9) ~ Y(1,3,9,10,3) ==<br /> (0)(1)(2,1)(3) = 1,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1) = 1,3,9,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1) = 1,3,9,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,9,3,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,3,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,3,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4) = 1,3,9,4<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1) = 1,3,9,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2) = 1,3,9,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1) = 1,3,9,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2) = 1,3,9,7,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9) = 1,3,9,7,14,27,55<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,7,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,7,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5) = 1,3,9,7,17,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1) = 1,3,9,7,17,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1) = 1,3,9,7,17,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2,1) = 1,3,9,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(5) = 1,3,9,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1) = 1,3,9,10,2<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1) = 1,3,9,10,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10,2,5,14,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(2) = 1,3,9,10,2,5,14,15,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(3,1)(4,2,1) = 1,3,9,10,2,5,14,15,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,15,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(4) = 1,3,9,10,2,5,14,15,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1) = 1,3,9,10,2,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1) = 1,3,9,10,2,5,14,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2) = 1,3,9,10,2,5,14,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1) = 1,3,9,10,2,5,14,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,19,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3) = 1,3,9,10,2,5,14,19,30,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1) = 1,3,9,10,2,5,14,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1) = 1,3,9,10,2,5,14,20,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,20,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(4) = 1,3,9,10,2,5,14,20,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5) = 1,3,9,10,2,5,14,20,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1) = 1,3,9,10,2,5,14,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1) = 1,3,9,10,2,5,14,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,22,14,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4) = 1,3,9,10,2,5,14,22,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5) = 1,3,9,10,2,5,14,22,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,28,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(6,2,1)(7) = 1,3,9,10,2,5,14,22,30,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2) = 1,3,9,10,2,5,14,22,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,36,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1) = 1,3,9,10,2,5,14,22,37<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3,1) = 1,3,9,10,2,5,14,22,38<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6) = 1,3,9,10,2,5,14,22,38,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5) = 1,3,9,10,2,5,14,22,38,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,44,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,52,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,63,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3)(6,4,1)(7) = 1,3,9,10,2,5,14,22,38,65,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3,1) = 1,3,9,10,2,5,14,22,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,22,41,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2,1) = 1,3,9,10,2,5,14,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2,1)(5) = 1,3,9,10,2,5,14,22,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(5) = 1,3,9,10,2,5,14,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1) = 1,3,9,10,2,5,14,23,25<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,22,38,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,22,41,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(4) = 1,3,9,10,2,5,14,23,29,22,41,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,41,40<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1)(7,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,78,41<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,78,63,111<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(7) = 1,3,9,10,2,5,14,23,29,22,43,64,78,64<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8) = 1,3,9,10,2,5,14,23,29,22,43,64,78,65<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2) = 1,3,9,10,2,5,14,23,29,22,43,64,78,93<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,79<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8) = 1,3,9,10,2,5,14,23,29,22,43,64,80,81<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8,2)(9,3,1)(10,4,2,1)(11) = 1,3,9,10,2,5,14,23,29,22,43,64,80,110,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8,2)(9,3,1)(10,4,2,1)(11,1)(10,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,80,111<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,2) = 1,3,9,10,2,5,14,23,29,22,43,64,81<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,3,1)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,81,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,23,29,23,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,22,41,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7) = 1,3,9,10,2,5,14,23,29,23,22,38,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,38,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,1)(6,3,1) = 1,3,9,10,2,5,14,23,29,23,22,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,41,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(9,2,1)(10,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,80,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(6,3,1)(7,4,2,1)(8,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1)(7,3,1)(8,4,2,1)(9,3,1)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,64,63,43,64,81,64<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,23,22,14,23,29,23,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5) = 1,3,9,10,2,5,14,23,29,23,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,29,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,29,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(5) = 1,3,9,10,2,5,14,23,29,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(6,2,1)(7,1)(6,2,1) = 1,3,9,10,2,5,14,23,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2) = 1,3,9,10,2,5,14,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1) = 1,3,9,10,3<br /> <br /> == Y(1,3,9,10,3) ~ Y(1,3,9,25) ==<br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1) = 1,3,9,10,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1)(5) = 1,3,9,16,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4) = 1,3,9,16,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,10,2,5,14,30,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1) = 1,3,9,16,10,2,5,14,30,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(4) = 1,3,9,16,10,2,5,14,30,22,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,16,10,2,5,14,30,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(5,2,1)(5,2) = 1,3,9,16,10,2,5,14,30,23,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(5,2,1)(5,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,10,2,5,14,30,23,39,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,2) = 1,3,9,16,10,2,5,14,30,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,2)(3,1)(4,2,1) = 1,3,9,16,10,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5) = 1,3,9,16,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,17,2,5,14,30,36,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,1)(6,2,1)(7,1)(6,2,1) = 1,3,9,16,17,2,5,14,30,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,2) = 1,3,9,16,17,2,5,14,30,40<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3) = 1,3,9,16,17,2,5,14,30,47<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3)(3,1)(4,2,1) = 1,3,9,16,17,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,23,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3)(6,4,1) = 1,3,9,16,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(5,3,1) = 1,3,9,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6) = 1,3,9,18,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(4) = 1,3,9,18,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,1)(4) = 1,3,9,18,30,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8) = 1,3,9,18,33,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,1)(7,5,2,1) = 1,3,9,18,34<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,1)(7,5,2,1)(8,1)(7,5,2,1) = 1,3,9,18,35,52,65,51,83<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1) = 1,3,9,18,35,52,65,52<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2) = 1,3,9,18,35,53<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1) = 1,3,9,18,35,62<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1)(9) = 1,3,9,18,35,64,35<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1)(9,4,1)(6,4,1)(7,5,2,1)(8,1)(7,5,2,1) = 1,3,9,18,35,64,35,52,65,34<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1)(9,4,1)(8,6,3)(9,7,4,1)(10,4,1)(7) = 1,3,9,18,35,64,109,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3,1) = 1,3,9,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3,1)(5,3,1) = 1,3,9,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,22,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1)(6,4,2,1) = 1,3,9,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2,1) = 1,3,9,25<br /> [[分类:分析]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=3075 2026-05-22T04:06:04Z

<p>Alice：​</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''magma'''：展开的两种模式，影响展开结果。<br /> <br /> '''试展开'''：指以 strong magma 展开 1 次。<br /> <br /> '''最终展开'''：指以 weak magma 展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> strong magma 与 weak magma 的小展开一致。<br /> <br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> # 若为 strong magma 展开，则若某一项与坏项位于同一行，且其下方一项的祖先项包含坏项的下方一项，则本项为上升项。如果本项与坏项都位于第 0 行，本条件视为成立。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> # 若某一项的父项是坏项或填充项，则本项是填充项。<br /> # 若为 strong magma 展开，则若某一项下方一项的祖先项包含坏项的下方一项，则本项为填充项。如果本项与坏项都位于第 0 行，本条件视为成立。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 若为 weak magma 展开，将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> # 若为 strong magma 展开，将所有填充项（位于第 j 列）的下方一项分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。若填充项位于第 0 行，则被复制的项为一个父项为左侧相邻一列的虚拟项。<br /> <br /> 事实上，完全展开与 1-Y 的展开过程是很相似的。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为'''后继矩阵'''，删除最右列并不进行展开，得到的矩阵为其前驱。否则为'''极限矩阵'''，取其父项矩阵。<br /> <br /> 从右到左找到每一个检测项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2,1) = Y(1,3,9,24)。<br /> <br /> 0 ~ Y(1,3,7) : [[DSM分析Part1]]<br /> <br /> Y(1,3,7) ~ Y(1,3,9) : [[DSM分析Part2]]<br /> <br /> Y(1,3,9) + : [[DSM分析Part3]]{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=3074 2026-05-22T04:04:51Z

<p>Alice：​</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''magma'''：展开的两种模式，影响展开结果。<br /> <br /> '''试展开'''：指以 strong magma 展开 1 次。<br /> <br /> '''最终展开'''：指以 weak magma 展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> strong magma 与 weak magma 的小展开一致。<br /> <br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> # 若为 strong magma 展开，则若某一项下方一项的祖先项包含坏项的下方一项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> # 若某一项的父项是坏项或填充项，则本项是填充项。<br /> # 若为 strong magma 展开，则若某一项的左下项的上方一项存在，且其祖先项包含坏项，则本项为填充项。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 若为 weak magma 展开，将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> # 若为 strong magma 展开，将所有填充项（位于第 j 列）的下方一项分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。若填充项位于第 0 行，则被复制的项为一个父项为左侧相邻一列的虚拟项。<br /> <br /> 事实上，完全展开与 1-Y 的展开过程是很相似的。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为'''后继矩阵'''，删除最右列并不进行展开，得到的矩阵为其前驱。否则为'''极限矩阵'''，取其父项矩阵。<br /> <br /> 从右到左找到每一个检测项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2,1) = Y(1,3,9,24)。<br /> <br /> 0 ~ Y(1,3,7) : [[DSM分析Part1]]<br /> <br /> Y(1,3,7) ~ Y(1,3,9) : [[DSM分析Part2]]<br /> <br /> Y(1,3,9) + : [[DSM分析Part3]]{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part3&diff=3073 2026-05-22T03:00:02Z

<p>Alice：​</p> <hr /> <div>本分析由 test_alpha0 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == Y(1,3,9) ~ Y(1,3,9,10,3) ==<br /> (0)(1)(2,1)(3) = 1,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1) = 1,3,9,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1) = 1,3,9,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,9,3,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,3,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,3,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4) = 1,3,9,4<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1) = 1,3,9,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2) = 1,3,9,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1) = 1,3,9,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2) = 1,3,9,7,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9) = 1,3,9,7,14,27,55<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,7,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,7,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5) = 1,3,9,7,17,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1) = 1,3,9,7,17,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1) = 1,3,9,7,17,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2,1) = 1,3,9,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(5) = 1,3,9,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1) = 1,3,9,10,2<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1) = 1,3,9,10,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10,2,5,14,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(2) = 1,3,9,10,2,5,14,15,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(3,1)(4,2,1) = 1,3,9,10,2,5,14,15,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,15,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(4) = 1,3,9,10,2,5,14,15,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1) = 1,3,9,10,2,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1) = 1,3,9,10,2,5,14,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2) = 1,3,9,10,2,5,14,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1) = 1,3,9,10,2,5,14,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,19,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3) = 1,3,9,10,2,5,14,19,30,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1) = 1,3,9,10,2,5,14,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1) = 1,3,9,10,2,5,14,20,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,20,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(4) = 1,3,9,10,2,5,14,20,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5) = 1,3,9,10,2,5,14,20,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1) = 1,3,9,10,2,5,14,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1) = 1,3,9,10,2,5,14,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,22,14,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4) = 1,3,9,10,2,5,14,22,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5) = 1,3,9,10,2,5,14,22,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,28,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(6,2,1)(7) = 1,3,9,10,2,5,14,22,30,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2) = 1,3,9,10,2,5,14,22,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,36,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1) = 1,3,9,10,2,5,14,22,37<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3,1) = 1,3,9,10,2,5,14,22,38<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6) = 1,3,9,10,2,5,14,22,38,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5) = 1,3,9,10,2,5,14,22,38,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,44,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,52,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,63,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3)(6,4,1)(7) = 1,3,9,10,2,5,14,22,38,65,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3,1) = 1,3,9,10,2,5,14,22,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,22,41,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2,1) = 1,3,9,10,2,5,14,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2,1)(5) = 1,3,9,10,2,5,14,22,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(5) = 1,3,9,10,2,5,14,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1) = 1,3,9,10,2,5,14,23,25<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,22,38,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,22,41,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(4) = 1,3,9,10,2,5,14,23,29,22,41,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,41,40<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1)(7,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,78,41<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,78,63,111<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(7) = 1,3,9,10,2,5,14,23,29,22,43,64,78,64<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8) = 1,3,9,10,2,5,14,23,29,22,43,64,78,65<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2) = 1,3,9,10,2,5,14,23,29,22,43,64,78,93<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,79<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8) = 1,3,9,10,2,5,14,23,29,22,43,64,80,81<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8,2)(9,3,1)(10,4,2,1)(11) = 1,3,9,10,2,5,14,23,29,22,43,64,80,110,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8,2)(9,3,1)(10,4,2,1)(11,1)(10,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,80,111<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,2) = 1,3,9,10,2,5,14,23,29,22,43,64,81<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,3,1)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,81,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,23,29,23,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,22,41,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7) = 1,3,9,10,2,5,14,23,29,23,22,38,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,38,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,1)(6,3,1) = 1,3,9,10,2,5,14,23,29,23,22,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,41,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(9,2,1)(10,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,80,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(6,3,1)(7,4,2,1)(8,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1)(7,3,1)(8,4,2,1)(9,3,1)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,64,63,43,64,81,64<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,23,22,14,23,29,23,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5) = 1,3,9,10,2,5,14,23,29,23,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,29,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,29,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(5) = 1,3,9,10,2,5,14,23,29,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(6,2,1)(7,1)(6,2,1) = 1,3,9,10,2,5,14,23,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2) = 1,3,9,10,2,5,14,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1) = 1,3,9,10,3<br /> <br /> == Y(1,3,9,10,3) ~ Y(1,3,9,24) ==<br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1) = 1,3,9,10,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1)(5) = 1,3,9,16,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4) = 1,3,9,16,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,10,2,5,14,30,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1) = 1,3,9,16,10,2,5,14,30,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(4) = 1,3,9,16,10,2,5,14,30,22,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,16,10,2,5,14,30,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(5,2,1)(5,2) = 1,3,9,16,10,2,5,14,30,23,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(5,2,1)(5,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,10,2,5,14,30,23,39,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,2) = 1,3,9,16,10,2,5,14,30,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,2)(3,1)(4,2,1) = 1,3,9,16,10,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5) = 1,3,9,16,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,17,2,5,14,30,36,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,1)(6,2,1)(7,1)(6,2,1) = 1,3,9,16,17,2,5,14,30,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,2) = 1,3,9,16,17,2,5,14,30,40<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3) = 1,3,9,16,17,2,5,14,30,47<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3)(3,1)(4,2,1) = 1,3,9,16,17,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,23,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3)(6,4,1) = 1,3,9,16,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(5,3,1) = 1,3,9,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6) = 1,3,9,18,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(4) = 1,3,9,18,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,1)(4) = 1,3,9,18,30,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8) = 1,3,9,18,33,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,1)(7,5,2,1) = 1,3,9,18,34<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,1)(7,5,2,1)(8,1)(7,5,2,1) = 1,3,9,18,35,52,65,51,83<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1) = 1,3,9,18,35,52,65,52<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2) = 1,3,9,18,35,53<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1) = 1,3,9,18,35,62<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1)(9) = 1,3,9,18,35,64,35<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1)(9,4,1)(6,4,1)(7,5,2,1)(8,1)(7,5,2,1) = 1,3,9,18,35,64,35,52,65,34<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1)(9,4,1)(8,6,3)(9,7,4,1)(10,4,1)(7) = 1,3,9,18,35,64,109,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3,1) = 1,3,9,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3,1)(5,3,1) = 1,3,9,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,22,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1)(6,4,2,1) = 1,3,9,24<br /> [[分类:分析]]</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part3&diff=3069 2026-05-21T15:25:54Z

<p>Alice：​</p> <hr /> <div>本分析由 test_alpha0 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == Y(1,3,9) ~ Y(1,3,9,10,3) ==<br /> (0)(1)(2,1)(3) = 1,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1) = 1,3,9,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1) = 1,3,9,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,9,3,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,3,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,3,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4) = 1,3,9,4<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1) = 1,3,9,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2) = 1,3,9,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1) = 1,3,9,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2) = 1,3,9,7,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9) = 1,3,9,7,14,27,55<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,7,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,7,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5) = 1,3,9,7,17,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1) = 1,3,9,7,17,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1) = 1,3,9,7,17,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2,1) = 1,3,9,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(5) = 1,3,9,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1) = 1,3,9,10,2<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1) = 1,3,9,10,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10,2,5,14,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(2) = 1,3,9,10,2,5,14,15,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(3,1)(4,2,1) = 1,3,9,10,2,5,14,15,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,15,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(4) = 1,3,9,10,2,5,14,15,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1) = 1,3,9,10,2,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1) = 1,3,9,10,2,5,14,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2) = 1,3,9,10,2,5,14,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1) = 1,3,9,10,2,5,14,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,19,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3) = 1,3,9,10,2,5,14,19,30,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1) = 1,3,9,10,2,5,14,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1) = 1,3,9,10,2,5,14,20,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,20,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(4) = 1,3,9,10,2,5,14,20,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5) = 1,3,9,10,2,5,14,20,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1) = 1,3,9,10,2,5,14,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1) = 1,3,9,10,2,5,14,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,22,14,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4) = 1,3,9,10,2,5,14,22,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5) = 1,3,9,10,2,5,14,22,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,28,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(6,2,1)(7) = 1,3,9,10,2,5,14,22,30,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2) = 1,3,9,10,2,5,14,22,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,36,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1) = 1,3,9,10,2,5,14,22,37<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3,1) = 1,3,9,10,2,5,14,22,38<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6) = 1,3,9,10,2,5,14,22,38,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5) = 1,3,9,10,2,5,14,22,38,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,44,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,52,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,63,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3)(6,4,1)(7) = 1,3,9,10,2,5,14,22,38,65,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3,1) = 1,3,9,10,2,5,14,22,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,22,41,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2,1) = 1,3,9,10,2,5,14,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2,1)(5) = 1,3,9,10,2,5,14,22,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(5) = 1,3,9,10,2,5,14,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1) = 1,3,9,10,2,5,14,23,25<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,22,38,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,22,41,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(4) = 1,3,9,10,2,5,14,23,29,22,41,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,41,40<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1)(7,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,78,41<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,78,63,111<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(7) = 1,3,9,10,2,5,14,23,29,22,43,64,78,64<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8) = 1,3,9,10,2,5,14,23,29,22,43,64,78,65<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2) = 1,3,9,10,2,5,14,23,29,22,43,64,78,93<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,79<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8) = 1,3,9,10,2,5,14,23,29,22,43,64,80,81<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8,2)(9,3,1)(10,4,2,1)(11) = 1,3,9,10,2,5,14,23,29,22,43,64,80,110,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8,2)(9,3,1)(10,4,2,1)(11,1)(10,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,80,111<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,2) = 1,3,9,10,2,5,14,23,29,22,43,64,81<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,3,1)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,81,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,23,29,23,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,22,41,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7) = 1,3,9,10,2,5,14,23,29,23,22,38,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,38,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,1)(6,3,1) = 1,3,9,10,2,5,14,23,29,23,22,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,41,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(9,2,1)(10,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,80,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(6,3,1)(7,4,2,1)(8,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1)(7,3,1)(8,4,2,1)(9,3,1)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,64,63,43,64,81,64<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,23,22,14,23,29,23,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5) = 1,3,9,10,2,5,14,23,29,23,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,29,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,29,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(5) = 1,3,9,10,2,5,14,23,29,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(6,2,1)(7,1)(6,2,1) = 1,3,9,10,2,5,14,23,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2) = 1,3,9,10,2,5,14,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1) = 1,3,9,10,3<br /> <br /> == Y(1,3,9,10,3) ~ Y(1,3,9,23) ==<br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1) = 1,3,9,10,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1)(5) = 1,3,9,16,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4) = 1,3,9,16,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,10,2,5,14,30,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1) = 1,3,9,16,10,2,5,14,30,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(4) = 1,3,9,16,10,2,5,14,30,22,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,16,10,2,5,14,30,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(5,2,1)(5,2) = 1,3,9,16,10,2,5,14,30,23,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(5,2,1)(5,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,10,2,5,14,30,23,39,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,2) = 1,3,9,16,10,2,5,14,30,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,2)(3,1)(4,2,1) = 1,3,9,16,10,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5) = 1,3,9,16,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,17,2,5,14,30,36,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,1)(6,2,1)(7,1)(6,2,1) = 1,3,9,16,17,2,5,14,30,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,2) = 1,3,9,16,17,2,5,14,30,40<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3) = 1,3,9,16,17,2,5,14,30,47<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3)(3,1)(4,2,1) = 1,3,9,16,17,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,23,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3)(6,4,1) = 1,3,9,16,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(5,3,1) = 1,3,9,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6) = 1,3,9,18,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(4) = 1,3,9,18,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,1)(4) = 1,3,9,18,30,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8) = 1,3,9,18,33,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,1)(7,5,2,1) = 1,3,9,18,34<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,1)(7,5,2,1)(8,1)(7,5,2,1) = 1,3,9,18,35,52,65,51,83<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1) = 1,3,9,18,35,52,65,52<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2) = 1,3,9,18,35,53<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1) = 1,3,9,18,35,62<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1)(9) = 1,3,9,18,35,64,35<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1)(9,4,1)(6,4,1)(7,5,2,1)(8,1)(7,5,2,1) = 1,3,9,18,35,64,35,52,65,34<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1)(9,4,1)(8,6,3)(9,7,4,1)(10,4,1)(7) = 1,3,9,18,35,64,109,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3,1) = 1,3,9,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3,1)(5,3,1) = 1,3,9,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,22,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,23<br /> [[分类:分析]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=3056 2026-05-20T00:03:14Z

<p>Alice：​</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''magma'''：展开的两种模式，影响展开结果。<br /> <br /> '''试展开'''：指以 strong magma 展开 1 次。<br /> <br /> '''最终展开'''：指以 weak magma 展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> strong magma 与 weak magma 的小展开一致。<br /> <br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> # 若为 strong magma 展开，则若某一项的左下项的上方一项存在，且其祖先项包含坏项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> # 若某一项的父项是坏项或填充项，则本项是填充项。<br /> # 若为 strong magma 展开，则若某一项的左下项的上方一项存在，且其祖先项包含坏项，则本项为填充项。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 若为 weak magma 展开，将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> # 若为 strong magma 展开，将所有填充项（位于第 j 列）的下方一项分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。若填充项位于第 0 行，则被复制的项为一个父项为左侧相邻一列的虚拟项。<br /> <br /> 事实上，完全展开与 1-Y 的展开过程是很相似的。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为'''后继矩阵'''，删除最右列并不进行展开，得到的矩阵为其前驱。否则为'''极限矩阵'''，取其父项矩阵。<br /> <br /> 从右到左找到每一个检测项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2,1) = Y(1,3,9,24)。<br /> <br /> 0 ~ Y(1,3,7) : [[DSM分析Part1]]<br /> <br /> Y(1,3,7) ~ Y(1,3,9) : [[DSM分析Part2]]<br /> <br /> Y(1,3,9) + : [[DSM分析Part3]]{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part3&diff=3055 2026-05-20T00:02:24Z

<p>Alice：​</p> <hr /> <div>本分析由 test_alpha0 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == Y(1,3,9) ~ Y(1,3,9,10,3) ==<br /> (0)(1)(2,1)(3) = 1,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1) = 1,3,9,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1) = 1,3,9,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,9,3,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,3,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,3,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4) = 1,3,9,4<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1) = 1,3,9,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2) = 1,3,9,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1) = 1,3,9,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2) = 1,3,9,7,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9) = 1,3,9,7,14,27,55<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,7,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,7,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5) = 1,3,9,7,17,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1) = 1,3,9,7,17,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1) = 1,3,9,7,17,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2,1) = 1,3,9,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(5) = 1,3,9,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1) = 1,3,9,10,2<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1) = 1,3,9,10,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10,2,5,14,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(2) = 1,3,9,10,2,5,14,15,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(3,1)(4,2,1) = 1,3,9,10,2,5,14,15,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,15,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(4) = 1,3,9,10,2,5,14,15,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1) = 1,3,9,10,2,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1) = 1,3,9,10,2,5,14,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2) = 1,3,9,10,2,5,14,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1) = 1,3,9,10,2,5,14,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,19,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3) = 1,3,9,10,2,5,14,19,30,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1) = 1,3,9,10,2,5,14,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1) = 1,3,9,10,2,5,14,20,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,20,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(4) = 1,3,9,10,2,5,14,20,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5) = 1,3,9,10,2,5,14,20,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1) = 1,3,9,10,2,5,14,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1) = 1,3,9,10,2,5,14,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,22,14,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4) = 1,3,9,10,2,5,14,22,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5) = 1,3,9,10,2,5,14,22,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,28,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(6,2,1)(7) = 1,3,9,10,2,5,14,22,30,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2) = 1,3,9,10,2,5,14,22,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,36,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1) = 1,3,9,10,2,5,14,22,37<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3,1) = 1,3,9,10,2,5,14,22,38<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6) = 1,3,9,10,2,5,14,22,38,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5) = 1,3,9,10,2,5,14,22,38,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,44,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,52,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,63,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3)(6,4,1)(7) = 1,3,9,10,2,5,14,22,38,65,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3,1) = 1,3,9,10,2,5,14,22,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,22,41,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2,1) = 1,3,9,10,2,5,14,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2,1)(5) = 1,3,9,10,2,5,14,22,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(5) = 1,3,9,10,2,5,14,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1) = 1,3,9,10,2,5,14,23,25<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,22,38,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,22,41,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(4) = 1,3,9,10,2,5,14,23,29,22,41,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,41,40<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1)(7,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,78,41<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,78,63,111<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(7) = 1,3,9,10,2,5,14,23,29,22,43,64,78,64<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8) = 1,3,9,10,2,5,14,23,29,22,43,64,78,65<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2) = 1,3,9,10,2,5,14,23,29,22,43,64,78,93<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,79<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8) = 1,3,9,10,2,5,14,23,29,22,43,64,80,81<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8,2)(9,3,1)(10,4,2,1)(11) = 1,3,9,10,2,5,14,23,29,22,43,64,80,110,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8,2)(9,3,1)(10,4,2,1)(11,1)(10,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,80,111<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,2) = 1,3,9,10,2,5,14,23,29,22,43,64,81<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,3,1)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,81,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,23,29,23,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,22,41,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7) = 1,3,9,10,2,5,14,23,29,23,22,38,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,38,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,1)(6,3,1) = 1,3,9,10,2,5,14,23,29,23,22,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,41,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(9,2,1)(10,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,80,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(6,3,1)(7,4,2,1)(8,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1)(7,3,1)(8,4,2,1)(9,3,1)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,64,63,43,64,81,64<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,23,22,14,23,29,23,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5) = 1,3,9,10,2,5,14,23,29,23,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,29,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,29,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(5) = 1,3,9,10,2,5,14,23,29,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(6,2,1)(7,1)(6,2,1) = 1,3,9,10,2,5,14,23,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2) = 1,3,9,10,2,5,14,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1) = 1,3,9,10,3<br /> <br /> == Y(1,3,9,10,3) ~ Y(1,3,9,24) ==<br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1) = 1,3,9,10,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1)(5) = 1,3,9,16,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4) = 1,3,9,16,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,10,2,5,14,30,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1) = 1,3,9,16,10,2,5,14,30,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(4) = 1,3,9,16,10,2,5,14,30,22,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,16,10,2,5,14,30,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(5,2,1)(5,2) = 1,3,9,16,10,2,5,14,30,23,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(5,2,1)(5,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,10,2,5,14,30,23,39,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,2) = 1,3,9,16,10,2,5,14,30,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,2)(3,1)(4,2,1) = 1,3,9,16,10,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5) = 1,3,9,16,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,17,2,5,14,30,36,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,1)(6,2,1)(7,1)(6,2,1) = 1,3,9,16,17,2,5,14,30,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,2) = 1,3,9,16,17,2,5,14,30,40<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3) = 1,3,9,16,17,2,5,14,30,47<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3)(3,1)(4,2,1) = 1,3,9,16,17,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,23,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3)(6,4,1) = 1,3,9,16,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(5,3,1) = 1,3,9,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6) = 1,3,9,18,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(4) = 1,3,9,18,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,1)(4) = 1,3,9,18,30,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8) = 1,3,9,18,33,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,1)(7,5,2,1) = 1,3,9,18,34<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,1)(7,5,2,1)(8,1)(7,5,2,1) = 1,3,9,18,35,52,65,51,83<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1) = 1,3,9,18,35,52,65,52<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2) = 1,3,9,18,35,53<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1) = 1,3,9,18,35,62<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1)(9) = 1,3,9,18,35,64,35<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1)(9,4,1)(6,4,1)(7,5,2,1)(8,1)(7,5,2,1) = 1,3,9,18,35,64,35,52,65,34<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1)(9,4,1)(8,6,3)(9,7,4,1)(10,4,1)(7) = 1,3,9,18,35,64,109,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3,1) = 1,3,9,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3,1)(5,3,1) = 1,3,9,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,22,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7,3,1)(6,4,2,1) = 1,3,9,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2,1) = 1,3,9,24<br /> [[分类:分析]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=3054 2026-05-18T13:33:19Z

<p>Alice：​</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''magma'''：展开的两种模式，影响展开结果。<br /> <br /> '''试展开'''：指以 strong magma 展开 1 次。<br /> <br /> '''最终展开'''：指以 weak magma 展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> strong magma 与 weak magma 的小展开一致。<br /> <br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> # 若为 strong magma 展开，则若某一项的左下项的上方一项存在，且其祖先项包含坏项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> # 若某一项的父项是坏项或填充项，则本项是填充项。<br /> # 若为 strong magma 展开，则若某一项的左下项的上方一项存在，且其祖先项包含坏项，则本项为填充项。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 若为 weak magma 展开，将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> # 若为 strong magma 展开，将所有填充项（位于第 j 列）的下方一项分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。若填充项位于第 0 行，则被复制的项为一个父项为左侧相邻一列的虚拟项。<br /> <br /> 事实上，完全展开与 1-Y 的展开过程是很相似的。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为'''后继矩阵'''，删除最右列并不进行展开，得到的矩阵为其前驱。否则为'''极限矩阵'''，取其父项矩阵。<br /> <br /> 从右到左找到每一个检测项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3,1) = Y(1,3,9,19)。<br /> <br /> 0 ~ Y(1,3,7) : [[DSM分析Part1]]<br /> <br /> Y(1,3,7) ~ Y(1,3,9) : [[DSM分析Part2]]<br /> <br /> Y(1,3,9) + : [[DSM分析Part3]]{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=3053 2026-05-18T13:31:48Z

<p>Alice：​</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''magma'''：展开的两种模式，影响展开结果。<br /> <br /> '''试展开'''：指以 strong magma 展开 1 次。<br /> <br /> '''最终展开'''：指以 weak magma 展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> strong magma 与 weak magma 的小展开一致。<br /> <br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> # 若为 strong magma 展开，则若某一项的左下项的上方一项存在，且其祖先项包含坏项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> # 若某一项的父项是坏项或填充项，则本项是填充项。<br /> # 若为 strong magma 展开，则若某一项的左下项的上方一项存在，且其祖先项包含坏项，则本项为填充项。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 若为 weak magma 展开，将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> # 若为 strong magma 展开，将所有填充项（位于第 j 列）的下方一项分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。若填充项位于第 0 行，则被复制的项为一个父项为左侧相邻一列的虚拟项。<br /> <br /> 事实上，完全展开与 1-Y 的展开过程是很相似的。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为'''后继矩阵'''，删除最右列并不进行展开，得到的矩阵为其前驱。否则为'''极限矩阵'''，取其父项矩阵。<br /> <br /> 从右到左找到每一个检测项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3,1) = Y(1,3,9,19)。<br /> <br /> 0 ~ Y(1,3,7) : [[DSM分析Part1]]<br /> <br /> Y(1,3,7) ~ Y(1,3,9) : [[DSM分析Part2]]<br /> <br /> Y(1,3,9) + : [[DSM分析Part3]]{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=3052 2026-05-18T13:31:13Z

<p>Alice：​/* 小展开 */</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''试展开'''：指以 strong magma 展开 1 次。<br /> <br /> '''最终展开'''：指以 weak magma 展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> strong magma 与 weak magma 的小展开一致。<br /> <br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> # 若为 strong magma 展开，则若某一项的左下项的上方一项存在，且其祖先项包含坏项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> # 若某一项的父项是坏项或填充项，则本项是填充项。<br /> # 若为 strong magma 展开，则若某一项的左下项的上方一项存在，且其祖先项包含坏项，则本项为填充项。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 若为 weak magma 展开，将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> # 若为 strong magma 展开，将所有填充项（位于第 j 列）的下方一项分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。若填充项位于第 0 行，则被复制的项为一个父项为左侧相邻一列的虚拟项。<br /> <br /> 事实上，完全展开与 1-Y 的展开过程是很相似的。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为'''后继矩阵'''，删除最右列并不进行展开，得到的矩阵为其前驱。否则为'''极限矩阵'''，取其父项矩阵。<br /> <br /> 从右到左找到每一个检测项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3,1) = Y(1,3,9,19)。<br /> <br /> 0 ~ Y(1,3,7) : [[DSM分析Part1]]<br /> <br /> Y(1,3,7) ~ Y(1,3,9) : [[DSM分析Part2]]<br /> <br /> Y(1,3,9) + : [[DSM分析Part3]]{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=3051 2026-05-18T13:30:28Z

<p>Alice：​</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''试展开'''：指以 strong magma 展开 1 次。<br /> <br /> '''最终展开'''：指以 weak magma 展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> # 若为 strong magma 展开，则若某一项的左下项的上方一项存在，且其祖先项包含坏项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> # 若某一项的父项是坏项或填充项，则本项是填充项。<br /> # 若为 strong magma 展开，则若某一项的左下项的上方一项存在，且其祖先项包含坏项，则本项为填充项。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> # 若为 weak magma 展开，将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> # 若为 strong magma 展开，将所有填充项（位于第 j 列）的下方一项分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。若填充项位于第 0 行，则被复制的项为一个父项为左侧相邻一列的虚拟项。<br /> <br /> 事实上，完全展开与 1-Y 的展开过程是很相似的。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为'''后继矩阵'''，删除最右列并不进行展开，得到的矩阵为其前驱。否则为'''极限矩阵'''，取其父项矩阵。<br /> <br /> 从右到左找到每一个检测项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3,1) = Y(1,3,9,19)。<br /> <br /> 0 ~ Y(1,3,7) : [[DSM分析Part1]]<br /> <br /> Y(1,3,7) ~ Y(1,3,9) : [[DSM分析Part2]]<br /> <br /> Y(1,3,9) + : [[DSM分析Part3]]{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part3&diff=3050 2026-05-18T13:24:47Z

<p>Alice：​</p> <hr /> <div>本分析由 test_alpha0 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == Y(1,3,9) ~ Y(1,3,9,10,3) ==<br /> (0)(1)(2,1)(3) = 1,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1) = 1,3,9,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1) = 1,3,9,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,9,3,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,3,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,3,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4) = 1,3,9,4<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1) = 1,3,9,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2) = 1,3,9,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1) = 1,3,9,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2) = 1,3,9,7,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9) = 1,3,9,7,14,27,55<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,7,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,7,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5) = 1,3,9,7,17,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1) = 1,3,9,7,17,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1) = 1,3,9,7,17,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2,1) = 1,3,9,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(5) = 1,3,9,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1) = 1,3,9,10,2<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1) = 1,3,9,10,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10,2,5,14,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(2) = 1,3,9,10,2,5,14,15,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(3,1)(4,2,1) = 1,3,9,10,2,5,14,15,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,15,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(4) = 1,3,9,10,2,5,14,15,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1) = 1,3,9,10,2,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1) = 1,3,9,10,2,5,14,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2) = 1,3,9,10,2,5,14,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1) = 1,3,9,10,2,5,14,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,19,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3) = 1,3,9,10,2,5,14,19,30,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1) = 1,3,9,10,2,5,14,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1) = 1,3,9,10,2,5,14,20,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,20,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(4) = 1,3,9,10,2,5,14,20,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5) = 1,3,9,10,2,5,14,20,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1) = 1,3,9,10,2,5,14,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1) = 1,3,9,10,2,5,14,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,22,14,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4) = 1,3,9,10,2,5,14,22,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5) = 1,3,9,10,2,5,14,22,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,28,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(6,2,1)(7) = 1,3,9,10,2,5,14,22,30,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2) = 1,3,9,10,2,5,14,22,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,36,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1) = 1,3,9,10,2,5,14,22,37<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3,1) = 1,3,9,10,2,5,14,22,38<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6) = 1,3,9,10,2,5,14,22,38,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5) = 1,3,9,10,2,5,14,22,38,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,44,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,52,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,63,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3)(6,4,1)(7) = 1,3,9,10,2,5,14,22,38,65,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3,1) = 1,3,9,10,2,5,14,22,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,22,41,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2,1) = 1,3,9,10,2,5,14,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2,1)(5) = 1,3,9,10,2,5,14,22,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(5) = 1,3,9,10,2,5,14,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1) = 1,3,9,10,2,5,14,23,25<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,22,38,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,22,41,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(4) = 1,3,9,10,2,5,14,23,29,22,41,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,41,40<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1)(7,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,78,41<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,78,63,111<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(7) = 1,3,9,10,2,5,14,23,29,22,43,64,78,64<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8) = 1,3,9,10,2,5,14,23,29,22,43,64,78,65<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2) = 1,3,9,10,2,5,14,23,29,22,43,64,78,93<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,79<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8) = 1,3,9,10,2,5,14,23,29,22,43,64,80,81<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8,2)(9,3,1)(10,4,2,1)(11) = 1,3,9,10,2,5,14,23,29,22,43,64,80,110,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8,2)(9,3,1)(10,4,2,1)(11,1)(10,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,80,111<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,2) = 1,3,9,10,2,5,14,23,29,22,43,64,81<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,3,1)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,81,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,23,29,23,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,22,41,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7) = 1,3,9,10,2,5,14,23,29,23,22,38,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,38,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,1)(6,3,1) = 1,3,9,10,2,5,14,23,29,23,22,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,41,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(9,2,1)(10,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,80,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(6,3,1)(7,4,2,1)(8,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1)(7,3,1)(8,4,2,1)(9,3,1)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,64,63,43,64,81,64<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,23,22,14,23,29,23,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5) = 1,3,9,10,2,5,14,23,29,23,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,29,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,29,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(5) = 1,3,9,10,2,5,14,23,29,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(6,2,1)(7,1)(6,2,1) = 1,3,9,10,2,5,14,23,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2) = 1,3,9,10,2,5,14,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1) = 1,3,9,10,3<br /> <br /> == Y(1,3,9,10,3) ~ Y(1,3,9,19) ==<br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1) = 1,3,9,10,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1)(5) = 1,3,9,16,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4) = 1,3,9,16,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,10,2,5,14,30,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1) = 1,3,9,16,10,2,5,14,30,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(4) = 1,3,9,16,10,2,5,14,30,22,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,16,10,2,5,14,30,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(5,2,1)(5,2) = 1,3,9,16,10,2,5,14,30,23,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,1)(5,2,1)(6,1)(5,2,1)(5,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,10,2,5,14,30,23,39,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,2) = 1,3,9,16,10,2,5,14,30,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(4,2)(3,1)(4,2,1) = 1,3,9,16,10,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5) = 1,3,9,16,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,17,2,5,14,30,36,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,1)(6,2,1)(7,1)(6,2,1) = 1,3,9,16,17,2,5,14,30,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,2) = 1,3,9,16,17,2,5,14,30,40<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3) = 1,3,9,16,17,2,5,14,30,47<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3)(3,1)(4,2,1) = 1,3,9,16,17,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3)(3,1)(4,2,1)(4,2,1) = 1,3,9,16,23,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3)(6,4,1) = 1,3,9,16,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(5,3,1) = 1,3,9,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6) = 1,3,9,18,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(4) = 1,3,9,18,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,1)(4) = 1,3,9,18,30,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8) = 1,3,9,18,33,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,1)(7,5,2,1) = 1,3,9,18,34<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,1)(7,5,2,1)(8,1)(7,5,2,1) = 1,3,9,18,35,52,65,51,83<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1) = 1,3,9,18,35,52,65,52<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2) = 1,3,9,18,35,53<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1) = 1,3,9,18,35,62<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1)(9) = 1,3,9,18,35,64,35<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1)(9,4,1)(6,4,1)(7,5,2,1)(8,1)(7,5,2,1) = 1,3,9,18,35,64,35,52,65,34<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3)(6,4,1)(7,5,2,1)(8,4,1)(7,5,2,1)(7,5,2)(8,6,3,1)(9,4,1)(8,6,3)(9,7,4,1)(10,4,1)(7) = 1,3,9,18,35,64,109,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(5,3,1)(6,1)(5,3,1) = 1,3,9,19<br /> [[分类:分析]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=3045 2026-05-17T03:16:24Z

<p>Alice：​</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''试展开'''：指展开 1 次。<br /> <br /> '''最终展开'''：指展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> 试坏项与试坏项同行右侧的所有候选项都是上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> 试坏项同行右侧的所有候选项都是填充项。（注意：试坏项本身不是填充项）<br /> <br /> 若某一项的父项是坏项或填充项，则本项是填充项。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> <br /> 事实上，完全展开与 1-Y 的展开过程是很相似的。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为'''后继矩阵'''，删除最右列并不进行展开，得到的矩阵为其前驱。否则为'''极限矩阵'''，取其父项矩阵。<br /> <br /> 从右到左找到每一个检测项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1) = 1-Y (1,3,9,10,3)。<br /> <br /> 0 ~ Y(1,3,7) : [[DSM分析Part1]]<br /> <br /> Y(1,3,7) ~ Y(1,3,9) : [[DSM分析Part2]]<br /> <br /> Y(1,3,9) + : [[DSM分析Part3]]{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part1&diff=3044 2026-05-17T03:15:59Z

<p>Alice：​</p> <hr /> <div>本分析由 CXL 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == 0 ~ Y(1,3) ==<br /> (0) = 1<br /> <br /> (0)(1) = 1,2<br /> <br /> (0)(1)(2)(3,1) = 1,2,4<br /> <br /> (0)(1)(2)(3,1)(4,2)(5,3,1) = 1,2,4,8<br /> <br /> (0)(1)(2)(3,1)(4,2)(5,3,1)(6,4,2)(7,5,3,1) = 1,2,4,8,16<br /> <br /> (0)(1)(2,1) = 1,3<br /> <br /> == Y(1,3) ~ Y(1,3,7) ==<br /> (0)(1)(2,1) = 1,3<br /> <br /> (0)(1)(2,1)(1) = 1,3,2<br /> <br /> (0)(1)(2,1)(1)(2) = 1,3,2,3<br /> <br /> (0)(1)(2,1)(1)(2)(3,1) = 1,3,2,4<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2)(5,3,1) = 1,3,2,4,8<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2,1) = 1,3,2,5<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2,1)(3,1) = 1,3,2,5,4<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2,1)(3,1)(4,2)(5,3,1) = 1,3,2,5,4,8<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2,1)(3,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,2,5,4,9<br /> <br /> (0)(1)(2,1)(1)(2,1) = 1,3,3<br /> <br /> (0)(1)(2,1)(1)(2,1)(1)(2)(3,1)(4,2,1)(3,1)(4,2,1) = 1,3,3,2,5,5<br /> <br /> (0)(1)(2,1)(1)(2,1)(1)(2,1) = 1,3,3,3<br /> <br /> (0)(1)(2,1)(2) = 1,3,4<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1) = 1,3,4,2,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(2) = 1,3,4,2,5,3<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(2)(3,1)(4,2,1) = 1,3,4,2,5,3,6<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(3,1) = 1,3,4,2,5,4<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(3,1)(4,2,1) = 1,3,4,2,5,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4) = 1,3,4,2,5,6<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4)(3,1)(4,2,1) = 1,3,4,2,5,6,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1) = 1,3,4,2,5,7<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,1) = 1,3,4,2,5,7,4,9,11<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,1)(5,3,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(8,1)(7,5,3,1) = 1,3,4,2,5,7,4,9,11,8,17,19<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,1)(5,3,1)(6,4,2,1) = 1,3,4,2,5,7,4,9,11,9<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,1)(6) = 1,3,4,2,5,7,4,9,11,10<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,2) = 1,3,4,2,5,7,4,9,12<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,2)(5,3,1)(6,4,2,1) = 1,3,4,2,5,7,4,9,12,8,17,20,17<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,3) = 1,3,4,2,5,7,4,9,12,8,17,21<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,3)(5,3,1)(6,4,2,1) = 1,3,4,2,5,7,4,9,12,9<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,3,1)(5,3,1) = 1,3,4,2,5,7,4,9,13<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2,1) = 1,3,4,2,5,7,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2,1)(4,1) = 1,3,4,2,5,7,5,7<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(4) = 1,3,4,2,5,7,6<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(4,1) = 1,3,4,2,5,7,7<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,1) = 1,3,4,2,5,7,9<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2) = 1,3,4,2,5,7,10<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,3,1)(7,4,2) = 1,3,4,2,5,7,10,4,9,13,20<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(3,1)(4,2,1) = 1,3,4,2,5,7,10,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1) = 1,3,4,2,5,7,11<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1) = 1,3,4,2,5,7,12<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1)(7,3,1) = 1,3,4,2,5,7,12,16<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1)(7,3,1)(6,3,1)(7,4,2,1) = 1,3,4,2,5,7,12,16,12<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1)(7,3,1)(8,4,2)(9,5,3,1) = 1,3,4,2,5,7,12,16,24<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1)(7,3,1)(8,4,2)(9,5,3,1)(10,6,4,2,1) = 1,3,4,2,5,7,12,16,25<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,4,2,5,8<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,2) = 1,3,4,2,5,9<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,2)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2) = 1,3,4,2,5,9,4,9,18<br /> <br /> (0)(1)(2,1)(2)(1)(2,1) = 1,3,4,3<br /> <br /> (0)(1)(2,1)(2)(2) = 1,3,4,4<br /> <br /> (0)(1)(2,1)(2)(3)(4,1) = 1,3,4,6<br /> <br /> (0)(1)(2,1)(2)(3)(4,1)(5,2,1) = 1,3,4,7<br /> <br /> (0)(1)(2,1)(2)(3)(4,1)(5,2,1)(5,2)(6,3)(7,4,1)(8,5,2,1) = 1,3,4,7,11,18<br /> <br /> (0)(1)(2,1)(2)(3,1) = 1,3,5<br /> <br /> (0)(1)(2,1)(2)(3,1)(1)(2,1) = 1,3,5,3<br /> <br /> (0)(1)(2,1)(2)(3,1)(1)(2,1)(2)(3,1) = 1,3,5,3,5<br /> <br /> (0)(1)(2,1)(2)(3,1)(2) = 1,3,5,4<br /> <br /> (0)(1)(2,1)(2)(3,1)(2)(3,1) = 1,3,5,5<br /> <br /> (0)(1)(2,1)(2)(3,1)(3) = 1,3,5,6<br /> <br /> (0)(1)(2,1)(2)(3,1)(3)(4,1) = 1,3,5,7<br /> <br /> (0)(1)(2,1)(2)(3,1)(3,1) = 1,3,6<br /> <br /> (0)(1)(2,1)(2)(3,1)(4)(5,1) = 1,3,6,8<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,1) = 1,3,6,9<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2) = 1,3,6,10<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2)(5,3,1) = 1,3,6,11<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,6,12<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1) = 1,3,7<br /> [[分类:分析]]</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part2&diff=3043 2026-05-17T03:15:35Z

<p>Alice：​</p> <hr /> <div>本分析由 CXL 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == Y(1,3,7) ~ Y(1,3,8) ==<br /> (0)(1)(2,1)(2)(3,1)(4,2,1) = 1,3,7<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(1)(2,1) = 1,3,7,3<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(1)(2,1)(2)(3,1)(4,2,1) = 1,3,7,3,7<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(2) = 1,3,7,4<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(2)(3,1) = 1,3,7,5<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(2)(3,1)(4,2,1) = 1,3,7,5,9<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(3) = 1,3,7,5,9,6<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(3)(4,1) = 1,3,7,5,9,7<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(3)(4,1)(5,2,1) = 1,3,7,5,9,7,11<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(3,1) = 1,3,7,6<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(3,1)(4,2,1) = 1,3,7,7<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4) = 1,3,7,8<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4)(5,1) = 1,3,7,9<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4)(5,1)(6,2,1) = 1,3,7,9,13<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,1) = 1,3,7,10<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,7,11<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,1)(5,2,1)(5,1)(6,2,1) = 1,3,7,11,15<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2) = 1,3,7,12<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,7,13<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(3)(4,1)(5,2,1)(5,1)(6,2,1) = 1,3,7,13,5,9,13<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(3)(4,1)(5,2,1)(5,2) = 1,3,7,13,5,9,14<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(3)(4,1)(5,2,1)(5,2)(6,3,1) = 1,3,7,13,5,9,15<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(3,1) = 1,3,7,13,6<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(3,1)(4,2,1) = 1,3,7,13,7<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,7,13,7,11<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(3,1)(4,2,1)(4,2) = 1,3,7,13,7,12<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,7,13,7,13<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4) = 1,3,7,13,8<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4)(5,1) = 1,3,7,13,9<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4)(5,1)(6,2,1) = 1,3,7,13,9,13<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4)(5,1)(6,2,1)(6,2) = 1,3,7,13,9,13,18<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4)(5,1)(6,2,1)(6,2)(7,3,1) = 1,3,7,13,9,13,19<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4,1) = 1,3,7,13,10<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4,1)(5,2,1) = 1,3,7,13,11<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4,1)(5,2,1)(5,2) = 1,3,7,13,11,16<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4,1)(5,2,1)(5,2)(6,3,1) = 1,3,7,13,11,17<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4,2) = 1,3,7,13,12<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4,2)(5,3,1) = 1,3,7,13,13<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5) = 1,3,7,13,14<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5)(6,1)(7,2,1) = 1,3,7,13,15,19<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5)(6,1)(7,2,1)(7,2)(8,3,1) = 1,3,7,13,15,19,25<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,1) = 1,3,7,13,16<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,1)(6,2,1) = 1,3,7,13,17<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,1)(6,2,1)(6,2) = 1,3,7,13,17,22<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,1)(6,2,1)(6,2)(7,3,1) = 1,3,7,13,17,23<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,2) = 1,3,7,13,18<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,2)(6,3,1) = 1,3,7,13,19<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,3) = 1,3,7,13,20<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,3)(6,4,1) = 1,3,7,13,21<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,3,1) = 1,3,7,14<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,7,15<br /> <br /> (0)(1)(2,1)(2,1) = 1,3,8<br /> <br /> == Y(1,3,8) ~ Y(1,3,9) ==<br /> (0)(1)(2,1)(2,1) = 1,3,8<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1) = 1,3,8,3<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1)(2)(3,1)(4,2,1) = 1,3,8,3,7<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1) = 1,3,8,3,8<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(3,1) = 1,3,8,6<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(3,1)(4,2,1) = 1,3,8,7<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,8,7,15<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,8,7,16<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1)(5,3,1)(6,4,2,1) = 1,3,8,7,16,15<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1)(2,1) = 1,3,8,8<br /> <br /> (0)(1)(2,1)(2,1)(2) = 1,3,8,9<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1) = 1,3,8,9,3<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1) = 1,3,8,9,3,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(3,1) = 1,3,8,9,3,8,6<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(3,1)(4,2,1) = 1,3,8,9,3,8,7<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(3,1)(4,2,1)(4,2,1) = 1,3,8,9,3,8,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4) = 1,3,8,9,3,8,9<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4)(3)(4,1)(5,2,1) = 1,3,8,9,5,9<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4)(3)(4,1)(5,2,1)(5,2,1)(5) = 1,3,8,9,5,10,11<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4)(3,1) = 1,3,8,9,6<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4)(3,1)(4,2,1)(4,2,1) = 1,3,8,9,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4)(5,1) = 1,3,8,10<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4)(5,1)(6,2,1)(6,2,1) = 1,3,8,10,15<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1) = 1,3,8,11<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1) = 1,3,8,12<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2)(6,3,1) = 1,3,8,12,18<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1) = 1,3,8,12,20<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(7,4,2,1) = 1,3,8,12,21<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(7,4,2,1)(6,3,1)(7,4,2,1)(7,4,2,1) = 1,3,8,12,21,21<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(7,4,2,1)(7,2)(8,3,1)(9,4,2) = 1,3,8,12,21,19<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(7,4,2,1)(7,2)(8,3,1)(9,4,2,1)(9,4,2,1)(7,2)(8,3,1) = 1,3,8,12,21,21,18<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(7,4,2,1)(7,3,1) = 1,3,8,12,21,28<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(7,4,2,1)(7,3,1)(8,4,2,1) = 1,3,8,12,21,29<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2,1) = 1,3,8,13<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2) = 1,3,8,14<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2) = 1,3,8,14,7,16,31<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2,1) = 1,3,8,14,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2,1)(2) = 1,3,8,14,8,9<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2,1)(2)(1)(2,1)(2,1) = 1,3,8,14,8,14,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(2) = 1,3,8,14,10<br /> <br /> (0)(1)(2,1)(2,1)(2)(2)(1)(2,1)(2,1) = 1,3,8,14,14,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3) = 1,3,8,14,15<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(3,1)(4,2,1)(4,2,1) = 1,3,8,14,15,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(4)(5,1) = 1,3,8,14,15,10<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(4,1) = 1,3,8,14,15,11<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(4,1)(5,2,1) = 1,3,8,14,15,12<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(4,1)(5,2,1)(5,2,1) = 1,3,8,14,15,13<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(4,1)(5,2,1)(5,2,1)(5,2) = 1,3,8,14,15,13,19<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(4,1)(5,2,1)(5,2,1)(5,2)(6) = 1,3,8,14,15,13,19,20<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(4,2) = 1,3,8,14,15,14<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(4,2)(5) = 1,3,8,14,15,14,15<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(6,1) = 1,3,8,14,16<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(6,1)(7,2,1)(7,2,1)(7,2) = 1,3,8,14,16,21,27<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,1) = 1,3,8,14,17<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,1)(6,2,1) = 1,3,8,14,18<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,1)(6,2,1)(6,2)(7,3,1)(8,4,2,1)(8,4,2,1)(8,4,2)(9,3,1)(10,4,2,1) = 1,3,8,14,18,27,43,51<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,1)(6,2,1)(6,2,1) = 1,3,8,14,19<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,1)(6,2,1)(6,2,1)(6,2) = 1,3,8,14,19,25<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,2) = 1,3,8,14,20<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3) = 1,3,8,14,21<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2)(7,5,3) = 1,3,8,14,21,7,16,31,53<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2,1) = 1,3,8,14,21,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(4) = 1,3,8,14,21,22<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(4)(1)(2,1)(2,1) = 1,3,8,14,21,29,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(4,1) = 1,3,8,14,22<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(4,1)(5,2,1) = 1,3,8,14,23<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(4,1)(5,2,1)(5,2,1) = 1,3,8,14,23,40<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1) = 1,3,8,15<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3) = 1,3,8,15,16<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5)(3,1)(4,2,1)(4,2,1) = 1,3,8,15,16,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5)(6,1) = 1,3,8,15,17<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5,1) = 1,3,8,15,18<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5,1)(6,2,1) = 1,3,8,15,19<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5,1)(6,2,1)(6,2,1) = 1,3,8,15,20<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5,1)(6,2,1)(6,2,1)(6,2)(7,3,1) = 1,3,8,15,20,27<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5,2) = 1,3,8,15,21<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5,2)(6,3,1) = 1,3,8,15,22<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5,3) = 1,3,8,15,23<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2,1) = 1,3,8,15,23,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(2) = 1,3,8,15,23,9<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(2)(3,1) = 1,3,8,15,23,15<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(3) = 1,3,8,15,23,16<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(4) = 1,3,8,15,23,24<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(4)(1)(2,1)(2,1) = 1,3,8,15,23,32,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(4,1) = 1,3,8,15,24<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(4,1)(4)(5,1) = 1,3,8,15,24,35<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(4,1)(4,1) = 1,3,8,15,25<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(4,1)(5,2,1) = 1,3,8,15,26<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(4,1)(5,2,1)(5,2,1) = 1,3,8,15,27<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(4,1)(5,2,1)(5,2,1)(5,2) = 1,3,8,15,27,45<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1) = 1,3,8,16<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(1)(2,1)(2,1) = 1,3,8,16,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(1)(2,1)(2,1)(2)(3,1)(3,1) = 1,3,8,16,8,16<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(2) = 1,3,8,16,10<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(2)(3,1)(3,1) = 1,3,8,16,16<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(3) = 1,3,8,16,17<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(3)(1)(2,1)(2,1)(2)(3,1)(3,1) = 1,3,8,16,25,8,16<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(3)(4,1) = 1,3,8,16,26<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(3)(4,1)(4,1) = 1,3,8,16,27<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(3,1) = 1,3,8,17<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4) = 1,3,8,17,18<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(1)(2,1)(2,1) = 1,3,8,17,27,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(5,1) = 1,3,8,17,28<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(5,1)(5)(6,1) = 1,3,8,17,28,41<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(5,1)(5)(6,1)(7,1) = 1,3,8,17,28,42<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(5,1)(5)(6,1)(7,2,1) = 1,3,8,17,28,43<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(5,1)(5)(6,1)(7,2,1)(7,2,1) = 1,3,8,17,28,44<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(5,1)(5)(6,1)(7,2,1)(7,2,1)(7,2)(8,3,1)(8,3,1)(8,3,1) = 1,3,8,17,28,44,69<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(5,1)(5,1) = 1,3,8,17,29<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(5,1)(5,1)(5,1) = 1,3,8,17,29,45<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4,1) = 1,3,8,17,30<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4,2) = 1,3,8,17,31<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4,2,1) = 1,3,8,18<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,8,18,38<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4,2,1)(4,2,1) = 1,3,8,19<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,8,19,42<br /> <br /> (0)(1)(2,1)(2,1)(2,1) = 1,3,8,20<br /> <br /> (0)(1)(2,1)(3) = 1,3,9<br /> [[分类:分析]]</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part3&diff=3042 2026-05-17T03:15:01Z

<p>Alice：​</p> <hr /> <div>本分析由 test_alpha0 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == Y(1,3,9) ~ Y(1,3,9,10,3) ==<br /> (0)(1)(2,1)(3) = 1,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1) = 1,3,9,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1) = 1,3,9,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,9,3,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,3,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,3,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4) = 1,3,9,4<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1) = 1,3,9,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2) = 1,3,9,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1) = 1,3,9,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2) = 1,3,9,7,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9) = 1,3,9,7,14,27,55<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,7,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,7,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5) = 1,3,9,7,17,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1) = 1,3,9,7,17,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1) = 1,3,9,7,17,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2,1) = 1,3,9,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(5) = 1,3,9,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1) = 1,3,9,10,2<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1) = 1,3,9,10,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10,2,5,14,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(2) = 1,3,9,10,2,5,14,15,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(3,1)(4,2,1) = 1,3,9,10,2,5,14,15,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,15,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(4) = 1,3,9,10,2,5,14,15,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1) = 1,3,9,10,2,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1) = 1,3,9,10,2,5,14,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2) = 1,3,9,10,2,5,14,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1) = 1,3,9,10,2,5,14,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,19,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3) = 1,3,9,10,2,5,14,19,30,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1) = 1,3,9,10,2,5,14,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1) = 1,3,9,10,2,5,14,20,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,20,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(4) = 1,3,9,10,2,5,14,20,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5) = 1,3,9,10,2,5,14,20,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1) = 1,3,9,10,2,5,14,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1) = 1,3,9,10,2,5,14,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,22,14,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4) = 1,3,9,10,2,5,14,22,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5) = 1,3,9,10,2,5,14,22,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,28,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(6,2,1)(7) = 1,3,9,10,2,5,14,22,30,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2) = 1,3,9,10,2,5,14,22,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,36,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1) = 1,3,9,10,2,5,14,22,37<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3,1) = 1,3,9,10,2,5,14,22,38<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6) = 1,3,9,10,2,5,14,22,38,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5) = 1,3,9,10,2,5,14,22,38,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,44,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,52,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,63,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3)(6,4,1)(7) = 1,3,9,10,2,5,14,22,38,65,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3,1) = 1,3,9,10,2,5,14,22,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,22,41,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2,1) = 1,3,9,10,2,5,14,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2,1)(5) = 1,3,9,10,2,5,14,22,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(5) = 1,3,9,10,2,5,14,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1) = 1,3,9,10,2,5,14,23,25<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,22,38,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,22,41,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(4) = 1,3,9,10,2,5,14,23,29,22,41,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,41,40<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1)(7,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,78,41<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,78,63,111<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(7) = 1,3,9,10,2,5,14,23,29,22,43,64,78,64<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8) = 1,3,9,10,2,5,14,23,29,22,43,64,78,65<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2) = 1,3,9,10,2,5,14,23,29,22,43,64,78,93<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,79<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8) = 1,3,9,10,2,5,14,23,29,22,43,64,80,81<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8,2)(9,3,1)(10,4,2,1)(11) = 1,3,9,10,2,5,14,23,29,22,43,64,80,110,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8,2)(9,3,1)(10,4,2,1)(11,1)(10,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,80,111<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,2) = 1,3,9,10,2,5,14,23,29,22,43,64,81<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,3,1)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,81,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,23,29,23,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,22,41,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7) = 1,3,9,10,2,5,14,23,29,23,22,38,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,38,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,1)(6,3,1) = 1,3,9,10,2,5,14,23,29,23,22,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,41,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(9,2,1)(10,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,80,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(6,3,1)(7,4,2,1)(8,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1)(7,3,1)(8,4,2,1)(9,3,1)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,64,63,43,64,81,64<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,23,22,14,23,29,23,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5) = 1,3,9,10,2,5,14,23,29,23,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,29,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,29,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(5) = 1,3,9,10,2,5,14,23,29,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(6,2,1)(7,1)(6,2,1) = 1,3,9,10,2,5,14,23,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2) = 1,3,9,10,2,5,14,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1) = 1,3,9,10,3<br /> [[分类:分析]]</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part3&diff=3041 2026-05-17T03:14:15Z

<p>Alice：​</p> <hr /> <div>本分析由 test_alpha0 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == Y(1,3,9) ~ Y(1,3,9,10,3) ==<br /> (0)(1)(2,1)(3) = 1,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1) = 1,3,9,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1) = 1,3,9,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,9,3,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,3,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,3,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4) = 1,3,9,4<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1) = 1,3,9,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2) = 1,3,9,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1) = 1,3,9,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2) = 1,3,9,7,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9) = 1,3,9,7,14,27,55<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,7,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,7,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5) = 1,3,9,7,17,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1) = 1,3,9,7,17,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1) = 1,3,9,7,17,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2,1) = 1,3,9,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(5) = 1,3,9,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1) = 1,3,9,10,2<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1) = 1,3,9,10,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10,2,5,14,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(2) = 1,3,9,10,2,5,14,15,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(3,1)(4,2,1) = 1,3,9,10,2,5,14,15,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,15,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4)(4) = 1,3,9,10,2,5,14,15,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1) = 1,3,9,10,2,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1) = 1,3,9,10,2,5,14,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2) = 1,3,9,10,2,5,14,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1) = 1,3,9,10,2,5,14,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,19,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3) = 1,3,9,10,2,5,14,19,30,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1) = 1,3,9,10,2,5,14,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1) = 1,3,9,10,2,5,14,20,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,20,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(4) = 1,3,9,10,2,5,14,20,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5) = 1,3,9,10,2,5,14,20,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1) = 1,3,9,10,2,5,14,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1) = 1,3,9,10,2,5,14,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,22,14,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4) = 1,3,9,10,2,5,14,22,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5) = 1,3,9,10,2,5,14,22,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,28,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(6,2,1)(7) = 1,3,9,10,2,5,14,22,30,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2) = 1,3,9,10,2,5,14,22,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,36,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1) = 1,3,9,10,2,5,14,22,37<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3,1) = 1,3,9,10,2,5,14,22,38<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6) = 1,3,9,10,2,5,14,22,38,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5) = 1,3,9,10,2,5,14,22,38,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,44,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,52,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,38,63,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3)(6,4,1)(7) = 1,3,9,10,2,5,14,22,38,65,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6)(5,3,1) = 1,3,9,10,2,5,14,22,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,22,41,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2,1) = 1,3,9,10,2,5,14,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2,1)(5) = 1,3,9,10,2,5,14,22,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(5) = 1,3,9,10,2,5,14,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1) = 1,3,9,10,2,5,14,23,25<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,22,38,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,22,41,14,23,29,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(4) = 1,3,9,10,2,5,14,23,29,22,41,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,41,40<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1)(7,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,78,41<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,78,63,111<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(7) = 1,3,9,10,2,5,14,23,29,22,43,64,78,64<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8) = 1,3,9,10,2,5,14,23,29,22,43,64,78,65<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2) = 1,3,9,10,2,5,14,23,29,22,43,64,78,93<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,79<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8) = 1,3,9,10,2,5,14,23,29,22,43,64,80,81<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8,2)(9,3,1)(10,4,2,1)(11) = 1,3,9,10,2,5,14,23,29,22,43,64,80,110,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,1)(8,2,1)(9,1)(8,2)(9,3,1)(10,4,2,1)(11,1)(10,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,80,111<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,2) = 1,3,9,10,2,5,14,23,29,22,43,64,81<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2)(5,3,1)(6,4,2,1)(7,3,1)(5,3,1)(6,4,2,1)(7,1)(6,4,2,1) = 1,3,9,10,2,5,14,23,29,22,43,64,81,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,23,29,23,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,22,41,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7) = 1,3,9,10,2,5,14,23,29,23,22,38,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,38,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,1)(6,3,1) = 1,3,9,10,2,5,14,23,29,23,22,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,41,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,1)(9,2,1)(10,1)(3,1)(4,2,1)(5,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,80,14,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(6,3,1)(7,4,2,1)(8,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1)(7,3,1)(8,4,2,1)(9,3,1)(6,3,1)(7,4,2,1)(8,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,23,29,23,22,43,64,81,64,63,43,64,81,64<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(4,1)(5,2,1)(6,1)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,23,22,14,23,29,23,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5) = 1,3,9,10,2,5,14,23,29,23,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,29,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,23,29,23,29,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(4,1)(5,2,1)(6,1)(5,2,1) = 1,3,9,10,2,5,14,23,29,23,29,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(5) = 1,3,9,10,2,5,14,23,29,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,1)(5,2,1)(6,1)(5,2,1)(5,1)(6,2,1)(7,1)(6,2,1) = 1,3,9,10,2,5,14,23,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2) = 1,3,9,10,2,5,14,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5,1)(4,2,1)(4,2)(3,1)(4,2,1) = 1,3,9,10,3</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=3024 2026-05-08T13:56:44Z

<p>Alice：​</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''试展开'''：指展开 1 次。<br /> <br /> '''最终展开'''：指展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> 试坏项与试坏项同行右侧的所有候选项都是上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> 试坏项同行右侧的所有候选项都是填充项。（注意：试坏项本身不是填充项）<br /> <br /> 若某一项的父项是坏项或填充项，则本项是填充项。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> <br /> 事实上，完全展开与 1-Y 的展开过程是很相似的。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为'''后继矩阵'''，删除最右列并不进行展开，得到的矩阵为其前驱。否则为'''极限矩阵'''，取其父项矩阵。<br /> <br /> 从右到左找到每一个检测项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3) = 1-Y (1,3,9)。<br /> <br /> 0 ~ Y(1,3,7) : [[DSM分析Part1]]<br /> <br /> Y(1,3,7) ~ Y(1,3,9) : [[DSM分析Part2]]<br /> <br /> Y(1,3,9) + : [[DSM分析Part3]]{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=3017 2026-05-06T14:19:13Z

<p>Alice：​</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''试展开'''：指展开 1 次。<br /> <br /> '''最终展开'''：指展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> 试坏项与试坏项同行右侧的所有候选项都是上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> 试坏项同行右侧的所有候选项都是填充项。（注意：试坏项本身不是填充项）<br /> <br /> 若某一项的父项是坏项或填充项，则本项是填充项。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> <br /> 事实上，完全展开与 1-Y 的展开过程是很相似的。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为后继矩阵，删除最右列并不进行展开，得到的矩阵为其前驱。否则为极限矩阵，取其父项矩阵。<br /> <br /> 从右到左找到每一个检测项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3) = 1-Y (1,3,9)。<br /> <br /> 0 ~ Y(1,3,7) : [[DSM分析Part1]]<br /> <br /> Y(1,3,7) ~ Y(1,3,9) : [[DSM分析Part2]]<br /> <br /> Y(1,3,9) + : [[DSM分析Part3]]{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part3&diff=3011 2026-05-05T10:05:37Z

<p>Alice：​</p> <hr /> <div>本分析由 CXL 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == Y(1,3,9) ~ Y(1,3,9,10,3) (WIP) ==<br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1) = 1,3,9,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1) = 1,3,9,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,9,3,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2) = 1,3,9,3,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,3,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,3,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4) = 1,3,9,4<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1) = 1,3,9,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,5,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2) = 1,3,9,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1) = 1,3,9,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,7,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5) = 1,3;9,7,17,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2) = 1,3,9,7,17,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,7,17,11,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3) = 1,3,9,7,17,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3)(6,4,1) = 1,3,9,7,17,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1) = 1,3,9,7,17,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1) = 1,3,9,7,17,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2,1) = 1,3,9,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,8,21,19,43,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2,1)(4,2,1) = 1,3,9,8,21,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(5) = 1,3,9,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1) = 1,3,9,10,2,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,16,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,9,10,2,5,14,16,5,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2) = 1,3,9,10,2,5,14,16,5,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,10,2,5,14,16,5,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4) = 1,3,9,10,2,5,14,16,5,14,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1) = 1,3,9,10,2,5,14,16,5,14,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,16,5,14,8,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2) = 1,3,9,10,2,5,14,16,5,14,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1) = 1,3,9,10,2,5,14,16,5,14,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,5,14,10,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5) = 1,3,9,10,2,5,14,16,5,14,10,21,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1) = 1,3,9,10,2,5,14,16,5,14,10,21,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1) = 1,3,9,10,2,5,14,16,5,14,10,21,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,16,5,14,10,21,13,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2) = 1,3,9,10,2,5,14,16,5,14,10,21,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2)(6,3,1) = 1,3,9,10,2,5,14,16,5,14,10,21,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,16,5,14,10,21,15,26<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3) = 1,3,9,10,2,5,14,16,5,14,10,21,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3)(6,4,1) = 1,3,9,10,2,5,14,16,5,14,10,21,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3)(6,4,1)(7,5,2,1)(8) = 1,3,9,10,2,5,14,16,5,14,10,21,17,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1) = 1,3,9,10,2,5,14,16,5,14,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,14,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,14,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,14,13,34,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,5,14,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6) = 1,3,9,10,2,5,14,16,5,14,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1) = 1,3,9,10,2,5,14,16,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,16,5,14,16,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4) = 1,3,9,10,2,5,14,16,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1) = 1,3,9,10,2,5,14,16,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1) = 1,3,9,10,2,5,14,16,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2) = 1,3,9,10,2,5,14,16,8,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1) = 1,3,9,10,2,5,14,16,8,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,16,8,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,16,8,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8)(7,1) = 1,3,9,10,2,5,14,16,8,17,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2) = 1,3,9,10,2,5,14,16,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1) = 1,3,9,10,2,5,14,16,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,10,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,10,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1) = 1,3,9,10,2,5,14,16,10,21,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5) = 1,3,9,10,2,5,14,16,10,21,23,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,2)(6,3,1)(7,4,2,1)(8)(7,1) = 1,3,9,10,2,5,14,16,10,21,23,15,26,28<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3) = 1,3,9,10,2,5,14,16,10,21,23,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3)(6,4,1)(7,5,2,1)(8)(7,1) = 1,3,9,10,2,5,14,16,10,21,23,17,30,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1) = 1,3,9,10,2,5,14,16,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(6) = 1,3,9,10,2,5,14,16,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2) = 1,3,9,10,2,5,14,16,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1) = 1,3,9,10,2,5,14,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1)(7,2)(8,3,1)(9,4,2,1)(10) = 1,3,9,10,2,5,14,17,26<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2) = 1,3,9,10,2,5,14,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1) = 1,3,9,10,2,5,14,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,19,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3) = 1,3,9,10,2,5,14,19,30,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1) = 1,3,9,10,2,5,14,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1) = 1,3,9,10,2,5,14,20,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,20,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9) = 1,3,9,10,2,5,14,20,12,29<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1) = 1,3,9,10,2,5,14,20,12,29,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1) = 1,3,9,10,2,5,14,20,13,34,51<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1)(7,5,3,1)(8,6,4,2,1)(8,6,4,2,1) = 1,3,9,10,2,5,14,20,13,34,51,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13,34,51,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(4) = 1,3,9,10,2,5,14,20,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(4,1) = 1,3,9,10,2,5,14,20,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(4,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,20,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5) = 1,3,9,10,2,5,14,20,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,1) = 1,3,9,10,2,5,14,20,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,26,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,1)(6) = 1,3,9,10,2,5,14,20,26,27<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2) = 1,3,9,10,2,5,14,20,27<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(3,1)(4,2,1) = 1,3,9,10,2,5,14,20,27,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(7,4,2)(5,3,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1)(9,6) = 1,3,9,10,2,5,14,20,27,12,29,35,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(7,4,2)(5,3,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1)(9,6,4) = 1,3,9,10,2,5,14,20,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(7,4,2)(5,3,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1)(9,6,4,2) = 1,3,9,10,2,5,14,20,30,12,29,43,68<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,30,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,30,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(6,2) = 1,3,9,10,2,5,14,20,30,37<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(6,2)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,30,40,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(6,3) = 1,3,9,10,2,5,14,20,30,41<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(6,3)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,30,45,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(6,3,1) = 1,3,9,10,2,5,14,20,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1) = 1,3,9,10,2,5,14,20,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8)(7,3,1)(8,4,2,1)(8,4,2)(9,5,3,1)(10,6,4,2,1)(11)(10,5,3,1)(11,6,4,2,1) = 1,3,9,10,2,5,14,21,38,53<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1) = 1,3,9,10,2,5,14,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1)(3,1)(4,2,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,13,34,53,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,22,13,34,53,34<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1)(5,2,1) = 1,3,9,10,2,5,14,22,13,34,54<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1) = 1,3,9,10,2,5,14,22,14,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4) = 1,3,9,10,2,5,14,22,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4,1)(5,2,1)(5,2,1) = 1,3,9,10,2,5,14,22,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5) = 1,3,9,10,2,5,14,22,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(6,2,1)(6,2,1) = 1,3,9,10,2,5,14,22,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(6,2,1)(7) = 1,3,9,10,2,5,14,22,30,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2) = 1,3,9,10,2,5,14,22,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1) = 1,3,9,10,2,5,14,22,31,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4) = 1,3,9,10,2,5,14,22,31,5,14,22,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,22,31,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4)(6) = 1,3,9,10,2,5,14,22,31,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4)(6,2) = 1,3,9,10,2,5,14,22,31,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4)(6,3,1) = 1,3,9,10,2,5,14,22,31,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,22,31,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4)(6,3,1)(7,4,2,1)(8)(7,4) = 1,3,9,10,2,5,14,22,31,22,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4)(6,4) = 1,3,9,10,2,5,14,22,31,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4)(7,3,1) = 1,3,9,10,2,5,14,22,31,37<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4)(7,3,1)(8,4,2,1)(9)(8,4) = 1,3,9,10,2,5,14,22,31,39,48<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4)(7,4) = 1,3,9,10,2,5,14,22,31,40<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4)(7,5) = 1,3,9,10,2,5,14,22,31,41<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4)(7,5,1) = 1,3,9,10,2,5,14,22,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,1) = 1,3,9,10,2,5,14,22,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,1)(7,5,2,1) = 1,3,9,10,2,5,14,22,34<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,1)(7,5,2,1)(8) = 1,3,9,10,2,5,14,22,35,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2) = 1,3,9,10,2,5,14,22,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,36,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,22,36,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(4) = 1,3,9,10,2,5,14,22,36,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(4,1)(5,2,1)(6)(5,2) = 1,3,9,10,2,5,14,22,36,22,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(4,1)(5,2,1)(6)(5,2)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,22,36,22,36,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(4,1)(5,2,1)(6)(5,2)(5) = 1,3,9,10,2,5,14,22,36,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(4,1)(5,2,1)(6)(5,2)(5,1)(6,2,1)(7)(6,2) = 1,3,9,10,2,5,14,22,36,30,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(4,2) = 1,3,9,10,2,5,14,22,36,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5) = 1,3,9,10,2,5,14,22,36,37<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,2) = 1,3,9,10,2,5,14,22,36,45<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,2)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,22,36,50,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,2)(6,2) = 1,3,9,10,2,5,14,22,36,50,59<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3) = 1,3,9,10,2,5,14,22,36,51<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3) = 1,3,9,10,2,5,14,22,36,57<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1) = 1,3,9,10,2,5,14,22,37</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part1&diff=3009 2026-05-02T14:05:08Z

<p>Alice：​</p> <hr /> <div>本分析由 CXL 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == 0 ~ Y(1,3) ==<br /> (0) = 1<br /> <br /> (0)(1) = 1,2<br /> <br /> (0)(1)(2)(3,1) = 1,2,4<br /> <br /> (0)(1)(2)(3,1)(4,2)(5,3,1) = 1,2,4,8<br /> <br /> (0)(1)(2)(3,1)(4,2)(5,3,1)(6,4,2)(7,5,3,1) = 1,2,4,8,16<br /> <br /> (0)(1)(2,1) = 1,3<br /> <br /> == Y(1,3) ~ Y(1,3,7) ==<br /> (0)(1)(2,1) = 1,3<br /> <br /> (0)(1)(2,1)(1) = 1,3,2<br /> <br /> (0)(1)(2,1)(1)(2) = 1,3,2,3<br /> <br /> (0)(1)(2,1)(1)(2)(3,1) = 1,3,2,4<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2)(5,3,1) = 1,3,2,4,8<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2,1) = 1,3,2,5<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2,1)(3,1) = 1,3,2,5,4<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2,1)(3,1)(4,2)(5,3,1) = 1,3,2,5,4,8<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2,1)(3,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,2,5,4,9<br /> <br /> (0)(1)(2,1)(1)(2,1) = 1,3,3<br /> <br /> (0)(1)(2,1)(1)(2,1)(1)(2)(3,1)(4,2,1)(3,1)(4,2,1) = 1,3,3,2,5,5<br /> <br /> (0)(1)(2,1)(1)(2,1)(1)(2,1) = 1,3,3,3<br /> <br /> (0)(1)(2,1)(2) = 1,3,4<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1) = 1,3,4,2,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(2) = 1,3,4,2,5,3<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(2)(3,1)(4,2,1) = 1,3,4,2,5,3,6<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(3,1) = 1,3,4,2,5,4<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(3,1)(4,2,1) = 1,3,4,2,5,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4) = 1,3,4,2,5,6<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4)(3,1)(4,2,1) = 1,3,4,2,5,6,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1) = 1,3,4,2,5,7<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,1) = 1,3,4,2,5,7,4,9,11<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,1)(5,3,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(8,1)(7,5,3,1) = 1,3,4,2,5,7,4,9,11,8,17,19<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,1)(5,3,1)(6,4,2,1) = 1,3,4,2,5,7,4,9,11,9<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,1)(6) = 1,3,4,2,5,7,4,9,11,10<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,2) = 1,3,4,2,5,7,4,9,12<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,2)(5,3,1)(6,4,2,1) = 1,3,4,2,5,7,4,9,12,8,17,20,17<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,3) = 1,3,4,2,5,7,4,9,12,8,17,21<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,3)(5,3,1)(6,4,2,1) = 1,3,4,2,5,7,4,9,12,9<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,3,1)(5,3,1) = 1,3,4,2,5,7,4,9,13<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2,1) = 1,3,4,2,5,7,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2,1)(4,1) = 1,3,4,2,5,7,5,7<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(4) = 1,3,4,2,5,7,6<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(4,1) = 1,3,4,2,5,7,7<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,1) = 1,3,4,2,5,7,9<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2) = 1,3,4,2,5,7,10<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,3,1)(7,4,2) = 1,3,4,2,5,7,10,4,9,13,20<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(3,1)(4,2,1) = 1,3,4,2,5,7,10,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1) = 1,3,4,2,5,7,11<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1) = 1,3,4,2,5,7,12<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1)(7,3,1) = 1,3,4,2,5,7,12,16<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1)(7,3,1)(6,3,1)(7,4,2,1) = 1,3,4,2,5,7,12,16,12<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1)(7,3,1)(8,4,2)(9,5,3,1) = 1,3,4,2,5,7,12,16,24<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1)(7,3,1)(8,4,2)(9,5,3,1)(10,6,4,2,1) = 1,3,4,2,5,7,12,16,25<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,4,2,5,8<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,2) = 1,3,4,2,5,9<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,2)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2) = 1,3,4,2,5,9,4,9,18<br /> <br /> (0)(1)(2,1)(2)(1)(2,1) = 1,3,4,3<br /> <br /> (0)(1)(2,1)(2)(2) = 1,3,4,4<br /> <br /> (0)(1)(2,1)(2)(3)(4,1) = 1,3,4,6<br /> <br /> (0)(1)(2,1)(2)(3)(4,1)(5,2,1) = 1,3,4,7<br /> <br /> (0)(1)(2,1)(2)(3)(4,1)(5,2,1)(5,2)(6,3)(7,4,1)(8,5,2,1) = 1,3,4,7,11,18<br /> <br /> (0)(1)(2,1)(2)(3,1) = 1,3,5<br /> <br /> (0)(1)(2,1)(2)(3,1)(1)(2,1) = 1,3,5,3<br /> <br /> (0)(1)(2,1)(2)(3,1)(1)(2,1)(2)(3,1) = 1,3,5,3,5<br /> <br /> (0)(1)(2,1)(2)(3,1)(2) = 1,3,5,4<br /> <br /> (0)(1)(2,1)(2)(3,1)(2)(3,1) = 1,3,5,5<br /> <br /> (0)(1)(2,1)(2)(3,1)(3) = 1,3,5,6<br /> <br /> (0)(1)(2,1)(2)(3,1)(3)(4,1) = 1,3,5,7<br /> <br /> (0)(1)(2,1)(2)(3,1)(3,1) = 1,3,6<br /> <br /> (0)(1)(2,1)(2)(3,1)(4)(5,1) = 1,3,6,8<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,1) = 1,3,6,9<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2) = 1,3,6,10<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2)(5,3,1) = 1,3,6,11<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,6,12<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1) = 1,3,7</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part3&diff=3008 2026-05-02T05:44:53Z

<p>Alice：​</p> <hr /> <div>本分析由 CXL 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == Y(1,3,9) ~ Y(1,3,9,10,3) (WIP) ==<br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1) = 1,3,9,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1) = 1,3,9,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,9,3,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2) = 1,3,9,3,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,3,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,3,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4) = 1,3,9,4<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1) = 1,3,9,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,5,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2) = 1,3,9,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1) = 1,3,9,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,7,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5) = 1,3;9,7,17,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2) = 1,3,9,7,17,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,7,17,11,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3) = 1,3,9,7,17,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3)(6,4,1) = 1,3,9,7,17,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1) = 1,3,9,7,17,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1) = 1,3,9,7,17,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2,1) = 1,3,9,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,8,21,19,43,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2,1)(4,2,1) = 1,3,9,8,21,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(5) = 1,3,9,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1) = 1,3,9,10,2,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,16,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,9,10,2,5,14,16,5,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2) = 1,3,9,10,2,5,14,16,5,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,10,2,5,14,16,5,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4) = 1,3,9,10,2,5,14,16,5,14,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1) = 1,3,9,10,2,5,14,16,5,14,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,16,5,14,8,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2) = 1,3,9,10,2,5,14,16,5,14,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1) = 1,3,9,10,2,5,14,16,5,14,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,5,14,10,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5) = 1,3,9,10,2,5,14,16,5,14,10,21,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1) = 1,3,9,10,2,5,14,16,5,14,10,21,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1) = 1,3,9,10,2,5,14,16,5,14,10,21,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,16,5,14,10,21,13,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2) = 1,3,9,10,2,5,14,16,5,14,10,21,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2)(6,3,1) = 1,3,9,10,2,5,14,16,5,14,10,21,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,16,5,14,10,21,15,26<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3) = 1,3,9,10,2,5,14,16,5,14,10,21,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3)(6,4,1) = 1,3,9,10,2,5,14,16,5,14,10,21,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3)(6,4,1)(7,5,2,1)(8) = 1,3,9,10,2,5,14,16,5,14,10,21,17,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1) = 1,3,9,10,2,5,14,16,5,14,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,14,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,14,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,14,13,34,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,5,14,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6) = 1,3,9,10,2,5,14,16,5,14,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1) = 1,3,9,10,2,5,14,16,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,16,5,14,16,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4) = 1,3,9,10,2,5,14,16,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1) = 1,3,9,10,2,5,14,16,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1) = 1,3,9,10,2,5,14,16,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2) = 1,3,9,10,2,5,14,16,8,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1) = 1,3,9,10,2,5,14,16,8,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,16,8,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,16,8,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8)(7,1) = 1,3,9,10,2,5,14,16,8,17,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2) = 1,3,9,10,2,5,14,16,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1) = 1,3,9,10,2,5,14,16,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,10,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,10,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1) = 1,3,9,10,2,5,14,16,10,21,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5) = 1,3,9,10,2,5,14,16,10,21,23,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,2)(6,3,1)(7,4,2,1)(8)(7,1) = 1,3,9,10,2,5,14,16,10,21,23,15,26,28<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3) = 1,3,9,10,2,5,14,16,10,21,23,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3)(6,4,1)(7,5,2,1)(8)(7,1) = 1,3,9,10,2,5,14,16,10,21,23,17,30,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1) = 1,3,9,10,2,5,14,16,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(6) = 1,3,9,10,2,5,14,16,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2) = 1,3,9,10,2,5,14,16,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1) = 1,3,9,10,2,5,14,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1)(7,2)(8,3,1)(9,4,2,1)(10) = 1,3,9,10,2,5,14,17,26<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2) = 1,3,9,10,2,5,14,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1) = 1,3,9,10,2,5,14,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,19,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3) = 1,3,9,10,2,5,14,19,30,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1) = 1,3,9,10,2,5,14,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1) = 1,3,9,10,2,5,14,20,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,20,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9) = 1,3,9,10,2,5,14,20,12,29<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1) = 1,3,9,10,2,5,14,20,12,29,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1) = 1,3,9,10,2,5,14,20,13,34,51<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1)(7,5,3,1)(8,6,4,2,1)(8,6,4,2,1) = 1,3,9,10,2,5,14,20,13,34,51,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13,34,51,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(4) = 1,3,9,10,2,5,14,20,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(4,1) = 1,3,9,10,2,5,14,20,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(4,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,20,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5) = 1,3,9,10,2,5,14,20,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,1) = 1,3,9,10,2,5,14,20,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,26,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,1)(6) = 1,3,9,10,2,5,14,20,26,27<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2) = 1,3,9,10,2,5,14,20,27<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(3,1)(4,2,1) = 1,3,9,10,2,5,14,20,27,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(7,4,2)(5,3,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1)(9,6) = 1,3,9,10,2,5,14,20,27,12,29,35,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(7,4,2)(5,3,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1)(9,6,4) = 1,3,9,10,2,5,14,20,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(7,4,2)(5,3,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1)(9,6,4,2) = 1,3,9,10,2,5,14,20,30,12,29,43,68<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,30,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,30,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(6,2) = 1,3,9,10,2,5,14,20,30,37<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(6,2)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,30,40,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(6,3) = 1,3,9,10,2,5,14,20,30,41<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(6,3)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,30,45,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2)(6,3,1) = 1,3,9,10,2,5,14,20,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1) = 1,3,9,10,2,5,14,20,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8)(7,3,1)(8,4,2,1)(8,4,2)(9,5,3,1)(10,6,4,2,1)(11)(10,5,3,1)(11,6,4,2,1) = 1,3,9,10,2,5,14,21,38,53<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1) = 1,3,9,10,2,5,14,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1)(3,1)(4,2,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,22,13,34,53,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,22,13,34,53,34<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1)(5,2,1) = 1,3,9,10,2,5,14,22,13,34,54<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5)(4,1)(5,2,1)(5,2,1) = 1,3,9,10,2,5,14,22,14,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,14,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4) = 1,3,9,10,2,5,14,22,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4,1)(5,2,1)(5,2,1) = 1,3,9,10,2,5,14,22,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(4,1)(5,2,1)(6) = 1,3,9,10,2,5,14,22,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5) = 1,3,9,10,2,5,14,22,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(6,2,1)(6,2,1) = 1,3,9,10,2,5,14,22,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(5,2,1)(6)(5,1)(6,2,1)(7) = 1,3,9,10,2,5,14,22,30,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2) = 1,3,9,10,2,5,14,22,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1) = 1,3,9,10,2,5,14,22,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,1) = 1,3,9,10,2,5,14,22,32,34<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,1)(6,2,1) = 1,3,9,10,2,5,14,22,32,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,1)(6,2,1)(7) = 1,3,9,10,2,5,14,22,32,40,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,1)(6,2,1)(7)(6,2)(7,3,1) = 1,3,9,10,2,5,14,22,32,40,50<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,2) = 1,3,9,10,2,5,14,22,32,41<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,2)(6,3,1) = 1,3,9,10,2,5,14,22,32,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3) = 1,3,9,10,2,5,14,22,32,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1) = 1,3,9,10,2,5,14,22,32,43,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5) = 1,3,9,10,2,5,14,22,32,43,5,14,22,32,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,22,32,43,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,22,32,43,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6) = 1,3,9,10,2,5,14,22,32,43,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,1) = 1,3,9,10,2,5,14,22,32,43,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,1)(7,2,1) = 1,3,9,10,2,5,14,22,32,43,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,2) = 1,3,9,10,2,5,14,22,32,43,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,2)(7,3,1) = 1,3,9,10,2,5,14,22,32,43,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3) = 1,3,9,10,2,5,14,22,32,43,19,30,40,51,25<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1) = 1,3,9,10,2,5,14,22,32,43,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,22,32,43,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1)(7,4,2,1) = 1,3,9,10,2,5,14,22,32,43,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,22,32,43,22,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1)(8)(7,4,2) = 1,3,9,10,2,5,14,22,32,43,22,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1)(8)(7,4,2)(8,5,3,1) = 1,3,9,10,2,5,14,22,32,43,22,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1)(8)(7,4,2)(8,5,3,1)(8,5) = 1,3,9,10,2,5,14,22,32,43,22,32,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1)(8)(7,4,2)(8,5,3,1)(8,5)(7) = 1,3,9,10,2,5,14,22,32,43,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1)(8)(7,4,2)(8,5,3,1)(8,5)(7,1) = 1,3,9,10,2,5,14,22,32,43,24<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1)(8)(7,4,2)(8,5,3,1)(8,5)(7,1)(8,2,1) = 1,3,9,10,2,5,14,22,32,43,25<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1)(8)(7,4,2)(8,5,3,1)(8,5)(7,2) = 1,3,9,10,2,5,14,22,32,43,26<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(<br /> <br /> 5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1)(8)(7,4,2)(8,5,3,1)(8,5)(7,2)(8,3,1) = 1,3,9,10,2,5,14,22,32,43,27<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1)(8)(7,4,2)(8,5,3,1)(8,5)(7,3,1) = 1,3,9,10,2,5,14,22,32,43,28<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1)(8)(7,4,2)(8,5,3,1)(8,5)(7,3,1)(8,4,2,1) = 1,3,9,10,2,5,14,22,32,43,29<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1)(8)(7,4,2)(8,5,3,1)(8,5)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,22,32,43,30,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1)(8)(7,4,2)(8,5,3,1)(8,5)(7,3,1)(8,4,2,1)(9)(8,4,2) = 1,3,9,10,2,5,14,22,32,43,30,39<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1)(8)(7,4,2)(8,5,3,1)(8,5)(7,3,1)(8,4,2,1)(9)(8,4,2)(9,5,3,1) = 1,3,9,10,2,5,14,22,32,43,30,40<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,3,1)(7,4,2,1)(8)(7,4,2)(8,5,3,1)(8,5)(7,3,1)(8,4,2,1)(9)(8,4,2)(9,5,3,1)(9,5) = 1,3,9,10,2,5,14,22,32,43,30,40,51<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,4) = 1,3,9,10,2,5,14,22,32,43,31<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,4)(7,5,1) = 1,3,9,10,2,5,14,22,32,43,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,4)(7,5,1)(7,5) = 1,3,9,10,2,5,14,22,32,43,32,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,4)(7,5,1)(7,5)(7,5) = 1,3,9,10,2,5,14,22,32,43,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,4)(7,5,1)(7,5)(8,6,1) = 1,3,9,10,2,5,14,22,32,44<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,4)(7,5,1)(7,5)(8,6,1)(8,6)(9,7,1) = 1,3,9,10,2,5,14,22,32,44,58<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,4)(7,5,1)(7,5,1) = 1,3,9,10,2,5,14,22,32,45<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,4)(7,5,1)(8,6,2,1) = 1,3,9,10,2,5,14,22,32,46<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,4)(7,5,1)(8,6,2,1)(9) = 1,3,9,10,2,5,14,22,32,48<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,4)(7,5,1)(8,6,2,1)(9)(8,6,2) = 1,3,9,10,2,5,14,22,32,48,63,79<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,4)(7,5,1)(8,6,2,1)(9)(8,6,2)(9,7,3,1)(9,7) = 1,3,9,10,2,5,14,22,32,48,63,80,98<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,2)(5,3,1)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,4,2)(7,5,3,1)(7,5)(6,4,1) = 1,3,9,10,2,5,14,22,33</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part3&diff=3007 2026-05-02T05:40:33Z

<p>Alice：​</p> <hr /> <div>本分析由 CXL 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == Y(1,3,9) ~ Y(1,3,9,10,3) (WIP) ==<br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1) = 1,3,9,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1) = 1,3,9,3<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,9,3,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2) = 1,3,9,3,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,3,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,3,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4) = 1,3,9,4<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1) = 1,3,9,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,5,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2) = 1,3,9,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1) = 1,3,9,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,7,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,7,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5) = 1,3;9,7,17,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2) = 1,3,9,7,17,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,7,17,11,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3) = 1,3,9,7,17,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3)(6,4,1) = 1,3,9,7,17,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1) = 1,3,9,7,17,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1) = 1,3,9,7,17,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2,1) = 1,3,9,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,8,21,19,43,42<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(4,2,1)(4,2,1) = 1,3,9,8,21,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(3,1)(4,2,1)(5) = 1,3,9,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4) = 1,3,9,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1) = 1,3,9,10,2,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,16,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,9,10,2,5,14,16,5,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2) = 1,3,9,10,2,5,14,16,5,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,10,2,5,14,16,5,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4) = 1,3,9,10,2,5,14,16,5,14,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1) = 1,3,9,10,2,5,14,16,5,14,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,16,5,14,8,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2) = 1,3,9,10,2,5,14,16,5,14,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1) = 1,3,9,10,2,5,14,16,5,14,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,5,14,10,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5) = 1,3,9,10,2,5,14,16,5,14,10,21,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1) = 1,3,9,10,2,5,14,16,5,14,10,21,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1) = 1,3,9,10,2,5,14,16,5,14,10,21,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,16,5,14,10,21,13,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2) = 1,3,9,10,2,5,14,16,5,14,10,21,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2)(6,3,1) = 1,3,9,10,2,5,14,16,5,14,10,21,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,16,5,14,10,21,15,26<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3) = 1,3,9,10,2,5,14,16,5,14,10,21,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3)(6,4,1) = 1,3,9,10,2,5,14,16,5,14,10,21,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3)(6,4,1)(7,5,2,1)(8) = 1,3,9,10,2,5,14,16,5,14,10,21,17,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1) = 1,3,9,10,2,5,14,16,5,14,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,14,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,14,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,14,13,34,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,5,14,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6) = 1,3,9,10,2,5,14,16,5,14,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1) = 1,3,9,10,2,5,14,16,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,16,5,14,16,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4) = 1,3,9,10,2,5,14,16,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1) = 1,3,9,10,2,5,14,16,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1) = 1,3,9,10,2,5,14,16,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2) = 1,3,9,10,2,5,14,16,8,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1) = 1,3,9,10,2,5,14,16,8,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,16,8,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,16,8,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8)(7,1) = 1,3,9,10,2,5,14,16,8,17,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2) = 1,3,9,10,2,5,14,16,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1) = 1,3,9,10,2,5,14,16,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,10,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,10,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1) = 1,3,9,10,2,5,14,16,10,21,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5) = 1,3,9,10,2,5,14,16,10,21,23,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,2)(6,3,1)(7,4,2,1)(8)(7,1) = 1,3,9,10,2,5,14,16,10,21,23,15,26,28<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3) = 1,3,9,10,2,5,14,16,10,21,23,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3)(6,4,1)(7,5,2,1)(8)(7,1) = 1,3,9,10,2,5,14,16,10,21,23,17,30,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1) = 1,3,9,10,2,5,14,16,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(6) = 1,3,9,10,2,5,14,16,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2) = 1,3,9,10,2,5,14,16,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1) = 1,3,9,10,2,5,14,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1)(7,2)(8,3,1)(9,4,2,1)(10) = 1,3,9,10,2,5,14,17,26<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2) = 1,3,9,10,2,5,14,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1) = 1,3,9,10,2,5,14,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,19,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3) = 1,3,9,10,2,5,14,19,30,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1) = 1,3,9,10,2,5,14,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1) = 1,3,9,10,2,5,14,20,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,20,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9) = 1,3,9,10,2,5,14,20,12,29<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1) = 1,3,9,10,2,5,14,20,12,29,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1) = 1,3,9,10,2,5,14,20,13,34,51<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1)(7,5,3,1)(8,6,4,2,1)(8,6,4,2,1) = 1,3,9,10,2,5,14,20,13,34,51,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13,34,51,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,14</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part3&diff=3006 2026-05-02T05:39:38Z

<p>Alice：​</p> <hr /> <div>本分析由 CXL 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == Y(1,3,9) ~ Y(1,3,9,10,3) (WIP) ==<br /> (0)(1)(2,1)(3) = 1,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1) = 1,3,9,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1) = 1,3,9,10,2,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,16,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,9,10,2,5,14,16,5,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2) = 1,3,9,10,2,5,14,16,5,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,10,2,5,14,16,5,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4) = 1,3,9,10,2,5,14,16,5,14,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1) = 1,3,9,10,2,5,14,16,5,14,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,16,5,14,8,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2) = 1,3,9,10,2,5,14,16,5,14,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1) = 1,3,9,10,2,5,14,16,5,14,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,5,14,10,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5) = 1,3,9,10,2,5,14,16,5,14,10,21,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1) = 1,3,9,10,2,5,14,16,5,14,10,21,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1) = 1,3,9,10,2,5,14,16,5,14,10,21,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,16,5,14,10,21,13,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2) = 1,3,9,10,2,5,14,16,5,14,10,21,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2)(6,3,1) = 1,3,9,10,2,5,14,16,5,14,10,21,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,16,5,14,10,21,15,26<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3) = 1,3,9,10,2,5,14,16,5,14,10,21,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3)(6,4,1) = 1,3,9,10,2,5,14,16,5,14,10,21,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3)(6,4,1)(7,5,2,1)(8) = 1,3,9,10,2,5,14,16,5,14,10,21,17,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1) = 1,3,9,10,2,5,14,16,5,14,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,14,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,14,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,14,13,34,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,5,14,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6) = 1,3,9,10,2,5,14,16,5,14,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1) = 1,3,9,10,2,5,14,16,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,16,5,14,16,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4) = 1,3,9,10,2,5,14,16,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1) = 1,3,9,10,2,5,14,16,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1) = 1,3,9,10,2,5,14,16,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2) = 1,3,9,10,2,5,14,16,8,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1) = 1,3,9,10,2,5,14,16,8,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,16,8,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,16,8,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8)(7,1) = 1,3,9,10,2,5,14,16,8,17,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2) = 1,3,9,10,2,5,14,16,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1) = 1,3,9,10,2,5,14,16,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,10,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,10,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1) = 1,3,9,10,2,5,14,16,10,21,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5) = 1,3,9,10,2,5,14,16,10,21,23,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,2)(6,3,1)(7,4,2,1)(8)(7,1) = 1,3,9,10,2,5,14,16,10,21,23,15,26,28<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3) = 1,3,9,10,2,5,14,16,10,21,23,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3)(6,4,1)(7,5,2,1)(8)(7,1) = 1,3,9,10,2,5,14,16,10,21,23,17,30,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1) = 1,3,9,10,2,5,14,16,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(6) = 1,3,9,10,2,5,14,16,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2) = 1,3,9,10,2,5,14,16,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1) = 1,3,9,10,2,5,14,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1)(7,2)(8,3,1)(9,4,2,1)(10) = 1,3,9,10,2,5,14,17,26<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2) = 1,3,9,10,2,5,14,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1) = 1,3,9,10,2,5,14,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,19,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3) = 1,3,9,10,2,5,14,19,30,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1) = 1,3,9,10,2,5,14,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1) = 1,3,9,10,2,5,14,20,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,20,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9) = 1,3,9,10,2,5,14,20,12,29<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1) = 1,3,9,10,2,5,14,20,12,29,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1) = 1,3,9,10,2,5,14,20,13,34,51<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1)(7,5,3,1)(8,6,4,2,1)(8,6,4,2,1) = 1,3,9,10,2,5,14,20,13,34,51,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13,34,51,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,14</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=3004 2026-05-01T17:29:08Z

<p>Alice：​</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''试展开'''：指展开 1 次。<br /> <br /> '''最终展开'''：指展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> 试坏项与试坏项同行右侧的所有候选项都是上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> 试坏项同行右侧的所有候选项都是填充项。（注意：试坏项本身不是填充项）<br /> <br /> 若某一项的父项是坏项或填充项，则本项是填充项。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为后继矩阵，删除最右列并不进行展开，得到的矩阵为其前驱。否则为极限矩阵，取其父项矩阵。<br /> <br /> 从右到左找到每一个候选项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3) = 1-Y (1,3,9)。<br /> <br /> 0 ~ Y(1,3,7) : [[DSM分析Part1]]<br /> <br /> Y(1,3,7) ~ Y(1,3,9) : [[DSM分析Part2]]<br /> <br /> Y(1,3,9) + : [[DSM分析Part3]]{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part3&diff=3003 2026-05-01T17:27:39Z

<p>Alice：​创建页面，内容为“本分析由 CXL 提供。左侧为 DSM，右侧为 Y。 == Y(1,3,9) ~ Y(1,3,9,3) (WIP) == (0)(1)(2,1)(3) = 1,3,9 (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1) = 1,3,9,2,5 (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,2,5,14 (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1) = 1,3,9,10,2,5,14,16 (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,16,5 (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,9,10,2,5,14,16,5,10 (0)(1)(2,1)(3)(1)(2…”</p> <hr /> <div>本分析由 CXL 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == Y(1,3,9) ~ Y(1,3,9,3) (WIP) ==<br /> (0)(1)(2,1)(3) = 1,3,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1) = 1,3,9,2,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5) = 1,3,9,2,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1) = 1,3,9,10,2,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,16,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,9,10,2,5,14,16,5,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2) = 1,3,9,10,2,5,14,16,5,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,9,10,2,5,14,16,5,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,5,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4) = 1,3,9,10,2,5,14,16,5,14,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1) = 1,3,9,10,2,5,14,16,5,14,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,16,5,14,8,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2) = 1,3,9,10,2,5,14,16,5,14,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1) = 1,3,9,10,2,5,14,16,5,14,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,5,14,10,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5) = 1,3,9,10,2,5,14,16,5,14,10,21,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1) = 1,3,9,10,2,5,14,16,5,14,10,21,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1) = 1,3,9,10,2,5,14,16,5,14,10,21,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,1)(6,2,1)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,16,5,14,10,21,13,22<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2) = 1,3,9,10,2,5,14,16,5,14,10,21,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2)(6,3,1) = 1,3,9,10,2,5,14,16,5,14,10,21,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,16,5,14,10,21,15,26<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3) = 1,3,9,10,2,5,14,16,5,14,10,21,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3)(6,4,1) = 1,3,9,10,2,5,14,16,5,14,10,21,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3)(6,4,1)(7,5,2,1)(8) = 1,3,9,10,2,5,14,16,5,14,10,21,17,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1) = 1,3,9,10,2,5,14,16,5,14,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,14,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,14,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,5,14,13,34,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,5,14,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6) = 1,3,9,10,2,5,14,16,5,14,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1) = 1,3,9,10,2,5,14,16,5,14,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(3,1)(4,2,1) = 1,3,9,10,2,5,14,16,5,14,16,5<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4) = 1,3,9,10,2,5,14,16,6<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1) = 1,3,9,10,2,5,14,16,7<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1) = 1,3,9,10,2,5,14,16,8<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2) = 1,3,9,10,2,5,14,16,8,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1) = 1,3,9,10,2,5,14,16,8,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1) = 1,3,9,10,2,5,14,16,8,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8) = 1,3,9,10,2,5,14,16,8,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(8)(7,1) = 1,3,9,10,2,5,14,16,8,17,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2) = 1,3,9,10,2,5,14,16,9<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1) = 1,3,9,10,2,5,14,16,10<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,10,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,10,21<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1) = 1,3,9,10,2,5,14,16,10,21,23<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5) = 1,3,9,10,2,5,14,16,10,21,23,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,2)(6,3,1)(7,4,2,1)(8)(7,1) = 1,3,9,10,2,5,14,16,10,21,23,15,26,28<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3) = 1,3,9,10,2,5,14,16,10,21,23,16<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3)(6,4,1)(7,5,2,1)(8)(7,1) = 1,3,9,10,2,5,14,16,10,21,23,17,30,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1) = 1,3,9,10,2,5,14,16,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,9,10,2,5,14,16,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(5,3,1)(6,4,2,1)(7) = 1,3,9,10,2,5,14,16,14<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(6) = 1,3,9,10,2,5,14,16,15<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2) = 1,3,9,10,2,5,14,16,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1) = 1,3,9,10,2,5,14,17<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,1)(7,2,1)(7,2)(8,3,1)(9,4,2,1)(10) = 1,3,9,10,2,5,14,17,26<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2) = 1,3,9,10,2,5,14,18<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1) = 1,3,9,10,2,5,14,19<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,2)(7,3,1)(8,4,2,1)(9) = 1,3,9,10,2,5,14,19,30<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3) = 1,3,9,10,2,5,14,19,30,36<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1) = 1,3,9,10,2,5,14,20<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1) = 1,3,9,10,2,5,14,20,11<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1) = 1,3,9,10,2,5,14,20,12<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9) = 1,3,9,10,2,5,14,20,12,29<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1) = 1,3,9,10,2,5,14,20,12,29,43<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1) = 1,3,9,10,2,5,14,20,13,34,51<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(7)(6,3,1)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(9)(8,5,3,1)(7,5,3,1)(8,6,4,2,1)(8,6,4,2,1) = 1,3,9,10,2,5,14,20,13,34,51,32<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(4,2,1)(4,2,1) = 1,3,9,10,2,5,14,20,13,34,51,33<br /> <br /> (0)(1)(2,1)(3)(1)(2)(3,1)(4,2,1)(5)(4,1)(3,1)(4,2,1)(5) = 1,3,9,10,2,5,14,20,14</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part2&diff=3002 2026-05-01T17:24:48Z

<p>Alice：​创建页面，内容为“本分析由 CXL 提供。左侧为 DSM，右侧为 Y。 == Y(1,3,7) ~ Y(1,3,8) == (0)(1)(2,1)(2)(3,1)(4,2,1) = 1,3,7 (0)(1)(2,1)(2)(3,1)(4,2,1)(1)(2,1) = 1,3,7,3 (0)(1)(2,1)(2)(3,1)(4,2,1)(1)(2,1)(2)(3,1)(4,2,1) = 1,3,7,3,7 (0)(1)(2,1)(2)(3,1)(4,2,1)(2) = 1,3,7,4 (0)(1)(2,1)(2)(3,1)(4,2,1)(2)(3,1) = 1,3,7,5 (0)(1)(2,1)(2)(3,1)(4,2,1)(2)(3,1)(4,2,1) = 1,3,7,5,9 (0)(1)(2,1)(2)(3,1)(4,2,1)(3) = 1,3,7,5,9,6 (0)(1)(2,1)(2)(3,1)(4,2,1)(3)(4,1) = 1,3,7,5,9,7…”</p> <hr /> <div>本分析由 CXL 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == Y(1,3,7) ~ Y(1,3,8) ==<br /> (0)(1)(2,1)(2)(3,1)(4,2,1) = 1,3,7<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(1)(2,1) = 1,3,7,3<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(1)(2,1)(2)(3,1)(4,2,1) = 1,3,7,3,7<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(2) = 1,3,7,4<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(2)(3,1) = 1,3,7,5<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(2)(3,1)(4,2,1) = 1,3,7,5,9<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(3) = 1,3,7,5,9,6<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(3)(4,1) = 1,3,7,5,9,7<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(3)(4,1)(5,2,1) = 1,3,7,5,9,7,11<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(3,1) = 1,3,7,6<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(3,1)(4,2,1) = 1,3,7,7<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4) = 1,3,7,8<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4)(5,1) = 1,3,7,9<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4)(5,1)(6,2,1) = 1,3,7,9,13<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,1) = 1,3,7,10<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,7,11<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,1)(5,2,1)(5,1)(6,2,1) = 1,3,7,11,15<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2) = 1,3,7,12<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,7,13<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(3)(4,1)(5,2,1)(5,1)(6,2,1) = 1,3,7,13,5,9,13<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(3)(4,1)(5,2,1)(5,2) = 1,3,7,13,5,9,14<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(3)(4,1)(5,2,1)(5,2)(6,3,1) = 1,3,7,13,5,9,15<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(3,1) = 1,3,7,13,6<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(3,1)(4,2,1) = 1,3,7,13,7<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,7,13,7,11<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(3,1)(4,2,1)(4,2) = 1,3,7,13,7,12<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(3,1)(4,2,1)(4,2)(5,3,1) = 1,3,7,13,7,13<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4) = 1,3,7,13,8<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4)(5,1) = 1,3,7,13,9<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4)(5,1)(6,2,1) = 1,3,7,13,9,13<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4)(5,1)(6,2,1)(6,2) = 1,3,7,13,9,13,18<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4)(5,1)(6,2,1)(6,2)(7,3,1) = 1,3,7,13,9,13,19<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4,1) = 1,3,7,13,10<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4,1)(5,2,1) = 1,3,7,13,11<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4,1)(5,2,1)(5,2) = 1,3,7,13,11,16<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4,1)(5,2,1)(5,2)(6,3,1) = 1,3,7,13,11,17<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4,2) = 1,3,7,13,12<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(4,2)(5,3,1) = 1,3,7,13,13<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5) = 1,3,7,13,14<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5)(6,1)(7,2,1) = 1,3,7,13,15,19<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5)(6,1)(7,2,1)(7,2)(8,3,1) = 1,3,7,13,15,19,25<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,1) = 1,3,7,13,16<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,1)(6,2,1) = 1,3,7,13,17<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,1)(6,2,1)(6,2) = 1,3,7,13,17,22<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,1)(6,2,1)(6,2)(7,3,1) = 1,3,7,13,17,23<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,2) = 1,3,7,13,18<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,2)(6,3,1) = 1,3,7,13,19<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,3) = 1,3,7,13,20<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,3)(6,4,1) = 1,3,7,13,21<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(5,3,1) = 1,3,7,14<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,7,15<br /> <br /> (0)(1)(2,1)(2,1) = 1,3,8<br /> <br /> == Y(1,3,8) ~ Y(1,3,9) ==<br /> (0)(1)(2,1)(2,1) = 1,3,8<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1) = 1,3,8,3<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1)(2)(3,1)(4,2,1) = 1,3,8,3,7<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1) = 1,3,8,3,8<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(3,1) = 1,3,8,6<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(3,1)(4,2,1) = 1,3,8,7<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,8,7,15<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,8,7,16<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1)(5,3,1)(6,4,2,1) = 1,3,8,7,16,15<br /> <br /> (0)(1)(2,1)(2,1)(1)(2,1)(2,1) = 1,3,8,8<br /> <br /> (0)(1)(2,1)(2,1)(2) = 1,3,8,9<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1) = 1,3,8,9,3<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1) = 1,3,8,9,3,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(3,1) = 1,3,8,9,3,8,6<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(3,1)(4,2,1) = 1,3,8,9,3,8,7<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(3,1)(4,2,1)(4,2,1) = 1,3,8,9,3,8,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4) = 1,3,8,9,3,8,9<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4)(3)(4,1)(5,2,1) = 1,3,8,9,5,9<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4)(3)(4,1)(5,2,1)(5,2,1)(5) = 1,3,8,9,5,10,11<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4)(3,1) = 1,3,8,9,6<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4)(3,1)(4,2,1)(4,2,1) = 1,3,8,9,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4)(5,1) = 1,3,8,10<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4)(5,1)(6,2,1)(6,2,1) = 1,3,8,10,15<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1) = 1,3,8,11<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1) = 1,3,8,12<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2)(6,3,1) = 1,3,8,12,18<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1) = 1,3,8,12,20<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(7,4,2,1) = 1,3,8,12,21<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(7,4,2,1)(6,3,1)(7,4,2,1)(7,4,2,1) = 1,3,8,12,21,21<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(7,4,2,1)(7,2)(8,3,1)(9,4,2) = 1,3,8,12,21,19<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(7,4,2,1)(7,2)(8,3,1)(9,4,2,1)(9,4,2,1)(7,2)(8,3,1) = 1,3,8,12,21,21,18<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(7,4,2,1)(7,3,1) = 1,3,8,12,21,28<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2)(6,3,1)(7,4,2,1)(7,4,2,1)(7,3,1)(8,4,2,1) = 1,3,8,12,21,29<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,1)(5,2,1)(5,2,1) = 1,3,8,13<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2) = 1,3,8,14<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2) = 1,3,8,14,7,16,31<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2,1) = 1,3,8,14,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2,1)(2) = 1,3,8,14,8,9<br /> <br /> (0)(1)(2,1)(2,1)(2)(1)(2,1)(2,1)(2)(1)(2,1)(2,1) = 1,3,8,14,8,14,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(2) = 1,3,8,14,10<br /> <br /> (0)(1)(2,1)(2,1)(2)(2)(1)(2,1)(2,1) = 1,3,8,14,14,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3) = 1,3,8,14,15<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(3,1)(4,2,1)(4,2,1) = 1,3,8,14,15,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(4)(5,1) = 1,3,8,14,15,10<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(4,1) = 1,3,8,14,15,11<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(4,1)(5,2,1) = 1,3,8,14,15,12<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(4,1)(5,2,1)(5,2,1) = 1,3,8,14,15,13<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(4,1)(5,2,1)(5,2,1)(5,2) = 1,3,8,14,15,13,19<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(4,1)(5,2,1)(5,2,1)(5,2)(6) = 1,3,8,14,15,13,19,20<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(4,2) = 1,3,8,14,15,14<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(4,2)(5) = 1,3,8,14,15,14,15<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(6,1) = 1,3,8,14,16<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5)(6,1)(7,2,1)(7,2,1)(7,2) = 1,3,8,14,16,21,27<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,1) = 1,3,8,14,17<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,1)(6,2,1) = 1,3,8,14,18<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,1)(6,2,1)(6,2)(7,3,1)(8,4,2,1)(8,4,2,1)(8,4,2)(9,3,1)(10,4,2,1) = 1,3,8,14,18,27,43,51<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,1)(6,2,1)(6,2,1) = 1,3,8,14,19<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,1)(6,2,1)(6,2,1)(6,2) = 1,3,8,14,19,25<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,2) = 1,3,8,14,20<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3) = 1,3,8,14,21<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1)(6,4,2)(7,5,3) = 1,3,8,14,21,7,16,31,53<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(1)(2,1)(2,1) = 1,3,8,14,21,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(4) = 1,3,8,14,21,22<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(4)(1)(2,1)(2,1) = 1,3,8,14,21,29,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(4,1) = 1,3,8,14,22<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(4,1)(5,2,1) = 1,3,8,14,23<br /> <br /> (0)(1)(2,1)(2,1)(2)(3)(4,1)(5,2,1)(5,2,1) = 1,3,8,14,23,40<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1) = 1,3,8,15<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3) = 1,3,8,15,16<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5)(3,1)(4,2,1)(4,2,1) = 1,3,8,15,16,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5)(6,1) = 1,3,8,15,17<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5,1) = 1,3,8,15,18<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5,1)(6,2,1) = 1,3,8,15,19<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5,1)(6,2,1)(6,2,1) = 1,3,8,15,20<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5,1)(6,2,1)(6,2,1)(6,2)(7,3,1) = 1,3,8,15,20,27<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5,2) = 1,3,8,15,21<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5,2)(6,3,1) = 1,3,8,15,22<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(5,3) = 1,3,8,15,23<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(1)(2,1)(2,1) = 1,3,8,15,23,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(2) = 1,3,8,15,23,9<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(2)(3,1) = 1,3,8,15,23,15<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(3) = 1,3,8,15,23,16<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(4) = 1,3,8,15,23,24<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(4)(1)(2,1)(2,1) = 1,3,8,15,23,32,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(4,1) = 1,3,8,15,24<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(4,1)(4)(5,1) = 1,3,8,15,24,35<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(4,1)(4,1) = 1,3,8,15,25<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(4,1)(5,2,1) = 1,3,8,15,26<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(4,1)(5,2,1)(5,2,1) = 1,3,8,15,27<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3)(4,1)(5,2,1)(5,2,1)(5,2) = 1,3,8,15,27,45<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1) = 1,3,8,16<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(1)(2,1)(2,1) = 1,3,8,16,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(1)(2,1)(2,1)(2)(3,1)(3,1) = 1,3,8,16,8,16<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(2) = 1,3,8,16,10<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(2)(3,1)(3,1) = 1,3,8,16,16<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(3) = 1,3,8,16,17<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(3)(1)(2,1)(2,1)(2)(3,1)(3,1) = 1,3,8,16,25,8,16<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(3)(4,1) = 1,3,8,16,26<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(3)(4,1)(4,1) = 1,3,8,16,27<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(3,1)(3,1) = 1,3,8,17<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4) = 1,3,8,17,18<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(1)(2,1)(2,1) = 1,3,8,17,27,8<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(5,1) = 1,3,8,17,28<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(5,1)(5)(6,1) = 1,3,8,17,28,41<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(5,1)(5)(6,1)(7,1) = 1,3,8,17,28,42<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(5,1)(5)(6,1)(7,2,1) = 1,3,8,17,28,43<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(5,1)(5)(6,1)(7,2,1)(7,2,1) = 1,3,8,17,28,44<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(5,1)(5)(6,1)(7,2,1)(7,2,1)(7,2)(8,3,1)(8,3,1)(8,3,1) = 1,3,8,17,28,44,69<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(5,1)(5,1) = 1,3,8,17,29<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4)(5,1)(5,1)(5,1) = 1,3,8,17,29,45<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4,1) = 1,3,8,17,30<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4,2) = 1,3,8,17,31<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4,2,1) = 1,3,8,18<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,8,18,38<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4,2,1)(4,2,1) = 1,3,8,19<br /> <br /> (0)(1)(2,1)(2,1)(2)(3,1)(4,2,1)(4,2,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2,1) = 1,3,8,19,42<br /> <br /> (0)(1)(2,1)(2,1)(2,1) = 1,3,8,20<br /> <br /> (0)(1)(2,1)(3) = 1,3,9</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part1&diff=3001 2026-05-01T17:18:14Z

<p>Alice：​</p> <hr /> <div>本分析由 CXL 提供。左侧为 DSM，右侧为 Y。<br /> <br /> == 0 ~ Y(1,3) ==<br /> (0) = 1<br /> <br /> (0)(1) = 1,2<br /> <br /> (0)(1)(2)(3,1) = 1,2,4<br /> <br /> (0)(1)(2)(3,1)(4,2)(5,3,1) = 1,2,4,8<br /> <br /> (0)(1)(2)(3,1)(4,2)(5,3,1)(6,4,2)(7,5,3,1) = 1,2,4,8,16<br /> <br /> (0)(1)(2,1) = 1,3<br /> <br /> == Y(1,3) ~ Y(1,3,7) ==<br /> (0)(1)(2,1) = 1,3<br /> <br /> (0)(1)(2,1)(1) = 1,3,2<br /> <br /> (0)(1)(2,1)(1)(2) = 1,3,2,3<br /> <br /> (0)(1)(2,1)(1)(2)(3,1) = 1,3,2,4<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2)(5,3,1) = 1,3,2,4,8<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2,1) = 1,3,2,5<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2,1)(3,1) = 1,3,2,5,4<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2,1)(3,1)(4,2)(5,3,1) = 1,3,2,5,4,8<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2,1)(3,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,2,5,4,9<br /> <br /> (0)(1)(2,1)(1)(2,1) = 1,3,3<br /> <br /> (0)(1)(2,1)(1)(2,1)(1)(2)(3,1)(4,2,1)(3,1)(4,2,1) = 1,3,3,2,5,5<br /> <br /> (0)(1)(2,1)(1)(2,1)(1)(2,1) = 1,3,3,3<br /> <br /> (0)(1)(2,1)(2) = 1,3,4<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1) = 1,3,4,2,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(2) = 1,3,4,2,5,3<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(2)(3,1)(4,2,1) = 1,3,4,2,5,3,6<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(3,1) = 1,3,4,2,5,4<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(3,1)(4,2,1) = 1,3,4,2,5,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4) = 1,3,4,2,5,6<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4)(3,1)(4,2,1) = 1,3,4,2,5,6,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1) = 1,3,4,2,5,7<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,1) = 1,3,4,2,5,7,4,9,11<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,1)(5,3,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(8,1)(7,5,3,1) = 1,3,4,2,5,7,4,9,11,8,17,19<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,1)(5,3,1)(6,4,2,1) = 1,3,4,2,5,7,4,9,11,9<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,1)(6) = 1,3,4,2,5,7,4,9,11,10<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,2) = 1,3,4,2,5,7,4,9,12<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,2)(5,3,1)(6,4,2,1) = 1,3,4,2,5,7,4,9,12,8,17,20,17<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,3) = 1,3,4,2,5,7,4,9,12,8,17,21<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,3)(5,3,1)(6,4,2,1) = 1,3,4,2,5,7,4,9,12,9<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,3,1)(5,3,1) = 1,3,4,2,5,7,4,9,13<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2,1) = 1,3,4,2,5,7,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2,1)(4,1) = 1,3,4,2,5,7,5,7<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(4) = 1,3,4,2,5,7,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(4,1) = 1,3,4,2,5,7,7<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,1) = 1,3,4,2,5,7,9<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2) = 1,3,4,2,5,7,10<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,3,1)(7,4,2) = 1,3,4,2,5,7,10,4,9,13,20<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(3,1)(4,2,1) = 1,3,4,2,5,7,10,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1) = 1,3,4,2,5,7,11<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1) = 1,3,4,2,5,7,12<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1)(7,3,1) = 1,3,4,2,5,7,12,16<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1)(7,3,1)(6,3,1)(7,4,2,1) = 1,3,4,2,5,7,12,16,12<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1)(7,3,1)(8,4,2)(9,5,3,1) = 1,3,4,2,5,7,12,16,24<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1)(7,3,1)(8,4,2)(9,5,3,1)(10,6,4,2,1) = 1,3,4,2,5,7,12,16,25<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,4,2,5,8<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,2) = 1,3,4,2,5,9<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,2)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2) = 1,3,4,2,5,9,4,9,18<br /> <br /> (0)(1)(2,1)(2)(1)(2,1) = 1,3,4,3<br /> <br /> (0)(1)(2,1)(2)(2) = 1,3,4,4<br /> <br /> (0)(1)(2,1)(2)(3)(4,1) = 1,3,4,6<br /> <br /> (0)(1)(2,1)(2)(3)(4,1)(5,2,1) = 1,3,4,7<br /> <br /> (0)(1)(2,1)(2)(3)(4,1)(5,2,1)(5,2)(6,3)(7,4,1)(8,5,2,1) = 1,3,4,7,11,18<br /> <br /> (0)(1)(2,1)(2)(3,1) = 1,3,5<br /> <br /> (0)(1)(2,1)(2)(3,1)(1)(2,1) = 1,3,5,3<br /> <br /> (0)(1)(2,1)(2)(3,1)(1)(2,1)(2)(3,1) = 1,3,5,3,5<br /> <br /> (0)(1)(2,1)(2)(3,1)(2) = 1,3,5,4<br /> <br /> (0)(1)(2,1)(2)(3,1)(2)(3,1) = 1,3,5,5<br /> <br /> (0)(1)(2,1)(2)(3,1)(3) = 1,3,5,6<br /> <br /> (0)(1)(2,1)(2)(3,1)(3)(4,1) = 1,3,5,7<br /> <br /> (0)(1)(2,1)(2)(3,1)(3,1) = 1,3,6<br /> <br /> (0)(1)(2,1)(2)(3,1)(4)(5,1) = 1,3,6,8<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,1) = 1,3,6,9<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2) = 1,3,6,10<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2)(5,3,1) = 1,3,6,11<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,6,12<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1) = 1,3,7</div>

Alice http://wiki.googology.top/index.php?title=DSM%E5%88%86%E6%9E%90Part1&diff=3000 2026-05-01T17:17:22Z

<p>Alice：​创建页面，内容为“本分析由 CXL 提供。 == 0 ~ Y(1,3) == (0) = 1 (0)(1) = 1,2 (0)(1)(2)(3,1) = 1,2,4 (0)(1)(2)(3,1)(4,2)(5,3,1) = 1,2,4,8 (0)(1)(2)(3,1)(4,2)(5,3,1)(6,4,2)(7,5,3,1) = 1,2,4,8,16 (0)(1)(2,1) = 1,3 == Y(1,3) ~ Y(1,3,7) == (0)(1)(2,1) = 1,3 (0)(1)(2,1)(1) = Y(1,3,2) (0)(1)(2,1)(1)(2) = Y(1,3,2,3) (0)(1)(2,1)(1)(2)(3,1) = Y(1,3,2,4) (0)(1)(2,1)(1)(2)(3,1)(4,2)(5,3,1) = Y(1,3,2,4,8) (0)(1)(2,1)(1)(2)(3,1)(4,2,1) = Y(1,3,2,5) (0)(1)(2,1)(1)(2)(3,1)(4,…”</p> <hr /> <div>本分析由 CXL 提供。<br /> <br /> == 0 ~ Y(1,3) ==<br /> (0) = 1<br /> <br /> (0)(1) = 1,2<br /> <br /> (0)(1)(2)(3,1) = 1,2,4<br /> <br /> (0)(1)(2)(3,1)(4,2)(5,3,1) = 1,2,4,8<br /> <br /> (0)(1)(2)(3,1)(4,2)(5,3,1)(6,4,2)(7,5,3,1) = 1,2,4,8,16<br /> <br /> (0)(1)(2,1) = 1,3<br /> <br /> == Y(1,3) ~ Y(1,3,7) ==<br /> (0)(1)(2,1) = 1,3<br /> <br /> (0)(1)(2,1)(1) = Y(1,3,2)<br /> <br /> (0)(1)(2,1)(1)(2) = Y(1,3,2,3)<br /> <br /> (0)(1)(2,1)(1)(2)(3,1) = Y(1,3,2,4)<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2)(5,3,1) = Y(1,3,2,4,8)<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2,1) = Y(1,3,2,5)<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2,1)(3,1) = Y(1,3,2,5,4)<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2,1)(3,1)(4,2)(5,3,1) = Y(1,3,2,5,4,8)<br /> <br /> (0)(1)(2,1)(1)(2)(3,1)(4,2,1)(3,1)(4,2)(5,3,1)(6,4,2,1) = Y(1,3,2,5,4,9)<br /> <br /> (0)(1)(2,1)(1)(2,1) = Y(1,3,3)<br /> <br /> (0)(1)(2,1)(1)(2,1)(1)(2)(3,1)(4,2,1)(3,1)(4,2,1) = Y(1,3,3,2,5,5)<br /> <br /> (0)(1)(2,1)(1)(2,1)(1)(2,1) = Y(1,3,3,3)<br /> <br /> (0)(1)(2,1)(2) = 1,3,4<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1) = 1,3,4,2,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(2) = 1,3,4,2,5,3<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(2)(3,1)(4,2,1) = 1,3,4,2,5,3,6<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(3,1) = 1,3,4,2,5,4<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(3,1)(4,2,1) = 1,3,4,2,5,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4) = 1,3,4,2,5,6<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4)(3,1)(4,2,1) = 1,3,4,2,5,6,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1) = 1,3,4,2,5,7<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,1) = 1,3,4,2,5,7,4,9,11<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,1)(5,3,1)(6,4,2)(7,5,3,1)(8,6,4,2,1)(8,1)(7,5,3,1) = 1,3,4,2,5,7,4,9,11,8,17,19<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,1)(5,3,1)(6,4,2,1) = 1,3,4,2,5,7,4,9,11,9<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,1)(6) = 1,3,4,2,5,7,4,9,11,10<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,2) = 1,3,4,2,5,7,4,9,12<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,2)(5,3,1)(6,4,2,1) = 1,3,4,2,5,7,4,9,12,8,17,20,17<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,3) = 1,3,4,2,5,7,4,9,12,8,17,21<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,3)(5,3,1)(6,4,2,1) = 1,3,4,2,5,7,4,9,12,9<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,3,1)(5,3,1) = 1,3,4,2,5,7,4,9,13<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2,1) = 1,3,4,2,5,7,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(3,1)(4,2,1)(4,1) = 1,3,4,2,5,7,5,7<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(4) = 1,3,4,2,5,7,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(4,1) = 1,3,4,2,5,7,7<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,1) = 1,3,4,2,5,7,9<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2) = 1,3,4,2,5,7,10<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,3,1)(7,4,2) = 1,3,4,2,5,7,10,4,9,13,20<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(3,1)(4,2,1) = 1,3,4,2,5,7,10,5<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1) = 1,3,4,2,5,7,11<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1) = 1,3,4,2,5,7,12<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1)(7,3,1) = 1,3,4,2,5,7,12,16<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1)(7,3,1)(6,3,1)(7,4,2,1) = 1,3,4,2,5,7,12,16,12<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1)(7,3,1)(8,4,2)(9,5,3,1) = 1,3,4,2,5,7,12,16,24<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2)(6,3,1)(7,4,2,1)(7,3,1)(8,4,2)(9,5,3,1)(10,6,4,2,1) = 1,3,4,2,5,7,12,16,25<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,1)(5,2,1) = 1,3,4,2,5,8<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,2) = 1,3,4,2,5,9<br /> <br /> (0)(1)(2,1)(2)(1)(2)(3,1)(4,2,1)(4,2)(3,1)(4,2)(5,3,1)(6,4,2,1)(6,4,2) = 1,3,4,2,5,9,4,9,18<br /> <br /> (0)(1)(2,1)(2)(1)(2,1) = 1,3,4,3<br /> <br /> (0)(1)(2,1)(2)(2) = 1,3,4,4<br /> <br /> (0)(1)(2,1)(2)(3)(4,1) = 1,3,4,6<br /> <br /> (0)(1)(2,1)(2)(3)(4,1)(5,2,1) = 1,3,4,7<br /> <br /> (0)(1)(2,1)(2)(3)(4,1)(5,2,1)(5,2)(6,3)(7,4,1)(8,5,2,1) = 1,3,4,7,11,18<br /> <br /> (0)(1)(2,1)(2)(3,1) = 1,3,5<br /> <br /> (0)(1)(2,1)(2)(3,1)(1)(2,1) = 1,3,5,3<br /> <br /> (0)(1)(2,1)(2)(3,1)(1)(2,1)(2)(3,1) = 1,3,5,3,5<br /> <br /> (0)(1)(2,1)(2)(3,1)(2) = 1,3,5,4<br /> <br /> (0)(1)(2,1)(2)(3,1)(2)(3,1) = 1,3,5,5<br /> <br /> (0)(1)(2,1)(2)(3,1)(3) = 1,3,5,6<br /> <br /> (0)(1)(2,1)(2)(3,1)(3)(4,1) = 1,3,5,7<br /> <br /> (0)(1)(2,1)(2)(3,1)(3,1) = 1,3,6<br /> <br /> (0)(1)(2,1)(2)(3,1)(4)(5,1) = 1,3,6,8<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,1) = 1,3,6,9<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2) = 1,3,6,10<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2)(5,3,1) = 1,3,6,11<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2)(5,3,1)(6,4,2,1) = 1,3,6,12<br /> <br /> (0)(1)(2,1)(2)(3,1)(4,2,1) = 1,3,7</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=2999 2026-05-01T14:48:25Z

<p>Alice：​</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''试展开'''：指展开 1 次。<br /> <br /> '''最终展开'''：指展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> 试坏项与试坏项同行右侧的所有候选项都是上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> 试坏项同行右侧的所有候选项都是填充项。（注意：试坏项本身不是填充项）<br /> <br /> 若某一项的父项是坏项或填充项，则本项是填充项。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为后继矩阵，删除最右列并不进行展开，得到的矩阵为其前驱。否则为极限矩阵，取其父项矩阵。<br /> <br /> 从右到左找到每一个候选项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3) = 1-Y (1,3,9)。分析文档待创建。{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=2998 2026-05-01T14:47:49Z

<p>Alice：​</p> <hr /> <div>DSM，全称 Diagonal Sudden Matrix，是 Alice 于 2026 年 4 月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''试展开'''：指展开 1 次。<br /> <br /> '''最终展开'''：指展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> 试坏项与试坏项同行右侧的所有候选项都是上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> 试坏项同行右侧的所有候选项都是填充项。（注意：试坏项本身不是填充项）<br /> <br /> 若某一项的父项是坏项或填充项，则本项是填充项。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为后继矩阵，删除最右列并不进行展开，得到的矩阵为其前驱。否则为极限矩阵，取其父项矩阵。<br /> <br /> 从右到左找到每一个候选项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3) = 1-Y (1,3,9) 。分析文档待创建。{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=2997 2026-05-01T14:41:23Z

<p>Alice：​</p> <hr /> <div>DSM，全称Diagonal Sudden Matrix，是Alice于2026年4月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且下方 1 项属于本项下方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''试展开'''：指展开 1 次。<br /> <br /> '''最终展开'''：指展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> 试坏项与试坏项同行右侧的所有候选项都是上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> 试坏项同行右侧的所有候选项都是填充项。（注意：试坏项本身不是填充项）<br /> <br /> 若某一项的父项是坏项或填充项，则本项是填充项。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为后继矩阵，删除最右列并不进行展开，得到的矩阵为其前驱。否则为极限矩阵，取其父项矩阵。<br /> <br /> 从右到左找到每一个候选项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3) = 1-Y (1,3,9) 。分析文档待创建。{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=2995 2026-05-01T14:40:02Z

<p>Alice：​</p> <hr /> <div>DSM，全称Diagonal Sudden Matrix，是Alice于2026年4月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分被视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> '''方向'''：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且上方 1 项属于本项上方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''试展开'''：指展开 1 次。<br /> <br /> '''最终展开'''：指展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> 试坏项与试坏项同行右侧的所有候选项都是上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> 试坏项同行右侧的所有候选项都是填充项。（注意：试坏项本身不是填充项）<br /> <br /> 若某一项的父项是坏项或填充项，则本项是填充项。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为后继矩阵，删除最右列并不进行展开，得到的矩阵为其前驱。否则为极限矩阵，取其父项矩阵。<br /> <br /> 从右到左找到每一个候选项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3) = 1-Y (1,3,9) 。分析文档待创建。{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=2992 2026-05-01T14:37:07Z

<p>Alice：​</p> <hr /> <div>DSM，全称Diagonal Sudden Matrix，是Alice于2026年4月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分被视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> 方向：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> '''项'''：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> '''父项'''：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且上方 1 项属于本项上方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> '''祖先链'''：某一项不断取父项得到的链。<br /> <br /> '''父项矩阵'''：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> '''左下项'''：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> '''复制'''：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> '''还原矩阵'''：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> # 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> # 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> # 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> '''LNZ'''：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> '''检测项'''：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> '''待定坏项'''：每一行最右侧的一个检测项为待定坏项。<br /> <br /> '''试展开'''：指展开 1 次。<br /> <br /> '''最终展开'''：指展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> '''比较矩阵'''：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> '''标准矩阵'''：LNZ 的父项的比较矩阵。<br /> <br /> ==== 矩阵比较 ====<br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 事实上，小展开与 BMS、0-Y 的展开规则是一致的。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行'''平行复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到'''上升项'''与'''填充项'''：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> 试坏项与试坏项同行右侧的所有候选项都是上升项。<br /> <br /> # 若某一项的父项为上升项，则本项为上升项。<br /> # 若某一项的左下项为上升项，则本项为上升项。<br /> # 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> 试坏项同行右侧的所有候选项都是填充项。（注意：试坏项本身不是填充项）<br /> <br /> 若某一项的父项是坏项或填充项，则本项是填充项。<br /> <br /> 接下来进行'''上升复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行'''填充复制'''：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为后继矩阵，删除最右列并不进行展开，得到的矩阵为其前驱。否则为极限矩阵，取其父项矩阵。<br /> <br /> 从右到左找到每一个候选项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3) = 1-Y (1,3,9) 。分析文档待创建。{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=2990 2026-05-01T14:33:09Z

<p>Alice：​</p> <hr /> <div>DSM，全称Diagonal Sudden Matrix，是Alice于2026年4月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分被视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> 方向：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> 项：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> 父项：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且上方 1 项属于本项上方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> 祖先链：某一项不断取父项得到的链。<br /> <br /> 父项矩阵：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> 左下项：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> 复制：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> 还原矩阵：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> 1. 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> <br /> 2. 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> <br /> 3. 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> LNZ：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> 检测项：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> 待定坏项：每一行最右侧的一个检测项为待定坏项。<br /> <br /> 试展开：指展开 1 次。<br /> <br /> 最终展开：指展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> 比较矩阵：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> 标准矩阵：LNZ 的父项的比较矩阵。<br /> <br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行平行复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到上升项与填充项：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> 试坏项与试坏项同行右侧的所有候选项都是上升项。<br /> <br /> 若某一项的父项为上升项，则本项为上升项。<br /> <br /> 若某一项的左下项为上升项，则本项为上升项。<br /> <br /> 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> 试坏项同行右侧的所有候选项都是填充项。（注意：试坏项本身不是填充项）<br /> <br /> 若某一项的父项是坏项或填充项，则本项是填充项。<br /> <br /> 接下来进行上升复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行填充复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为后继矩阵，删除最右列并不进行展开，得到的矩阵为其前驱。否则为极限矩阵，取其父项矩阵。<br /> <br /> 从右到左找到每一个候选项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> == 分析 ==<br /> 目前已分析至 DSM (0)(1)(2,1)(3) = 1-Y (1,3,9) 。分析文档待创建。{{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=2989 2026-05-01T14:30:42Z

<p>Alice：​</p> <hr /> <div>DSM，全称Diagonal Sudden Matrix，是Alice于2026年4月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分被视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> 方向：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> 项：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> 父项：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且上方 1 项属于本项上方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> 祖先链：某一项不断取父项得到的链。<br /> <br /> 父项矩阵：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> 左下项：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> 复制：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> 还原矩阵：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> 1. 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> <br /> 2. 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> <br /> 3. 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> LNZ：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> 检测项：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> 待定坏项：每一行最右侧的一个检测项为待定坏项。<br /> <br /> 试展开：指展开 1 次。<br /> <br /> 最终展开：指展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> 比较矩阵：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> 标准矩阵：LNZ 的父项的比较矩阵。<br /> <br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> ==== 小展开 ====<br /> 若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> ==== 完全展开 ====<br /> 复制以 yS 列为参考列。<br /> <br /> 首先进行平行复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到上升项与填充项：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> 试坏项与试坏项同行右侧的所有候选项都是上升项。<br /> <br /> 若某一项的父项为上升项，则本项为上升项。<br /> <br /> 若某一项的左下项为上升项，则本项为上升项。<br /> <br /> 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> 试坏项同行右侧的所有候选项都是填充项。（注意：试坏项本身不是填充项）<br /> <br /> 若某一项的父项是坏项或填充项，则本项是填充项。<br /> <br /> 接下来进行上升复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行填充复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为后继矩阵，删除最右列并不进行展开，得到的矩阵为其前驱。否则为极限矩阵，取其父项矩阵。<br /> <br /> 从右到左找到每一个候选项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> {{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=2988 2026-05-01T14:30:03Z

<p>Alice：​</p> <hr /> <div>DSM，全称Diagonal Sudden Matrix，是Alice于2026年4月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分被视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> 方向：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> <br /> ==== 基础名词 ====<br /> 项：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> 父项：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且上方 1 项属于本项上方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> 祖先链：某一项不断取父项得到的链。<br /> <br /> 父项矩阵：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> ==== 父项矩阵上的定义 ====<br /> 左下项：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> 复制：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> 还原矩阵：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> ==== 前置项 ====<br /> 有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> 1. 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> <br /> 2. 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> <br /> 3. 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> ==== 寻找坏项相关的定义 ====<br /> LNZ：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> 检测项：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> 待定坏项：每一行最右侧的一个检测项为待定坏项。<br /> <br /> 试展开：指展开 1 次。<br /> <br /> 最终展开：指展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> 比较矩阵：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> 标准矩阵：LNZ 的父项的比较矩阵。<br /> <br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> 小展开：若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 完全展开：复制以 yS 列为参考列。<br /> <br /> 首先进行平行复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到上升项与填充项：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> 试坏项与试坏项同行右侧的所有候选项都是上升项。<br /> <br /> 若某一项的父项为上升项，则本项为上升项。<br /> <br /> 若某一项的左下项为上升项，则本项为上升项。<br /> <br /> 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> 试坏项同行右侧的所有候选项都是填充项。（注意：试坏项本身不是填充项）<br /> <br /> 若某一项的父项是坏项或填充项，则本项是填充项。<br /> <br /> 接下来进行上升复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行填充复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为后继矩阵，删除最右列并不进行展开，得到的矩阵为其前驱。否则为极限矩阵，取其父项矩阵。<br /> <br /> 从右到左找到每一个候选项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> {{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=2987 2026-05-01T14:26:20Z

<p>Alice：​</p> <hr /> <div>DSM，全称Diagonal Sudden Matrix，是Alice于2026年4月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分被视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> 方向：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> 数值矩阵上的定义：<br /> <br /> 项：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> 父项：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且上方 1 项属于本项上方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> 祖先链：某一项不断取父项得到的链。<br /> <br /> 父项矩阵：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> 父项矩阵上的定义：<br /> <br /> 左下项：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> 复制：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> 还原矩阵：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> 前置项：有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> 1. 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> <br /> 2. 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> <br /> 3. 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> LNZ：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> 检测项：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> 待定坏项：每一行最右侧的一个检测项为待定坏项。<br /> <br /> 试展开：指展开 1 次。<br /> <br /> 最终展开：指展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> 比较矩阵：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> 标准矩阵：LNZ 的父项的比较矩阵。<br /> <br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> 小展开：若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 完全展开：复制以 yS 列为参考列。<br /> <br /> 首先进行平行复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到上升项与填充项：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> 试坏项与试坏项同行右侧的所有候选项都是上升项。<br /> <br /> 若某一项的父项为上升项，则本项为上升项。<br /> <br /> 若某一项的左下项为上升项，则本项为上升项。<br /> <br /> 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> 试坏项同行右侧的所有候选项都是填充项。（注意：试坏项本身不是填充项）<br /> <br /> 若某一项的父项是坏项或填充项，则本项是填充项。<br /> <br /> 接下来进行上升复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行填充复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> <br /> === 最终展开 ===<br /> 若最初矩阵的最右列所有项均为 0，则其为后继矩阵，删除最右列并不进行展开，得到的矩阵为其前驱。否则为极限矩阵，取其父项矩阵。<br /> <br /> 从右到左找到每一个候选项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> {{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=2986 2026-05-01T14:25:47Z

<p>Alice：​</p> <hr /> <div>DSM，全称Diagonal Sudden Matrix，是Alice于2026年4月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分被视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> 方向：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> === 名词定义 ===<br /> 数值矩阵上的定义：<br /> <br /> 项：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> 父项：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且上方 1 项属于本项上方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> 祖先链：某一项不断取父项得到的链。<br /> <br /> 父项矩阵：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> 父项矩阵上的定义：<br /> <br /> 左下项：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> 复制：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> 还原矩阵：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> 前置项：有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> 1. 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> <br /> 2. 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> <br /> 3. 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> LNZ：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> 检测项：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> 待定坏项：每一行最右侧的一个检测项为待定坏项。<br /> <br /> 试展开：指展开 1 次。<br /> <br /> 最终展开：指展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> 比较矩阵：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> 标准矩阵：LNZ 的父项的比较矩阵。<br /> <br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> === 展开 ===<br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> 小展开：若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 完全展开：复制以 yS 列为参考列。<br /> <br /> 首先进行平行复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到上升项与填充项：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> 试坏项与试坏项同行右侧的所有候选项都是上升项。<br /> <br /> 若某一项的父项为上升项，则本项为上升项。<br /> <br /> 若某一项的左下项为上升项，则本项为上升项。<br /> <br /> 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> 试坏项同行右侧的所有候选项都是填充项。（注意：试坏项本身不是填充项）<br /> <br /> 若某一项的父项是坏项或填充项，则本项是填充项。<br /> <br /> 接下来进行上升复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行填充复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有填充项（位于第 j 列）分别复制到第 j + dY * k 列的第 xS 行到第 xS + dX * k - 1 行。<br /> <br /> 若最初矩阵的最右列所有项均为 0，则其为后继矩阵，删除最右列并不进行展开，得到的矩阵为其前驱。否则为极限矩阵，取其父项矩阵。<br /> <br /> 从右到左找到每一个候选项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> {{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=2985 2026-05-01T14:23:58Z

<p>Alice：​</p> <hr /> <div>DSM，全称Diagonal Sudden Matrix，是Alice于2026年4月末创作的一个记号。<br /> <br /> == 定义 ==<br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分被视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> 方向：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> 数值矩阵上的定义：<br /> <br /> 项：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> 父项：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且上方 1 项属于本项上方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> 祖先链：某一项不断取父项得到的链。<br /> <br /> 父项矩阵：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> 父项矩阵上的定义：<br /> <br /> 左下项：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> 复制：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> 还原矩阵：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> 前置项：有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> 1. 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> <br /> 2. 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> <br /> 3. 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> LNZ：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> 检测项：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> 待定坏项：每一行最右侧的一个检测项为待定坏项。<br /> <br /> 试展开：指展开 1 次。<br /> <br /> 最终展开：指展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> 比较矩阵：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> 标准矩阵：LNZ 的父项的比较矩阵。<br /> <br /> 展开：<br /> <br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> 小展开：若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 完全展开：复制以 yS 列为参考列。<br /> <br /> 首先进行平行复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到上升项与填充项：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> 试坏项与试坏项同行右侧的所有候选项都是上升项。<br /> <br /> 若某一项的父项为上升项，则本项为上升项。<br /> <br /> 若某一项的左下项为上升项，则本项为上升项。<br /> <br /> 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> 试坏项同行右侧的所有候选项都是填充项。（注意：试坏项本身不是填充项）<br /> <br /> 若某一项的父项是坏项或填充项，则本项是填充项。<br /> <br /> 接下来进行上升复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行填充复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有填充项（位于第 j 列）分别复制到第 j + dY * k列的第 xS 行到第 xS + dX * k - 1 行。<br /> <br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> 若最初矩阵的最右列所有项均为 0，则其为后继矩阵，删除最右列并不进行展开，得到的矩阵为其前驱。否则为极限矩阵，取其父项矩阵。<br /> <br /> 从右到左找到每一个候选项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> <br /> {{默认排序:个人记号}}<br /> [[分类:记号]]</div>

Alice http://wiki.googology.top/index.php?title=DSM&diff=2984 2026-05-01T14:22:48Z

<p>Alice：​创建页面，内容为“DSM，全称Diagonal Sudden Matrix，是Alice于2026年4月末创作的一个记号。 基础定义： DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分被视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。 方向：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为…”</p> <hr /> <div>DSM，全称Diagonal Sudden Matrix，是Alice于2026年4月末创作的一个记号。<br /> <br /> 基础定义：<br /> <br /> DSM的表达式为一个若干行若干列的数值矩阵，极限表达式为 (0)(1)(2,1)(3,2,1)(4,3,2,1)…… 其中无数值的部分被视为 0。能从极限表达式通过若干次展开或取前驱得到的表达式为标准表达式。<br /> <br /> 方向：以下所说“下”为行数减小、“上”为行数增大、“左”为列数减小、“右”为列数增大。<br /> <br /> 数值矩阵上的定义：<br /> <br /> 项：每一行每一列为一项。无数值的位置也被视为一项，其数值为 0。<br /> <br /> 父项：数值为 0 的项没有父项。数值大于0的项的父项为其同行左侧最右侧的小于本项数值，且上方 1 项属于本项上方 1 项的项的祖先链的项。父项一定位于本行。<br /> <br /> 祖先链：某一项不断取父项得到的链。<br /> <br /> 父项矩阵：指记录数值矩阵每一项的父项所在列生成的矩阵。没有父项的位置置空。（注意：置空与 0 不同， 0 代表父项在第 0 列）<br /> <br /> 父项矩阵上的定义：<br /> <br /> 左下项：位于第 0 行的项没有左下项。下方 1 行的项没有父项的项没有左下项。其他项的左下项为下方 1 行的项的父项。<br /> <br /> 复制：将位置在 x1 行 y1 列的项、父项为 p1 列的项复制到第 x2 行 y2 列，参考列为 a 列，指在目标矩阵的 x2 行 y2 列生成一项，其父项 p2 列。若 p1 为空（无父项），则 p2 为空。否则若 p1 &lt; a，则 p2 = p1，否则 p2 = p1 + y2 - y1。若待复制位置已经有项，新生成的项会替换掉原始的项。（注意：复制为从原始矩阵复制一项到目标矩阵，不会改变原始矩阵）<br /> <br /> 还原矩阵：由父项矩阵生成一个数值矩阵，其中父项矩阵为空的项值为 0，否则为其父项对应在还原矩阵中的数值 + 1。（注意：每一行的父项关系构成若干棵树，因此可以按深度生成每一项）<br /> <br /> 前置项：有父项的项没有前置项。没有左下项的项没有前置项。否则进入以下流程，最初的当前项为本项：<br /> <br /> 1. 找到当前项的左下项，若其无父项，则其为前置项并结束。<br /> <br /> 2. 找到当前项左下项的上方 1 行的项，若其无父项，则其为前置项并结束。<br /> <br /> 3. 令当前项为其左下项的上方 1 行的项，回到第 1 步。<br /> <br /> 如果某一步失败了（找不到所要找的项），则视为无前置项。<br /> <br /> LNZ：父项矩阵最右侧的一列中最上方一个有父项的项。<br /> <br /> 检测项：从 LNZ 的父项开始，依次提取其前置项，得到一个链。（包含 LNZ 的父项本身）<br /> <br /> 待定坏项：每一行最右侧的一个检测项为待定坏项。<br /> <br /> 试展开：指展开 1 次。<br /> <br /> 最终展开：指展开后删除最右列，得到的矩阵的还原矩阵。<br /> <br /> 比较矩阵：以某一项作为试坏项进行试展开，得到的矩阵的还原矩阵。<br /> <br /> 标准矩阵：LNZ 的父项的比较矩阵。<br /> <br /> 展开：<br /> <br /> 展开接受一个父项矩阵、一个试坏项和一个展开次数，并返回一个父项矩阵。<br /> <br /> 试坏项位于 xS 行 yS 列。接受的父项矩阵的 LNZ 位于 xE 行 yE 列。令 dX = xE - xS, dY = yE - yS。<br /> <br /> 首先，找到父项矩阵的 LNZ。若 LNZ 与试坏项位于同一行，则进行小展开，否则进行完全展开。首先将原始矩阵复制一份，作为目标矩阵。<br /> <br /> 小展开：若展开次数为 n，以下步骤重复 k 从 1 到 n。复制以 yS 列为参考列。<br /> <br /> 首先，将第 yE 列的 0 到 xE - 1 行的项复制到同行第 yS + dY * k 列，将第 yS 列的 xE 及以上行的项复制到同行第 yS + dY * k 列。<br /> <br /> 接下来，将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列）复制到同行第 j + dY * k 列。<br /> <br /> 完全展开：复制以 yS 列为参考列。<br /> <br /> 首先进行平行复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将第 yS + 1 到第 yE 列的每一列的每一项（位于第 j 列），除 LNZ 以外，复制到同行第 j + dY * k 列。<br /> <br /> 接下来找到上升项与填充项：<br /> <br /> 所有上升项必须位于 xS 行及其上方。其下方的项即使满足要求也不能成为上升项。<br /> <br /> 试坏项与试坏项同行右侧的所有候选项都是上升项。<br /> <br /> 若某一项的父项为上升项，则本项为上升项。<br /> <br /> 若某一项的左下项为上升项，则本项为上升项。<br /> <br /> 若某一项上方 1 行的项为上升项，则本项为上升项。<br /> <br /> 所有填充项必须位于 xS 行。<br /> <br /> 试坏项同行右侧的所有候选项都是填充项。（注意：试坏项本身不是填充项）<br /> <br /> 若某一项的父项是坏项或填充项，则本项是填充项。<br /> <br /> 接下来进行上升复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有上升项（位于第 i 行第 j 列）复制到 i + dX * k 行 j + dY * k 列。<br /> <br /> 接下来进行填充复制：以下步骤重复 k 从 1 到 n。<br /> <br /> 将所有填充项（位于第 j 列）分别复制到第 j + dY * k列的第 xS 行到第 xS + dX * k - 1 行。<br /> <br /> 数值矩阵列字典序比较：从下到上比较每一项，其中最上方的 0 不参与比较。若比较完所有项仍未分出大小，则仍有未比较项的列更大。<br /> <br /> 数值矩阵字典序比较：从左到右比较每一列。若比较完所有列仍未分出大小，则仍有未比较列的矩阵更大。<br /> <br /> 若最初矩阵的最右列所有项均为 0，则其为后继矩阵，删除最右列并不进行展开，得到的矩阵为其前驱。否则为极限矩阵，取其父项矩阵。<br /> <br /> 从右到左找到每一个候选项，并生成其比较矩阵。若当前候选项的比较矩阵字典序小于标准矩阵，则其右侧最左的待定坏项为坏项，并结束比较。若比较完所有候选项仍未找到坏项，则最左的待定坏项为坏项。<br /> <br /> 以坏项进行最终展开 n 次，得到的矩阵即为最初矩阵的基本列第 n 项。<br /> [[分类:记号]]</div>

Alice