LPrSSψ分析:修订间差异
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|(0)(1,1,1)(2)(1,1,1) | |(0)(1,1,1)(2)(1,1,1) | ||
|- | |- | ||
|<math>\psi(\Omega_2\times\ | |<math>\psi(\Omega_2\times\varepsilon_0)</math> | ||
|<math>\psi(\Omega_\omega\times\ | |<math>\psi(\Omega_\omega\times\varepsilon_0)</math> | ||
|(0)(1,1,1)(2)(3,1) | |(0)(1,1,1)(2)(3,1) | ||
|- | |- | ||
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== 分析3:(0)(1,1,1)(2,1)~(0)(1,1,1)(2,1)(1,1,1) == | == 分析3:(0)(1,1,1)(2,1)~(0)(1,1,1)(2,1)(1,1,1) == | ||
分析进入提升阶段。可见LPrSSψ中,ψ中的一个Ω_2对应的不是BOCF中的一个Ω_ω,而是BMS中的一个(1,1,1)。类似的,BGO前许多阶差2的表达式对应BMS第三行的1。这里注意LPrSSψ一般不单独定义Ω_0,展开方式,Ω_2展开出ψ_1时,把外面的Ω变成了里面的Ω_2,以此类推,但ω不提升。因为阶差为d时,Ω_(n+1)变出的ψ_n只把外面的x>=n的Ω_x提升为Ω_(x+d)。不然,若定义Ω_0=ω,并在这种位置将其提升为Ω,会与没有【特别地,如果坏根中元素不是坏部中某项的祖先项,则该项在复制过程中将保持不变。】规则的BMS一样,发生无穷降链。此外,若无此种提升,可能可以得到类似IBMS的ILPrSSψ。 | |||
{| class="wikitable" | {| class="wikitable" | ||
|+分析3:(0)(1,1,1)(2,1)~(0)(1,1,1)(2,1)(1,1,1) | |+分析3:(0)(1,1,1)(2,1)~(0)(1,1,1)(2,1)(1,1,1) | ||
| 第443行: | 第443行: | ||
|(0)(1,1,1)(2,1)(1,1,1) | |(0)(1,1,1)(2,1)(1,1,1) | ||
|} | |} | ||
== 分析4:(0)(1,1,1)(2,1)(1,1,1)~TFBO == | |||
此阶段难度相对较低,LPrSSψ与BMS对应较为简单,BOCF有随时出现的Ω变Ω_ω提升。 | |||
{| class="wikitable" | |||
|+分析4:(0)(1,1,1)(2,1)(1,1,1)~TFBO | |||
!LPrSSψ | |||
!BOCF | |||
!BMS | |||
|- | |||
|<math>\psi(\Omega_2\times(\Omega+1))</math> | |||
|<math>\psi(\Omega_\omega^2)</math> | |||
|(0)(1,1,1)(2,1)(1,1,1) | |||
|- | |||
|<math>\psi(\Omega_2\times(\Omega+1)+\psi_1(\Omega_3))</math> | |||
|<math>\psi(\Omega_\omega^2+\psi_1(\Omega_\omega))</math> | |||
|(0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1) | |||
|- | |||
|<math>\psi(\Omega_2\times(\Omega+1)+\psi_1(\Omega_3\Omega))</math> | |||
|<math>\psi(\Omega_\omega^2+\psi_1(\Omega_\omega\Omega))</math> | |||
|(0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1)(3,1) | |||
|- | |||
|<math>\psi(\Omega_2\times(\Omega+1)+\psi_1(\Omega_3\Omega_2))</math> | |||
|<math>\psi(\Omega_\omega^2+\psi_1(\Omega_\omega\Omega_2))</math> | |||
|(0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1)(3,2) | |||
|- | |||
|<math>\psi(\Omega_2\times(\Omega+1)+\psi_1(\Omega_3\times(\Omega_2+1)))</math> | |||
|<math>\psi(\Omega_\omega^2+\psi_1(\Omega_\omega^2))</math> | |||
|(0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1)(3,2)(2,2,1) | |||
|- | |||
|<math>\psi(\Omega_2\times(\Omega+1)+\psi_1(\Omega_3\times(\Omega_2+1)+\Omega_2))</math> | |||
|<math>\psi(\Omega_\omega^2+\Omega_2)</math> | |||
|(0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1)(3,2)(2,2,1)(2,2) | |||
|- | |||
|<math>\psi(\Omega_2\times(\Omega+2))</math> | |||
|<math>\psi(\Omega_\omega^2+\Omega_\omega)</math> | |||
|(0)(1,1,1)(2,1)(1,1,1)(1,1,1) | |||
|- | |||
|<math>\psi(\Omega_2\times(\Omega+\omega))</math> | |||
|<math>\psi(\Omega_\omega^2+\Omega_\omega\omega)</math> | |||
|(0)(1,1,1)(2,1)(1,1,1)(2) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega2)</math> | |||
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega)</math> | |||
|(0)(1,1,1)(2,1)(1,1,1)(2,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega2+\psi_1(\Omega_3\times(\Omega_2+\Omega)))</math> | |||
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega+\psi_1(\Omega_\omega^2+\Omega_\omega\Omega))</math> | |||
|(0)(1,1,1)(2,1)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2,1)(3,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega2+\psi_1(\Omega_3\times(\Omega_2+\Omega)+\Omega_2))</math> | |||
|<math>\psi(\Omega_\omega^2+\Omega_\omega\times(\Omega+1))</math> | |||
|(0)(1,1,1)(2,1)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2,1)(3,1)(2,2,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega2+\psi_1(\Omega_3\times\Omega_22))</math> | |||
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega_2)</math> | |||
|(0)(1,1,1)(2,1)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2,1)(3,2) | |||
|- | |||
|<math>\psi(\Omega_2\times(\Omega2+1))</math> | |||
|<math>\psi(\Omega_\omega^22)</math> | |||
|(0)(1,1,1)(2,1)(1,1,1)(2,1)(1,1,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega\omega)</math> | |||
|<math>\psi(\Omega_\omega^2\omega)</math> | |||
|(0)(1,1,1)(2,1)(2) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega^2)</math> | |||
|<math>\psi(\Omega_\omega^2\Omega)</math> | |||
|(0)(1,1,1)(2,1)(2,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega^2+\psi_1(\Omega_3\Omega_2\Omega))</math> | |||
|<math>\psi(\Omega_\omega^2\Omega+\psi_1(\Omega_\omega^2\Omega))</math> | |||
|(0)(1,1,1)(2,1)(2,1)(1,1)(2,2,1)(3,2)(3,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega^2+\psi_1(\Omega_3\Omega_2\Omega+\Omega_2))</math> | |||
|<math>\psi(\Omega_\omega^2\Omega+\Omega_\omega)</math> | |||
|(0)(1,1,1)(2,1)(2,1)(1,1)(2,2,1)(3,2)(3,1)(2,2,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega^2+\psi_1(\Omega_3\times\Omega_2^2))</math> | |||
|<math>\psi(\Omega_\omega^2\Omega_2)</math> | |||
|(0)(1,1,1)(2,1)(2,1)(1,1)(2,2,1)(3,2)(3,2) | |||
|- | |||
|<math>\psi(\Omega_2\times(\Omega^2+1))</math> | |||
|<math>\psi(\Omega_\omega^3)</math> | |||
|(0)(1,1,1)(2,1)(2,1)(1,1,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega^\omega)</math> | |||
|<math>\psi(\Omega_\omega^\omega)</math> | |||
|(0)(1,1,1)(2,1)(3) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega^\Omega)</math> | |||
|<math>\psi(\Omega_\omega^\Omega)</math> | |||
|(0)(1,1,1)(2,1)(3,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega^\Omega+\psi_1(\Omega_3\times\Omega_2^\Omega))</math> | |||
|<math>\psi(\Omega_\omega^\Omega+\psi_1(\Omega_\omega^\Omega))</math> | |||
|(0)(1,1,1)(2,1)(3,1)(1,1)(2,2,1)(3,2)(4,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega^\Omega+\psi_1(\Omega_3\times\Omega_2^\Omega+\Omega_2))</math> | |||
|<math>\psi(\Omega_\omega^\Omega+\Omega_\omega)</math> | |||
|(0)(1,1,1)(2,1)(3,1)(1,1)(2,2,1)(3,2)(4,1)(2,2,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega^\Omega+\psi_1(\Omega_3\times\Omega_2^{\Omega_2}))</math> | |||
|<math>\psi(\Omega_\omega^{\Omega_2})</math> | |||
|(0)(1,1,1)(2,1)(3,1)(1,1)(2,2,1)(3,2)(4,2) | |||
|- | |||
|<math>\psi(\Omega_2\times(\Omega^\Omega+1))</math> | |||
|<math>\psi(\Omega_\omega^{\Omega_\omega})</math> | |||
|(0)(1,1,1)(2,1)(3,1)(1,1,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega^\Omega2)</math> | |||
|<math>\psi(\Omega_\omega^{\Omega_\omega}+\Omega_\omega^\Omega)</math> | |||
|(0)(1,1,1)(2,1)(3,1)(1,1,1)(2,1)(3,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega^{\Omega+1})</math> | |||
|<math>\psi(\Omega_\omega^{\Omega_\omega}\Omega)</math> | |||
|(0)(1,1,1)(2,1)(3,1)(2,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega^{\Omega2})</math> | |||
|<math>\psi(\Omega_\omega^{\Omega_\omega+\Omega})</math> | |||
|(0)(1,1,1)(2,1)(3,1)(2,1)(3,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega^{\Omega^2})</math> | |||
|<math>\psi(\Omega_\omega^{\Omega_\omega\Omega})</math> | |||
|(0)(1,1,1)(2,1)(3,1)(3,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\Omega^{\Omega^\Omega})</math> | |||
|<math>\psi(\Omega_\omega^{\Omega_\omega^\Omega})</math> | |||
|(0)(1,1,1)(2,1)(3,1)(4,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2))=\psi(\Omega_2\times\varepsilon_{\Omega+1})</math> | |||
|<math>\psi(\Omega_{\omega+1})</math> | |||
|(0)(1,1,1)(2,1)(3,2) | |||
|} | |||
== 分析5:TFBO~BiO == | |||
此阶段若对照BMS分析,难度相对较低,而BOCF有随时出现的各级提升。 | |||
{| class="wikitable" | |||
|+分析5:TFBO~BiO | |||
!LPrSSψ | |||
!BOCF | |||
!BMS | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2))</math> | |||
|<math>\psi(\Omega_{\omega+1})</math> | |||
|(0)(1,1,1)(2,1)(3,2) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2)+\psi_1(\Omega_3\times\psi_2(\Omega_3)))</math> | |||
|<math>\psi(\Omega_{\omega+1}+\psi_1(\Omega_{\omega+1}))</math> | |||
|(0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)(3,2)(4,3) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2)+\psi_1(\Omega_3\times\psi_2(\Omega_3)+\Omega_2))</math> | |||
|<math>\psi(\Omega_{\omega+1}+\Omega_2)</math> | |||
|(0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)(3,2)(4,3)(2,2) | |||
|- | |||
|<math>\psi(\Omega_2\times(\psi_1(\Omega_2)+1))</math> | |||
|<math>\psi(\Omega_{\omega+1}+\Omega_\omega)</math> | |||
|(0)(1,1,1)(2,1)(3,2)(1,1,1) | |||
|- | |||
|<math>\psi(\Omega_2\times(\psi_1(\Omega_2)+\Omega))</math> | |||
|<math>\psi(\Omega_{\omega+1}+\Omega_\omega\Omega)</math> | |||
|(0)(1,1,1)(2,1)(3,2)(1,1,1)(2,1) | |||
|- | |||
|<math>\psi(\Omega_2\times(\psi_1(\Omega_2)+\Omega+1))</math> | |||
|<math>\psi(\Omega_{\omega+1}+\Omega_\omega^2)</math> | |||
|(0)(1,1,1)(2,1)(3,2)(1,1,1)(2,1)(1,1,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2)\times2)</math> | |||
|<math>\psi(\Omega_{\omega+1}+\psi_\omega(\Omega_{\omega+1}))</math> | |||
|(0)(1,1,1)(2,1)(3,2)(1,1,1)(2,1)(3,2) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2+1))</math> | |||
|<math>\psi(\Omega_{\omega+1}+\psi_\omega(\Omega_{\omega+1}+1))</math> | |||
|(0)(1,1,1)(2,1)(3,2)(2) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2+\Omega))</math> | |||
|<math>\psi(\Omega_{\omega+1}+\psi_\omega(\Omega_{\omega+1}+\Omega))</math> | |||
|(0)(1,1,1)(2,1)(3,2)(2,1) | |||
|- | |||
|<math>\psi(\Omega_2\times(\psi_1(\Omega_2+\Omega)+1))</math> | |||
|<math>\psi(\Omega_{\omega+1}+\psi_\omega(\Omega_{\omega+1}+\Omega_\omega))</math> | |||
|(0)(1,1,1)(2,1)(3,2)(2,1)(1,1,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2+\psi_1(\Omega_2)))</math> | |||
|<math>\psi(\Omega_{\omega+1}+\psi_\omega(\Omega_{\omega+1}+\psi_\omega(\Omega_{\omega+1})))</math> | |||
|(0)(1,1,1)(2,1)(3,2)(2,1)(3,2) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2+\psi_1(\Omega_2+\Omega)))</math> | |||
|<math>\psi(\Omega_{\omega+1}+\psi_\omega(\Omega_{\omega+1}+\psi_\omega(\Omega_{\omega+1}+\Omega)))</math> | |||
|(0)(1,1,1)(2,1)(3,2)(3,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2))))</math> | |||
|<math>\psi(\Omega_{\omega+1}+\psi_\omega(\Omega_{\omega+1}+\psi_\omega(\Omega_{\omega+1}+\psi_\omega(\Omega_{\omega+1}))))</math> | |||
|(0)(1,1,1)(2,1)(3,2)(3,1)(4,2) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_22))</math> | |||
|<math>\psi(\Omega_{\omega+1}2)</math> | |||
|(0)(1,1,1)(2,1)(3,2)(3,2) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2\omega))</math> | |||
|<math>\psi(\Omega_{\omega+1}\omega)</math> | |||
|(0)(1,1,1)(2,1)(3,2)(4) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2\Omega))</math> | |||
|<math>\psi(\Omega_{\omega+1}\Omega)</math> | |||
|(0)(1,1,1)(2,1)(3,2)(4,1) | |||
|- | |||
|<math>\psi(\Omega_2\times(\psi_1(\Omega_2\Omega)+1))</math> | |||
|<math>\psi(\Omega_{\omega+1}\Omega_\omega)</math> | |||
|(0)(1,1,1)(2,1)(3,2)(4,1)(1,1,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2\times\psi_1(\Omega_2)))</math> | |||
|<math>\psi(\Omega_{\omega+1}\times\psi_\omega(\Omega_{\omega+1}))</math> | |||
|(0)(1,1,1)(2,1)(3,2)(4,1)(5,2) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2^2))</math> | |||
|<math>\psi(\Omega_{\omega+1}^2)</math> | |||
|(0)(1,1,1)(2,1)(3,2)(4,2) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2^\omega))</math> | |||
|<math>\psi(\Omega_{\omega+1}^\omega)</math> | |||
|(0)(1,1,1)(2,1)(3,2)(4,2)(5) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2^\Omega))</math> | |||
|<math>\psi(\Omega_{\omega+1}^\Omega)</math> | |||
|(0)(1,1,1)(2,1)(3,2)(4,2)(5,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_2^{\Omega_2}))</math> | |||
|<math>\psi(\Omega_{\omega+1}^{\Omega_{\omega+1}})</math> | |||
|(0)(1,1,1)(2,1)(3,2)(4,2)(5,2) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\psi_2(\Omega_3)))</math> | |||
|<math>\psi(\Omega_{\omega+2})</math> | |||
|(0)(1,1,1)(2,1)(3,2)(4,3) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\psi_2(\Omega_3)\times2))</math> | |||
|<math>\psi(\Omega_{\omega+2}+\psi_{\omega+1}(\Omega_{\omega+2}))</math> | |||
|(0)(1,1,1)(2,1)(3,2)(4,3)(3,2)(4,3) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\psi_2(\Omega_32)))</math> | |||
|<math>\psi(\Omega_{\omega+2}2)</math> | |||
|(0)(1,1,1)(2,1)(3,2)(4,3)(4,3) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\psi_2(\Omega_3^2)))</math> | |||
|<math>\psi(\Omega_{\omega+2}^2)</math> | |||
|(0)(1,1,1)(2,1)(3,2)(4,3)(5,3) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\psi_2(\psi_3(\Omega_4))))</math> | |||
|<math>\psi(\Omega_{\omega+3})</math> | |||
|(0)(1,1,1)(2,1)(3,2)(4,3)(5,4) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_3))</math> | |||
|<math>\psi(\Omega_{\omega2})</math> | |||
|(0)(1,1,1)(2,1)(3,2,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_3)\times2)</math> | |||
|<math>\psi(\Omega_{\omega2}+\psi_\omega(\Omega_{\omega2}))</math> | |||
|(0)(1,1,1)(2,1)(3,2,1)(1,1,1)(2,1)(3,2,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_3+1))</math> | |||
|<math>\psi(\Omega_{\omega2}+\psi_\omega(\Omega_{\omega2}+1))</math> | |||
|(0)(1,1,1)(2,1)(3,2,1)(2) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_3+\Omega))</math> | |||
|<math>\psi(\Omega_{\omega2}+\psi_\omega(\Omega_{\omega2}+\Omega))</math> | |||
|(0)(1,1,1)(2,1)(3,2,1)(2,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_3+\psi_1(\Omega_3)))</math> | |||
|<math>\psi(\Omega_{\omega2}+\psi_\omega(\Omega_{\omega2}+\psi_\omega(\Omega_{\omega2})))</math> | |||
|(0)(1,1,1)(2,1)(3,2,1)(2,1)(3,2,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_3+\Omega_2))</math> | |||
|<math>\psi(\Omega_{\omega2}+\Omega_{\omega+1})</math> | |||
|(0)(1,1,1)(2,1)(3,2,1)(3,2) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_32))</math> | |||
|<math>\psi(\Omega_{\omega2}2)</math> | |||
|(0)(1,1,1)(2,1)(3,2,1)(3,2,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_3\omega))</math> | |||
|<math>\psi(\Omega_{\omega2}\omega)</math> | |||
|(0)(1,1,1)(2,1)(3,2,1)(4) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_3\Omega))</math> | |||
|<math>\psi(\Omega_{\omega2}\Omega)</math> | |||
|(0)(1,1,1)(2,1)(3,2,1)(4,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_3\Omega_2))</math> | |||
|<math>\psi(\Omega_{\omega2}\Omega_{\omega+1})</math> | |||
|(0)(1,1,1)(2,1)(3,2,1)(4,2) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_3\times(\Omega_2+1)))</math> | |||
|<math>\psi(\Omega_{\omega2}^2)</math> | |||
|(0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_3\times\Omega_2^2))</math> | |||
|<math>\psi(\Omega_{\omega2}^2\times\Omega_{\omega+1})</math> | |||
|(0)(1,1,1)(2,1)(3,2,1)(4,2)(4,2) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_3\times\Omega_2^{\Omega_2}))</math> | |||
|<math>\psi(\Omega_{\omega2}^{\Omega_{\omega+1}})</math> | |||
|(0)(1,1,1)(2,1)(3,2,1)(4,2)(5,2) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_3\times\psi_2(\Omega_3)))</math> | |||
|<math>\psi(\Omega_{\omega2+1})</math> | |||
|(0)(1,1,1)(2,1)(3,2,1)(4,2)(5,3) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_3\times\psi_2(\psi_3(\Omega_4))))</math> | |||
|<math>\psi(\Omega_{\omega2+2})</math> | |||
|(0)(1,1,1)(2,1)(3,2,1)(4,2)(5,3)(6,4) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_3\times\psi_2(\Omega_4)))</math> | |||
|<math>\psi(\Omega_{\omega3})</math> | |||
|(0)(1,1,1)(2,1)(3,2,1)(4,2)(5,3,1) | |||
|- | |||
|<math>\psi(\Omega_2\times\psi_1(\Omega_3\times\psi_2(\Omega_4\times\psi_3(\Omega_5))))</math> | |||
|<math>\psi(\Omega_{\omega4})</math> | |||
|(0)(1,1,1)(2,1)(3,2,1)(4,2)(5,3,1)(6,3)(7,4,1) | |||
|- | |||
|<math>\psi(\Omega_2^2)</math> | |||
|<math>\psi(\Omega_{\omega^2})</math> | |||
|(0)(1,1,1)(2,1,1) | |||
|- | |||
|<math>\psi(\Omega_2^2+\Omega_2)</math> | |||
|<math>\psi(\Omega_{\omega^2}+\Omega_\omega)</math> | |||
|(0)(1,1,1)(2,1,1)(1,1,1) | |||
|- | |||
|<math>\psi(\Omega_2^2+\psi_1(\Omega_3))</math> | |||
|<math>\psi(\Omega_{\omega^2}+\psi_\omega(\Omega_{\omega2}))</math> | |||
|(0)(1,1,1)(2,1,1)(1,1,1)(2,1)(3,2,1) | |||
|- | |||
|<math>\psi(\Omega_2^2+\psi_1(\Omega_3^2))</math> | |||
|<math>\psi(\Omega_{\omega^2}+\psi_\omega(\Omega_{\omega^2}))</math> | |||
|(0)(1,1,1)(2,1,1)(1,1,1)(2,1)(3,2,1)(4,2,1) | |||
|- | |||
|<math>\psi(\Omega_2^2+\psi_1(\Omega_3^2+\Omega_3))</math> | |||
|<math>\psi(\Omega_{\omega^2}+\Omega_{\omega2})</math> | |||
|(0)(1,1,1)(2,1,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(3,2,1) | |||
|- | |||
|<math>\psi(\Omega_2^22)</math> | |||
|<math>\psi(\Omega_{\omega^2}2)</math> | |||
|(0)(1,1,1)(2,1,1)(1,1,1)(2,1,1) | |||
|- | |||
|<math>\psi(\Omega_2^2\Omega)</math> | |||
|<math>\psi(\Omega_{\omega^2}\Omega)</math> | |||
|(0)(1,1,1)(2,1,1)(2,1) | |||
|- | |||
|<math>\psi(\Omega_2^2\Omega+\Omega_2)</math> | |||
|<math>\psi(\Omega_{\omega^2}\Omega_\omega)</math> | |||
|(0)(1,1,1)(2,1,1)(2,1)(1,1,1) | |||
|- | |||
|<math>\psi(\Omega_2^2\times(\Omega+1))</math> | |||
|<math>\psi(\Omega_{\omega^2}^2)</math> | |||
|(0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1,1) | |||
|- | |||
|<math>\psi(\Omega_2^2\times\psi_1(\Omega_2))</math> | |||
|<math>\psi(\Omega_{\omega^2+1})</math> | |||
|(0)(1,1,1)(2,1,1)(2,1)(3,2) | |||
|- | |||
|<math>\psi(\Omega_2^2\times\psi_1(\Omega_3))</math> | |||
|<math>\psi(\Omega_{\omega^2+\omega})</math> | |||
|(0)(1,1,1)(2,1,1)(2,1)(3,2,1) | |||
|- | |||
|<math>\psi(\Omega_2^2\times\psi_1(\Omega_3^2))</math> | |||
|<math>\psi(\Omega_{\omega^22})</math> | |||
|(0)(1,1,1)(2,1,1)(2,1)(3,2,1)(4,2,1) | |||
|- | |||
|<math>\psi(\Omega_2^3)</math> | |||
|<math>\psi(\Omega_{\omega^3})</math> | |||
|(0)(1,1,1)(2,1,1)(2,1,1) | |||
|- | |||
|<math>\psi(\Omega_2^\omega)</math> | |||
|<math>\psi(\Omega_{\omega^\omega})</math> | |||
|(0)(1,1,1)(2,1,1)(3) | |||
|- | |||
|<math>\psi(\Omega_2^{\varepsilon_0})</math> | |||
|<math>\psi(\Omega_{\varepsilon_0})</math> | |||
|(0)(1,1,1)(2,1,1)(3)(4,1) | |||
|- | |||
|<math>\psi(\Omega_2^{\psi(\Omega_2)})</math> | |||
|<math>\psi(\Omega_{\psi(\Omega_\omega)})</math> | |||
|(0)(1,1,1)(2,1,1)(3)(4,1,1) | |||
|- | |||
|<math>\psi(\Omega_2^{\psi(\Omega_2^{\psi(\Omega_2)})})</math> | |||
|<math>\psi(\Omega_{\psi(\Omega_{\psi(\Omega_\omega)})})</math> | |||
|(0)(1,1,1)(2,1,1)(3)(4,1,1)(5,1,1)(6)(7,1,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega)</math> | |||
|<math>\psi(\Omega_\Omega)</math> | |||
|(0)(1,1,1)(2,1,1)(3,1) | |||
|} | |||
== 分析6:BiO~EBO == | |||
此阶段分析对照BMS难度较低。至此,我们可以总结出一些规律:BMS与LPrSSψ之间,第一行决定层数,即从最外面到这个位置套了几层ψ函数。第二行决定基数,即这里应该有个Ω_n的n,当没有第二行,说明这个位置有后继,0则整体为后继序数,>0则后继在ψ中,提到外面后变成×ω。第三行决定阶差,即这里的基数比所在的ψ输出的基数大多少,当没有第三行,说明这个位置阶差<=1,当第三行为1,在BGO前,对应一个阶差2的展开。 | |||
{| class="wikitable" | |||
|+分析6:BiO~EBO | |||
!LPrSSψ | |||
!BOCF | |||
!BMS | |||
|- | |||
|<math>\psi(\Omega_2^\Omega)</math> | |||
|<math>\psi(\Omega_\Omega)</math> | |||
|(0)(1,1,1)(2,1,1)(3,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3))</math> | |||
|<math>\psi(\Omega_\Omega+\psi_1(\Omega_\omega))</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^\Omega))</math> | |||
|<math>\psi(\Omega_\Omega+\psi_1(\Omega_\Omega))</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^\Omega+\Omega_2))</math> | |||
|<math>\psi(\Omega_\Omega+\Omega_2)</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(2,2) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^\Omega+\Omega_3))</math> | |||
|<math>\psi(\Omega_\Omega+\Omega_\omega)</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(2,2,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^\Omega2))</math> | |||
|<math>\psi(\Omega_\Omega2)</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(2,2,1)(3,2,1)(4,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^\Omega\omega))</math> | |||
|<math>\psi(\Omega_\Omega\omega)</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^\Omega\Omega))</math> | |||
|<math>\psi(\Omega_\Omega\Omega)</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^\Omega\Omega_2))</math> | |||
|<math>\psi(\Omega_\Omega\Omega_2)</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^\Omega\times(\Omega_2+1)))</math> | |||
|<math>\psi(\Omega_\Omega^2)</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)(2,2,1)(3,2,1)(4,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^\Omega\times\psi_2(\Omega_3)))</math> | |||
|<math>\psi(\Omega_{\Omega+1})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)(4,3) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^\Omega\times\psi_2(\Omega_4)))</math> | |||
|<math>\psi(\Omega_{\Omega+\omega})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)(4,3,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^\Omega\times\psi_2(\Omega_4^2)))</math> | |||
|<math>\psi(\Omega_{\Omega+\omega^\omega})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)(4,3,1)(5,4,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^\Omega\times\psi_2(\Omega_4^\Omega)))</math> | |||
|<math>\psi(\Omega_{\Omega2})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)(4,3,1)(5,4,1)(6,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^{\Omega+1}))</math> | |||
|<math>\psi(\Omega_{\Omega\omega})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^{\Omega+2}))</math> | |||
|<math>\psi(\Omega_{\Omega\times\omega^\omega})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2,1)(3,2,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^{\Omega2}))</math> | |||
|<math>\psi(\Omega_{\Omega^2})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2,1)(4,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^{\Omega^2}))</math> | |||
|<math>\psi(\Omega_{\Omega^\Omega})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(4,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^{\psi_1(\Omega_2)}))</math> | |||
|<math>\psi(\Omega_{\psi_1(\Omega_2)})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(5,2) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^{\psi_1(\Omega_3)}))</math> | |||
|<math>\psi(\Omega_{\psi_1(\Omega_\omega)})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(5,2,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^{\psi_1(\Omega_3^\Omega)}))</math> | |||
|<math>\psi(\Omega_{\psi_1(\Omega_\Omega)})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(5,2,1)(6,2,1)(7,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^{\Omega_2}))</math> | |||
|<math>\psi(\Omega_{\Omega_2})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,2) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\psi_1(\Omega_3^{\Omega_2}+\psi_2(\Omega_4^{\Omega_3})))</math> | |||
|<math>\psi(\Omega_{\Omega_3})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,2)(2,2)(3,3,1)(4,3,1)(5,3) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2)</math> | |||
|<math>\psi(\Omega_{\Omega_\omega})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_22)</math> | |||
|<math>\psi(\Omega_{\Omega_\omega}+\Omega_\omega)</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(1,1,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_2))</math> | |||
|<math>\psi(\Omega_{\Omega_\omega}+\psi_\omega(\Omega_{\omega+1}))</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_3))</math> | |||
|<math>\psi(\Omega_{\Omega_\omega}+\psi_\omega(\Omega_{\omega2}))</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_3^\Omega))</math> | |||
|<math>\psi(\Omega_{\Omega_\omega}+\psi_\omega(\Omega_{\Omega}))</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_3^\Omega+\Omega_2))</math> | |||
|<math>\psi(\Omega_{\Omega_\omega}+\Omega_{\omega+1})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(3,2) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_3^\Omega+\Omega_3))</math> | |||
|<math>\psi(\Omega_{\Omega_\omega}+\Omega_{\omega2})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(3,2,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_3^\Omega2))</math> | |||
|<math>\psi(\Omega_{\Omega_\omega}+\Omega_{\Omega})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(3,2,1)(4,3,1)(5,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_3^\Omega2+\Omega_3))</math> | |||
|<math>\psi(\Omega_{\Omega_\omega}2)</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(3,2,1)(4,3,1)(5,1)(1,1,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_3^\Omega\Omega))</math> | |||
|<math>\psi(\Omega_{\Omega_\omega}\Omega)</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(4,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_3^\Omega\Omega_2))</math> | |||
|<math>\psi(\Omega_{\Omega_\omega}\Omega_{\omega+1})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(4,2) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_3^\Omega\times\psi_2(\Omega_3)))</math> | |||
|<math>\psi(\Omega_{\Omega_\omega+1})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(4,2)(5,3) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_3^\Omega\times\psi_2(\Omega_4)))</math> | |||
|<math>\psi(\Omega_{\Omega_\omega+\omega})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(4,2)(5,3,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_3^{\Omega+1}))</math> | |||
|<math>\psi(\Omega_{\Omega_\omega\omega})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(4,2,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_3^{\Omega_2}))</math> | |||
|<math>\psi(\Omega_{\Omega_{\omega+1}})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,2) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_3^{\Omega_2}+\psi_2(\Omega_4^{\Omega_3})))</math> | |||
|<math>\psi(\Omega_{\Omega_{\omega+2}})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,2)(3,2)(4,3,1)(5,3,1)(6,3) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2\times\psi_1(\Omega_3^{\Omega_2}+\Omega_3))</math> | |||
|<math>\psi(\Omega_{\Omega_{\omega2}})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,2)(3,2,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2^2)</math> | |||
|<math>\psi(\Omega_{\Omega_{\omega^2}})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega+\Omega_2^\omega)</math> | |||
|<math>\psi(\Omega_{\Omega_{\omega^\omega}})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega2)</math> | |||
|<math>\psi(\Omega_{\Omega_\Omega})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega2+\Omega_2)</math> | |||
|<math>\psi(\Omega_{\Omega_{\Omega_\omega}})</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(1,1,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega3)</math> | |||
|<math>\psi(\Omega\downarrow\downarrow4)</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1) | |||
|- | |||
|<math>\psi(\Omega_2^\Omega\omega)</math> | |||
|<math>\psi(I)</math> | |||
|(0)(1,1,1)(2,1,1)(3,1)(2) | |||
|} | |||
下篇:[[LPrSSψ分析Part2]] | |||
[[分类:分析]] | [[分类:分析]] | ||
2026年5月6日 (三) 11:13的最新版本
以下为长初等序列序数折叠函数(LPrSSψ)的分析。LPrSSψ与BOCF在BHO前完全一致,但强度大得多,可达(0)(1,1,1)(2,2,1)(3)以上。
分析1:BHO~BO
此阶段分析很简单,仅需将每一层从对应的ψ拆出来即可。
| LPrSSψ | BOCF | BMS |
|---|---|---|
| (0)(1,1)(2,2) | ||
| (0)(1,1)(2,2)(1) | ||
| (0)(1,1)(2,2)(1,1) | ||
| (0)(1,1)(2,2)(1,1)(2,2) | ||
| (0)(1,1)(2,2)(1,1)(2,2)(1,1)(2,2) | ||
| (0)(1,1)(2,2)(2) | ||
| (0)(1,1)(2,2)(2)(3) | ||
| (0)(1,1)(2,2)(2,1) | ||
| (0)(1,1)(2,2)(2,1)(3,2) | ||
| (0)(1,1)(2,2)(2,1)(3,2)(3,1)(4,2) | ||
| (0)(1,1)(2,2)(2,2) | ||
| (0)(1,1)(2,2)(2,2)(1,1)(2,2)(2,2) | ||
| (0)(1,1)(2,2)(2,2)(2) | ||
| (0)(1,1)(2,2)(2,2)(2,2) | ||
| (0)(1,1)(2,2)(3) | ||
| (0)(1,1)(2,2)(3,1) | ||
| (0)(1,1)(2,2)(3,1)(4,2) | ||
| (0)(1,1)(2,2)(3,2) | ||
| (0)(1,1)(2,2)(3,2)(1,1)(2,2)(3,2) | ||
| (0)(1,1)(2,2)(3,2)(2,2) | ||
| (0)(1,1)(2,2)(3,2)(2,2)(3,2) | ||
| (0)(1,1)(2,2)(3,2)(3,2) | ||
| (0)(1,1)(2,2)(3,2)(4) | ||
| (0)(1,1)(2,2)(3,2)(4,1) | ||
| (0)(1,1)(2,2)(3,2)(4,1)(5,2) | ||
| (0)(1,1)(2,2)(3,2)(4,2) | ||
| (0)(1,1)(2,2)(3,2)(4,2)(5,2) | ||
| (0)(1,1)(2,2)(3,3) | ||
| (0)(1,1)(2,2)(3,3)(1,1)(2,2)(3,3) | ||
| (0)(1,1)(2,2)(3,3)(2) | ||
| (0)(1,1)(2,2)(3,3)(2,2) | ||
| (0)(1,1)(2,2)(3,3)(2,2)(3,3) | ||
| (0)(1,1)(2,2)(3,3)(3) | ||
| (0)(1,1)(2,2)(3,3)(3,2) | ||
| (0)(1,1)(2,2)(3,3)(3,2)(4,3) | ||
| (0)(1,1)(2,2)(3,3)(3,3) | ||
| (0)(1,1)(2,2)(3,3)(4) | ||
| (0)(1,1)(2,2)(3,3)(4,3) | ||
| (0)(1,1)(2,2)(3,3)(4,3)(5,3) | ||
| (0)(1,1)(2,2)(3,3)(4,4) | ||
| (0)(1,1)(2,2)(3,3)(4,4)(5,5) | ||
| (0)(1,1,1) |
分析2:BO~(0)(1,1,1)(2,1)
到(0)(1,1,1)(2,1)的分析仍较简单,仅需找层即可,但此后,LPrSSψ的行为更类似BMS,而不是BOCF,因为具有(0)(1,1,1)(2,1)(1,1,1)提升。
| LPrSSψ | BOCF | BMS |
|---|---|---|
| (0)(1,1,1) | ||
| (0)(1,1,1)(1) | ||
| (0)(1,1,1)(1,1) | ||
| (0)(1,1,1)(1,1)(2,2) | ||
| (0)(1,1,1)(1,1)(2,2)(3,3) | ||
| (0)(1,1,1)(1,1)(2,2,1) | ||
| (0)(1,1,1)(1,1)(2,2,1)(1,1)(2,2,1) | ||
| (0)(1,1,1)(1,1)(2,2,1)(2) | ||
| (0)(1,1,1)(1,1)(2,2,1)(2,1) | ||
| (0)(1,1,1)(1,1)(2,2,1)(2,1)(3,2) | ||
| (0)(1,1,1)(1,1)(2,2,1)(2,1)(3,2,1) | ||
| (0)(1,1,1)(1,1)(2,2,1)(2,2) | ||
| (0)(1,1,1)(1,1)(2,2,1)(2,2)(2,2) | ||
| (0)(1,1,1)(1,1)(2,2,1)(2,2)(3,2) | ||
| (0)(1,1,1)(1,1)(2,2,1)(2,2)(3,3) | ||
| (0)(1,1,1)(1,1)(2,2,1)(2,2)(3,3,1) | ||
| (0)(1,1,1)(1,1)(2,2,1)(2,2)(3,3,1)(3,3) | ||
| (0)(1,1,1)(1,1)(2,2,1)(2,2)(3,3,1)(3,3)(4,4,1) | ||
| (0)(1,1,1)(1,1,1) | ||
| (0)(1,1,1)(1,1,1)(1,1)(2,2,1) | ||
| (0)(1,1,1)(1,1,1)(1,1)(2,2,1)(2,2,1) | ||
| (0)(1,1,1)(1,1,1)(1,1)(2,2,1)(2,2,1)(2,2) | ||
| (0)(1,1,1)(1,1,1)(1,1,1) | ||
| (0)(1,1,1)(2) | ||
| (0)(1,1,1)(2)(1,1,1) | ||
| (0)(1,1,1)(2)(3,1) | ||
| (0)(1,1,1)(2)(3,1,1) | ||
| (0)(1,1,1)(2,1) |
分析3:(0)(1,1,1)(2,1)~(0)(1,1,1)(2,1)(1,1,1)
分析进入提升阶段。可见LPrSSψ中,ψ中的一个Ω_2对应的不是BOCF中的一个Ω_ω,而是BMS中的一个(1,1,1)。类似的,BGO前许多阶差2的表达式对应BMS第三行的1。这里注意LPrSSψ一般不单独定义Ω_0,展开方式,Ω_2展开出ψ_1时,把外面的Ω变成了里面的Ω_2,以此类推,但ω不提升。因为阶差为d时,Ω_(n+1)变出的ψ_n只把外面的x>=n的Ω_x提升为Ω_(x+d)。不然,若定义Ω_0=ω,并在这种位置将其提升为Ω,会与没有【特别地,如果坏根中元素不是坏部中某项的祖先项,则该项在复制过程中将保持不变。】规则的BMS一样,发生无穷降链。此外,若无此种提升,可能可以得到类似IBMS的ILPrSSψ。
| LPrSSψ | BOCF | BMS |
|---|---|---|
| (0)(1,1,1)(2,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,1)(3,2,1)(4,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,3,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,3,1)(4,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,3,1)(4,1)(3,3) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(2,2,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(3) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(3,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(3) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(3,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4,2) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4,2,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4,2,1)(5,1)(6,2,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)(3,3) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)(3,3,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)(3,3,1)(4,2) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)(5,3,1) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,3) | ||
| (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,3)(3,3)(4,4,1)(5,4) | ||
| (0)(1,1,1)(2,1)(1,1,1) |
分析4:(0)(1,1,1)(2,1)(1,1,1)~TFBO
此阶段难度相对较低,LPrSSψ与BMS对应较为简单,BOCF有随时出现的Ω变Ω_ω提升。
| LPrSSψ | BOCF | BMS |
|---|---|---|
| (0)(1,1,1)(2,1)(1,1,1) | ||
| (0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1) | ||
| (0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1)(3,1) | ||
| (0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1)(3,2) | ||
| (0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1)(3,2)(2,2,1) | ||
| (0)(1,1,1)(2,1)(1,1,1)(1,1)(2,2,1)(3,2)(2,2,1)(2,2) | ||
| (0)(1,1,1)(2,1)(1,1,1)(1,1,1) | ||
| (0)(1,1,1)(2,1)(1,1,1)(2) | ||
| (0)(1,1,1)(2,1)(1,1,1)(2,1) | ||
| (0)(1,1,1)(2,1)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2,1)(3,1) | ||
| (0)(1,1,1)(2,1)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2,1)(3,1)(2,2,1) | ||
| (0)(1,1,1)(2,1)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2,1)(3,2) | ||
| (0)(1,1,1)(2,1)(1,1,1)(2,1)(1,1,1) | ||
| (0)(1,1,1)(2,1)(2) | ||
| (0)(1,1,1)(2,1)(2,1) | ||
| (0)(1,1,1)(2,1)(2,1)(1,1)(2,2,1)(3,2)(3,1) | ||
| (0)(1,1,1)(2,1)(2,1)(1,1)(2,2,1)(3,2)(3,1)(2,2,1) | ||
| (0)(1,1,1)(2,1)(2,1)(1,1)(2,2,1)(3,2)(3,2) | ||
| (0)(1,1,1)(2,1)(2,1)(1,1,1) | ||
| (0)(1,1,1)(2,1)(3) | ||
| (0)(1,1,1)(2,1)(3,1) | ||
| (0)(1,1,1)(2,1)(3,1)(1,1)(2,2,1)(3,2)(4,1) | ||
| (0)(1,1,1)(2,1)(3,1)(1,1)(2,2,1)(3,2)(4,1)(2,2,1) | ||
| (0)(1,1,1)(2,1)(3,1)(1,1)(2,2,1)(3,2)(4,2) | ||
| (0)(1,1,1)(2,1)(3,1)(1,1,1) | ||
| (0)(1,1,1)(2,1)(3,1)(1,1,1)(2,1)(3,1) | ||
| (0)(1,1,1)(2,1)(3,1)(2,1) | ||
| (0)(1,1,1)(2,1)(3,1)(2,1)(3,1) | ||
| (0)(1,1,1)(2,1)(3,1)(3,1) | ||
| (0)(1,1,1)(2,1)(3,1)(4,1) | ||
| (0)(1,1,1)(2,1)(3,2) |
分析5:TFBO~BiO
此阶段若对照BMS分析,难度相对较低,而BOCF有随时出现的各级提升。
| LPrSSψ | BOCF | BMS |
|---|---|---|
| (0)(1,1,1)(2,1)(3,2) | ||
| (0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)(3,2)(4,3) | ||
| (0)(1,1,1)(2,1)(3,2)(1,1)(2,2,1)(3,2)(4,3)(2,2) | ||
| (0)(1,1,1)(2,1)(3,2)(1,1,1) | ||
| (0)(1,1,1)(2,1)(3,2)(1,1,1)(2,1) | ||
| (0)(1,1,1)(2,1)(3,2)(1,1,1)(2,1)(1,1,1) | ||
| (0)(1,1,1)(2,1)(3,2)(1,1,1)(2,1)(3,2) | ||
| (0)(1,1,1)(2,1)(3,2)(2) | ||
| (0)(1,1,1)(2,1)(3,2)(2,1) | ||
| (0)(1,1,1)(2,1)(3,2)(2,1)(1,1,1) | ||
| (0)(1,1,1)(2,1)(3,2)(2,1)(3,2) | ||
| (0)(1,1,1)(2,1)(3,2)(3,1) | ||
| (0)(1,1,1)(2,1)(3,2)(3,1)(4,2) | ||
| (0)(1,1,1)(2,1)(3,2)(3,2) | ||
| (0)(1,1,1)(2,1)(3,2)(4) | ||
| (0)(1,1,1)(2,1)(3,2)(4,1) | ||
| (0)(1,1,1)(2,1)(3,2)(4,1)(1,1,1) | ||
| (0)(1,1,1)(2,1)(3,2)(4,1)(5,2) | ||
| (0)(1,1,1)(2,1)(3,2)(4,2) | ||
| (0)(1,1,1)(2,1)(3,2)(4,2)(5) | ||
| (0)(1,1,1)(2,1)(3,2)(4,2)(5,1) | ||
| (0)(1,1,1)(2,1)(3,2)(4,2)(5,2) | ||
| (0)(1,1,1)(2,1)(3,2)(4,3) | ||
| (0)(1,1,1)(2,1)(3,2)(4,3)(3,2)(4,3) | ||
| (0)(1,1,1)(2,1)(3,2)(4,3)(4,3) | ||
| (0)(1,1,1)(2,1)(3,2)(4,3)(5,3) | ||
| (0)(1,1,1)(2,1)(3,2)(4,3)(5,4) | ||
| (0)(1,1,1)(2,1)(3,2,1) | ||
| (0)(1,1,1)(2,1)(3,2,1)(1,1,1)(2,1)(3,2,1) | ||
| (0)(1,1,1)(2,1)(3,2,1)(2) | ||
| (0)(1,1,1)(2,1)(3,2,1)(2,1) | ||
| (0)(1,1,1)(2,1)(3,2,1)(2,1)(3,2,1) | ||
| (0)(1,1,1)(2,1)(3,2,1)(3,2) | ||
| (0)(1,1,1)(2,1)(3,2,1)(3,2,1) | ||
| (0)(1,1,1)(2,1)(3,2,1)(4) | ||
| (0)(1,1,1)(2,1)(3,2,1)(4,1) | ||
| (0)(1,1,1)(2,1)(3,2,1)(4,2) | ||
| (0)(1,1,1)(2,1)(3,2,1)(4,2)(3,2,1) | ||
| (0)(1,1,1)(2,1)(3,2,1)(4,2)(4,2) | ||
| (0)(1,1,1)(2,1)(3,2,1)(4,2)(5,2) | ||
| (0)(1,1,1)(2,1)(3,2,1)(4,2)(5,3) | ||
| (0)(1,1,1)(2,1)(3,2,1)(4,2)(5,3)(6,4) | ||
| (0)(1,1,1)(2,1)(3,2,1)(4,2)(5,3,1) | ||
| (0)(1,1,1)(2,1)(3,2,1)(4,2)(5,3,1)(6,3)(7,4,1) | ||
| (0)(1,1,1)(2,1,1) | ||
| (0)(1,1,1)(2,1,1)(1,1,1) | ||
| (0)(1,1,1)(2,1,1)(1,1,1)(2,1)(3,2,1) | ||
| (0)(1,1,1)(2,1,1)(1,1,1)(2,1)(3,2,1)(4,2,1) | ||
| (0)(1,1,1)(2,1,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(3,2,1) | ||
| (0)(1,1,1)(2,1,1)(1,1,1)(2,1,1) | ||
| (0)(1,1,1)(2,1,1)(2,1) | ||
| (0)(1,1,1)(2,1,1)(2,1)(1,1,1) | ||
| (0)(1,1,1)(2,1,1)(2,1)(1,1,1)(2,1,1) | ||
| (0)(1,1,1)(2,1,1)(2,1)(3,2) | ||
| (0)(1,1,1)(2,1,1)(2,1)(3,2,1) | ||
| (0)(1,1,1)(2,1,1)(2,1)(3,2,1)(4,2,1) | ||
| (0)(1,1,1)(2,1,1)(2,1,1) | ||
| (0)(1,1,1)(2,1,1)(3) | ||
| (0)(1,1,1)(2,1,1)(3)(4,1) | ||
| (0)(1,1,1)(2,1,1)(3)(4,1,1) | ||
| (0)(1,1,1)(2,1,1)(3)(4,1,1)(5,1,1)(6)(7,1,1) | ||
| (0)(1,1,1)(2,1,1)(3,1) |
分析6:BiO~EBO
此阶段分析对照BMS难度较低。至此,我们可以总结出一些规律:BMS与LPrSSψ之间,第一行决定层数,即从最外面到这个位置套了几层ψ函数。第二行决定基数,即这里应该有个Ω_n的n,当没有第二行,说明这个位置有后继,0则整体为后继序数,>0则后继在ψ中,提到外面后变成×ω。第三行决定阶差,即这里的基数比所在的ψ输出的基数大多少,当没有第三行,说明这个位置阶差<=1,当第三行为1,在BGO前,对应一个阶差2的展开。
| LPrSSψ | BOCF | BMS |
|---|---|---|
| (0)(1,1,1)(2,1,1)(3,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(2,2) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(2,2,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(2,2,1)(3,2,1)(4,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)(2,2,1)(3,2,1)(4,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)(4,3) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)(4,3,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)(4,3,1)(5,4,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2)(4,3,1)(5,4,1)(6,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2,1)(3,2,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(3,2,1)(4,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(4,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(5,2) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(5,2,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,1)(5,2,1)(6,2,1)(7,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,2) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,2)(2,2)(3,3,1)(4,3,1)(5,3) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(1,1,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(3,2) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(3,2,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(3,2,1)(4,3,1)(5,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(3,2,1)(4,3,1)(5,1)(1,1,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(4,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(4,2) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(4,2)(5,3) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(4,2)(5,3,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,1)(4,2,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,2) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,2)(3,2)(4,3,1)(5,3,1)(6,3) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,3,1)(5,2)(3,2,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(1,1,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1) | ||
| (0)(1,1,1)(2,1,1)(3,1)(2) |