查看“︁LPrSSψ分析”︁的源代码

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。
{| class="wikitable"
|+分析1：BHO~BO
!LPrSSψ
!BOCF
!BMS
|-
|<math>\psi(\psi_1(\Omega_2))=\psi(\varepsilon_{\Omega+1})</math>
|<math>\psi(\Omega_2)</math>
|(0)(1,1)(2,2)
|-
|<math>\psi(\psi_1(\Omega_2)+1)</math>
|<math>\psi(\Omega_2+1)</math>
|(0)(1,1)(2,2)(1)
|-
|<math>\psi(\psi_1(\Omega_2)+\Omega)</math>
|<math>\psi(\Omega_2+\Omega)</math>
|(0)(1,1)(2,2)(1,1)
|-
|<math>\psi(\psi_1(\Omega_2)\times2)</math>
|<math>\psi(\Omega_2+\psi_1(\Omega_2))</math>
|(0)(1,1)(2,2)(1,1)(2,2)
|-
|<math>\psi(\psi_1(\Omega_2)\times3)</math>
|<math>\psi(\Omega_2+\psi_1(\Omega_2)\times2)</math>
|(0)(1,1)(2,2)(1,1)(2,2)(1,1)(2,2)
|-
|<math>\psi(\psi_1(\Omega_2+1))</math>
|<math>\psi(\Omega_2+\psi_1(\Omega_2+1))</math>
|(0)(1,1)(2,2)(2)
|-
|<math>\psi(\psi_1(\Omega_2+\omega))</math>
|<math>\psi(\Omega_2+\psi_1(\Omega_2+\omega))</math>
|(0)(1,1)(2,2)(2)(3)
|-
|<math>\psi(\psi_1(\Omega_2+\Omega))</math>
|<math>\psi(\Omega_2+\psi_1(\Omega_2+\Omega))</math>
|(0)(1,1)(2,2)(2,1)
|-
|<math>\psi(\psi_1(\Omega_2+\psi_1(\Omega_2)))</math>
|<math>\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)))</math>
|(0)(1,1)(2,2)(2,1)(3,2)
|-
|<math>\psi(\psi_1(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2))))</math>
|<math>\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2))))</math>
|(0)(1,1)(2,2)(2,1)(3,2)(3,1)(4,2)
|-
|<math>\psi(\psi_1(\Omega_22))=\psi(\varepsilon_{\Omega+2})</math>
|<math>\psi(\Omega_22)</math>
|(0)(1,1)(2,2)(2,2)
|-
|<math>\psi(\psi_1(\Omega_22)\times2)</math>
|<math>\psi(\Omega_22+\psi_1(\Omega_22))</math>
|(0)(1,1)(2,2)(2,2)(1,1)(2,2)(2,2)
|-
|<math>\psi(\psi_1(\Omega_22+1))</math>
|<math>\psi(\Omega_22+\psi_1(\Omega_22+1))</math>
|(0)(1,1)(2,2)(2,2)(2)
|-
|<math>\psi(\psi_1(\Omega_23))</math>
|<math>\psi(\Omega_23)</math>
|(0)(1,1)(2,2)(2,2)(2,2)
|-
|<math>\psi(\psi_1(\Omega_2\omega))=\psi(\varepsilon_{\Omega+\omega})</math>
|<math>\psi(\Omega_2\omega)</math>
|(0)(1,1)(2,2)(3)
|-
|<math>\psi(\psi_1(\Omega_2\Omega))=\psi(\varepsilon_{\Omega2})</math>
|<math>\psi(\Omega_2\Omega)</math>
|(0)(1,1)(2,2)(3,1)
|-
|<math>\psi(\psi_1(\Omega_2\times\psi_1(\Omega_2)))=\psi(\varepsilon_{\varepsilon_{\Omega+1}})</math>
|<math>\psi(\Omega_2\times\psi_1(\Omega_2))</math>
|(0)(1,1)(2,2)(3,1)(4,2)
|-
|<math>\psi(\psi_1(\Omega_2^2))=\psi(\zeta_{\Omega+1})</math>
|<math>\psi(\Omega_2^2)</math>
|(0)(1,1)(2,2)(3,2)
|-
|<math>\psi(\psi_1(\Omega_2^2)\times2)</math>
|<math>\psi(\Omega_2^2+\psi_1(\Omega_2^2))</math>
|(0)(1,1)(2,2)(3,2)(1,1)(2,2)(3,2)
|-
|<math>\psi(\psi_1(\Omega_2^2+\Omega_2))</math>
|<math>\psi(\Omega_2^2+\Omega_2)</math>
|(0)(1,1)(2,2)(3,2)(2,2)
|-
|<math>\psi(\psi_1(\Omega_2^22))</math>
|<math>\psi(\Omega_2^22)</math>
|(0)(1,1)(2,2)(3,2)(2,2)(3,2)
|-
|<math>\psi(\psi_1(\Omega_2^3))</math>
|<math>\psi(\Omega_2^3)</math>
|(0)(1,1)(2,2)(3,2)(3,2)
|-
|<math>\psi(\psi_1(\Omega_2^\omega))=\psi(\varphi(\omega,\Omega+1))</math>
|<math>\psi(\Omega_2^\omega)</math>
|(0)(1,1)(2,2)(3,2)(4)
|-
|<math>\psi(\psi_1(\Omega_2^\Omega))=\psi(\varphi(\Omega,1))</math>
|<math>\psi(\Omega_2^\Omega)</math>
|(0)(1,1)(2,2)(3,2)(4,1)
|-
|<math>\psi(\psi_1(\Omega_2^{\psi_1(\Omega_2)}))</math>
|<math>\psi(\Omega_2^{\psi_1(\Omega_2)})</math>
|(0)(1,1)(2,2)(3,2)(4,1)(5,2)
|-
|<math>\psi(\psi_1(\Omega_2^{\Omega_2}))=\psi(\Gamma_{\Omega+1})</math>
|<math>\psi(\Omega_2^{\Omega_2})</math>
|(0)(1,1)(2,2)(3,2)(4,2)
|-
|<math>\psi(\psi_1(\Omega_2\uparrow\uparrow3))</math>
|<math>\psi(\Omega_2\uparrow\uparrow3)</math>
|(0)(1,1)(2,2)(3,2)(4,2)(5,2)
|-
|<math>\psi(\psi_1(\psi_2(\Omega_3)))=\psi(\psi_1(\varepsilon_{\Omega_2+1}))</math>
|<math>\psi(\Omega_3)</math>
|(0)(1,1)(2,2)(3,3)
|-
|<math>\psi(\psi_1(\psi_2(\Omega_3))\times2)</math>
|<math>\psi(\Omega_3+\psi_1(\Omega_3))</math>
|(0)(1,1)(2,2)(3,3)(1,1)(2,2)(3,3)
|-
|<math>\psi(\psi_1(\psi_2(\Omega_3)+1))</math>
|<math>\psi(\Omega_3+\psi_1(\Omega_3+1))</math>
|(0)(1,1)(2,2)(3,3)(2)
|-
|<math>\psi(\psi_1(\psi_2(\Omega_3)+\Omega_2))</math>
|<math>\psi(\Omega_3+\Omega_2)</math>
|(0)(1,1)(2,2)(3,3)(2,2)
|-
|<math>\psi(\psi_1(\psi_2(\Omega_3)\times2))</math>
|<math>\psi(\Omega_3+\psi_2(\Omega_3))</math>
|(0)(1,1)(2,2)(3,3)(2,2)(3,3)
|-
|<math>\psi(\psi_1(\psi_2(\Omega_3+1)))</math>
|<math>\psi(\Omega_3+\psi_2(\Omega_3+1))</math>
|(0)(1,1)(2,2)(3,3)(3)
|-
|<math>\psi(\psi_1(\psi_2(\Omega_3+\Omega_2)))</math>
|<math>\psi(\Omega_3+\psi_2(\Omega_3+\Omega_2))</math>
|(0)(1,1)(2,2)(3,3)(3,2)
|-
|<math>\psi(\psi_1(\psi_2(\Omega_3+\psi_2(\Omega_3))))</math>
|<math>\psi(\Omega_3+\psi_2(\Omega_3+\psi_2(\Omega_3)))</math>
|(0)(1,1)(2,2)(3,3)(3,2)(4,3)
|-
|<math>\psi(\psi_1(\psi_2(\Omega_32)))</math>
|<math>\psi(\Omega_32)</math>
|(0)(1,1)(2,2)(3,3)(3,3)
|-
|<math>\psi(\psi_1(\psi_2(\Omega_3\omega)))</math>
|<math>\psi(\Omega_3\omega)</math>
|(0)(1,1)(2,2)(3,3)(4)
|-
|<math>\psi(\psi_1(\psi_2(\Omega_3^2)))</math>
|<math>\psi(\Omega_3^2)</math>
|(0)(1,1)(2,2)(3,3)(4,3)
|-
|<math>\psi(\psi_1(\psi_2(\Omega_3^{\Omega_3})))</math>
|<math>\psi(\Omega_3^{\Omega_3})</math>
|(0)(1,1)(2,2)(3,3)(4,3)(5,3)
|-
|<math>\psi(\psi_1(\psi_2(\psi_3(\Omega_4))))</math>
|<math>\psi(\Omega_4)</math>
|(0)(1,1)(2,2)(3,3)(4,4)
|-
|<math>\psi(\psi_1(\psi_2(\psi_3(\psi_4(\Omega_5)))))</math>
|<math>\psi(\Omega_5)</math>
|(0)(1,1)(2,2)(3,3)(4,4)(5,5)
|-
|<math>\psi(\Omega_2)=\psi(\psi_1(\psi_2(\psi_3(\psi_4(...)))))</math>
|<math>\psi(\Omega_\omega)</math>
|(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。
{| class="wikitable"
|+分析2：BO~FBLO
!LPrSSψ
!BOCF
!BMS
|-
|<math>\psi(\Omega_2)</math>
|<math>\psi(\Omega_\omega)</math>
|(0)(1,1,1)
|-
|<math>\psi(\Omega_2+1)</math>
|<math>\psi(\Omega_\omega+1)</math>
|(0)(1,1,1)(1)
|-
|<math>\psi(\Omega_2+\Omega)</math>
|<math>\psi(\Omega_\omega+\Omega)</math>
|(0)(1,1,1)(1,1)
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_2))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_2))</math>
|(0)(1,1,1)(1,1)(2,2)
|-
|<math>\psi(\Omega_2+\psi_1(\psi_2(\Omega_3)))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_3))</math>
|(0)(1,1,1)(1,1)(2,2)(3,3)
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_3))=\psi(\Omega_2+\psi_1(\psi_2(\psi_3(...))))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_\omega))</math>
|(0)(1,1,1)(1,1)(2,2,1)
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_3)\times2)</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_\omega)\times2)</math>
|(0)(1,1,1)(1,1)(2,2,1)(1,1)(2,2,1)
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_3+1))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_\omega+1))</math>
|(0)(1,1,1)(1,1)(2,2,1)(2)
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_3+\Omega))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_\omega+\Omega))</math>
|(0)(1,1,1)(1,1)(2,2,1)(2,1)
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_3+\psi_1(\Omega_2)))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_\omega+\psi_1(\Omega_2)))</math>
|(0)(1,1,1)(1,1)(2,2,1)(2,1)(3,2)
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_3+\psi_1(\Omega_3)))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_\omega+\psi_1(\Omega_\omega)))</math>
|(0)(1,1,1)(1,1)(2,2,1)(2,1)(3,2,1)
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_3+\Omega_2))</math>
|<math>\psi(\Omega_\omega+\Omega_2)</math>
|(0)(1,1,1)(1,1)(2,2,1)(2,2)
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_3+\Omega_22))</math>
|<math>\psi(\Omega_\omega+\Omega_22)</math>
|(0)(1,1,1)(1,1)(2,2,1)(2,2)(2,2)
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_3+\Omega_2^2))</math>
|<math>\psi(\Omega_\omega+\Omega_2^2)</math>
|(0)(1,1,1)(1,1)(2,2,1)(2,2)(3,2)
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_3+\psi_2(\Omega_3)))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_3))</math>
|(0)(1,1,1)(1,1)(2,2,1)(2,2)(3,3)
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_3+\psi_2(\Omega_4)))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_\omega))</math>
|(0)(1,1,1)(1,1)(2,2,1)(2,2)(3,3,1)
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_3+\psi_2(\Omega_4+\Omega_3)))</math>
|<math>\psi(\Omega_\omega+\Omega_3)</math>
|(0)(1,1,1)(1,1)(2,2,1)(2,2)(3,3,1)(3,3)
|-
|<math>\psi(\Omega_2+\psi_1(\Omega_3+\psi_2(\Omega_4+\psi_3(\Omega_5))))</math>
|<math>\psi(\Omega_\omega+\psi_3(\Omega_\omega))</math>
|(0)(1,1,1)(1,1)(2,2,1)(2,2)(3,3,1)(3,3)(4,4,1)
|-
|<math>\psi(\Omega_22)=\psi(\Omega_2+\psi_1(\Omega_3+\psi_2(\Omega_4+\psi_3(\Omega_5+...))))</math>
|<math>\psi(\Omega_\omega2)</math>
|(0)(1,1,1)(1,1,1)
|-
|<math>\psi(\Omega_22+\psi_1(\Omega_3))</math>
|<math>\psi(\Omega_\omega2+\psi_1(\Omega_\omega))</math>
|(0)(1,1,1)(1,1,1)(1,1)(2,2,1)
|-
|<math>\psi(\Omega_22+\psi_1(\Omega_32))</math>
|<math>\psi(\Omega_\omega2+\psi_1(\Omega_\omega2))</math>
|(0)(1,1,1)(1,1,1)(1,1)(2,2,1)(2,2,1)
|-
|<math>\psi(\Omega_22+\psi_1(\Omega_32+\Omega_2))</math>
|<math>\psi(\Omega_\omega2+\Omega_2)</math>
|(0)(1,1,1)(1,1,1)(1,1)(2,2,1)(2,2,1)(2,2)
|-
|<math>\psi(\Omega_23)</math>
|<math>\psi(\Omega_\omega3)</math>
|(0)(1,1,1)(1,1,1)(1,1,1)
|-
|<math>\psi(\Omega_2\omega)</math>
|<math>\psi(\Omega_\omega\omega)</math>
|(0)(1,1,1)(2)
|-
|<math>\psi(\Omega_2\times(\omega+1))</math>
|<math>\psi(\Omega_\omega\times(\omega+1))</math>
|(0)(1,1,1)(2)(1,1,1)
|-
|<math>\psi(\Omega_2\times\psi(\Omega))</math>
|<math>\psi(\Omega_\omega\times\psi(\Omega))</math>
|(0)(1,1,1)(2)(3,1)
|-
|<math>\psi(\Omega_2\times\psi(\Omega_2))</math>
|<math>\psi(\Omega_\omega\times\psi(\Omega_\omega))</math>
|(0)(1,1,1)(2)(3,1,1)
|-
|<math>\psi(\Omega_2\Omega)</math>
|<math>\psi(\Omega_\omega\Omega)</math>
|(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)。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"
|+分析3：(0)(1,1,1)(2,1)~(0)(1,1,1)(2,1)(1,1,1)
!LPrSSψ
!BOCF
!BMS
|-
|<math>\psi(\Omega_2\Omega)</math>
|<math>\psi(\Omega_\omega\Omega)</math>
|(0)(1,1,1)(2,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_1(\Omega_\omega))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_1(\Omega_\omega\Omega))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega+1))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_1(\Omega_\omega\Omega+1))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega+\Omega))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_1(\Omega_\omega\Omega+\Omega))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega+\psi_1(\Omega_3\Omega)))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_1(\Omega_\omega\Omega+\psi_1(\Omega_\omega\Omega)))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(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+\Omega_2)</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega+\psi_2(\Omega_4)))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_2(\Omega_\omega))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,3,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega+\psi_2(\Omega_4\Omega)))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_2(\Omega_\omega\Omega))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,3,1)(4,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega+\psi_2(\Omega_4\Omega+\Omega_3)))</math>
|<math>\psi(\Omega_\omega\Omega+\Omega_3)</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,3,1)(4,1)(3,3)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\times(\Omega+1)))=\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega+\psi_2(\Omega_4\Omega+...)))</math>
|<math>\psi(\Omega_\omega\times(\Omega+1))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\times(\Omega+2)))</math>
|<math>\psi(\Omega_\omega\times(\Omega+2))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(2,2,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\times(\Omega+\omega)))</math>
|<math>\psi(\Omega_\omega\times(\Omega+\omega))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(3)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\times\Omega2))</math>
|<math>\psi(\Omega_\omega\times\Omega2)</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(3,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\times\Omega\omega))</math>
|<math>\psi(\Omega_\omega\times\Omega\omega)</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(3)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\times\Omega^2))</math>
|<math>\psi(\Omega_\omega\times\Omega^2)</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(3,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\times\Omega^\omega))</math>
|<math>\psi(\Omega_\omega\times\Omega^\omega)</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\times\Omega^\Omega))</math>
|<math>\psi(\Omega_\omega\times\Omega^\Omega)</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\times\psi_1(\Omega_2)))</math>
|<math>\psi(\Omega_\omega\times\psi_1(\Omega_2))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4,2)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\times\psi_1(\Omega_3)))</math>
|<math>\psi(\Omega_\omega\times\psi_1(\Omega_\omega))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4,2,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\times\psi_1(\Omega_3\times\psi_1(\Omega_3))))</math>
|<math>\psi(\Omega_\omega\times\psi_1(\Omega_\omega\times\psi_1(\Omega_\omega)))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4,2,1)(5,1)(6,2,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega_2))</math>
|<math>\psi(\Omega_\omega\Omega_2)</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega_2+\Omega_2))</math>
|<math>\psi(\Omega_\omega\Omega_2+\Omega_2)</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega_2+\psi_2(\Omega_3)))</math>
|<math>\psi(\Omega_\omega\Omega_2+\psi_2(\Omega_3))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega_2+\psi_2(\Omega_4)))</math>
|<math>\psi(\Omega_\omega\Omega_2+\psi_2(\Omega_\omega))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega_2+\psi_2(\Omega_4\Omega)))</math>
|<math>\psi(\Omega_\omega\Omega_2+\psi_2(\Omega_\omega\Omega))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega_2+\psi_2(\Omega_4\Omega_2)))</math>
|<math>\psi(\Omega_\omega\Omega_2+\psi_2(\Omega_\omega\Omega_2))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega_2+\psi_2(\Omega_4\Omega_2+\Omega_3)))</math>
|<math>\psi(\Omega_\omega\Omega_2+\Omega_3)</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)(3,3)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega_2+\psi_2(\Omega_4\times(\Omega_2+1))))</math>
|<math>\psi(\Omega_\omega\times(\Omega_2+1))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)(3,3,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega_2+\psi_2(\Omega_4\times\Omega_22)))</math>
|<math>\psi(\Omega_\omega\times\Omega_22)</math>
|(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)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega_2+\psi_2(\Omega_4\times\psi_2(\Omega_4))))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_\omega))</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)(5,3,1)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega_2+\psi_2(\Omega_4\Omega_3)))</math>
|<math>\psi(\Omega_\omega\Omega_3)</math>
|(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,3)
|-
|<math>\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega_2+\psi_2(\Omega_4\Omega_3+\psi_3(\Omega_5\Omega_4))))</math>
|<math>\psi(\Omega_\omega\Omega_4)</math>
|(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)
|-
|<math>\psi(\Omega_2\times(\Omega+1))=\psi(\Omega_2\Omega+\psi_1(\Omega_3\Omega_2+\psi_2(\Omega_4\Omega_3+...)))</math>
|<math>\psi(\Omega_\omega^2)</math>
|(0)(1,1,1)(2,1)(1,1,1)
|}
未完待续