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0Yψ vs 拓展HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影分析

2026-08-20T21:58:50Z

量子杰克：到0,1111,211

上篇：[[0Yψ vs HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影分析]]

== 分析1：(0)(1,1,1,1)~(0)(1,1,1,1)(2,1) ==
{| class="wikitable" style="white-space: nowrap;"
|+分析1：(0)(1,1,1,1)~(0)(1,1,1,1)(2,1)
!0Yψ
!强LPrSS投影
!拓展HPrSSψ
!弱LPrSS投影
!弱LPrSS向上投影
!BMS
|-
|<math>\psi(\Omega_3)</math>
|<math>\psi(a)</math>
|<math>\psi(\Omega_\omega)</math>
|<math>\psi(\sigma^\omega a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega))</math>
|(0)(1,1,1,1)
|-
|<math>\psi(\Omega_3+\Omega)</math>
|<math>\psi(a+\Omega)</math>
|<math>\psi(\Omega_\omega+\Omega)</math>
|<math>\psi(\sigma^\omega a+\Omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\Omega)</math>
|(0)(1,1,1,1)(1,1)
|-
|<math>\psi(\Omega_3+\psi_1(\Omega_3))</math>
|<math>\psi(a+\psi_1(\Omega_3))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_3))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\Omega_3))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\Omega_3))</math>
|(0)(1,1,1,1)(1,1)(2,2,1)
|-
|<math>\psi(\Omega_3+\psi_1(\psi_3(\Omega_5)))</math>
|<math>\psi(a+\psi_1(\Omega_4))</math>
|<math>\psi(\Omega_\omega+\psi_1(\psi_3(\Omega_5)))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\Omega_4))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\Omega_4))</math>
|(0)(1,1,1,1)(1,1)(2,2,1)(3,3,1)
|-
|<math>\psi(\Omega_3+\psi_1(\psi_3(\Omega_6)))</math>
|<math>\psi(a+\psi_1(\psi_a(a_2)))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_4))</math>
|<math>\psi(\sigma^\omega a+\psi_1(a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(a))</math>
|(0)(1,1,1,1)(1,1)(2,2,1)(3,3,2)
|-
|<math>\psi(\Omega_3+\psi_1(\psi_3(\psi_6(\Omega_{10}))))</math>
|<math>\psi(a+\psi_1(\psi_a(\psi_{\sigma a}(\sigma a_2))))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_5))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\sigma a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\psi_S(\sigma S\times3)))</math>
|(0)(1,1,1,1)(1,1)(2,2,1)(3,3,2)(4,4,3)
|-
|<math>\psi(\Omega_3+\psi_1(\Omega_4))</math>
|<math>\psi(a+\psi_1(a))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(1,1)(2,2,1,1)
|-
|<math>\psi(\Omega_3+\psi_1(\Omega_4+\Omega_2))</math>
|<math>\psi(a+\psi_1(a+\Omega_2))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_\omega+\Omega_2))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\sigma^\omega a+\Omega_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\psi_S(\sigma S\times\omega)+\Omega_2))</math>
|(0)(1,1,1,1)(1,1)(2,2,1,1)(2,2)
|-
|<math>\psi(\Omega_3+\psi_1(\Omega_4+\psi_2(\Omega_5)))</math>
|<math>\psi(a+\psi_1(a+\psi_2(a)))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_\omega+\psi_2(\Omega_\omega)))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\sigma^\omega a+\psi_2(\sigma^\omega a)))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\psi_S(\sigma S\times\omega)+\psi_2(\psi_S(\sigma S\times\omega))))</math>
|(0)(1,1,1,1)(1,1)(2,2,1,1)(2,2)(3,3,1,1)
|-
|<math>\psi(\Omega_3+\Omega_2)</math>
|<math>\psi(a+\Omega_2)</math>
|<math>\psi(\Omega_\omega+\Omega_2)</math>
|<math>\psi(\sigma^\omega a+\Omega_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\Omega_2)</math>
|(0)(1,1,1,1)(1,1,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_4))</math>
|<math>\psi(a+\Omega_3)</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_4))</math>
|<math>\psi(\sigma^\omega a+\Omega_3)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\Omega_3)</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_4\omega))</math>
|<math>\psi(a+\Omega_\omega)</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_4\omega))</math>
|<math>\psi(\sigma^\omega a+\Omega_\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\Omega_\omega)</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)(3)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_4\Omega_3))</math>
|<math>\psi(a+\psi_a(\Omega_{a+1}a))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_4\Omega_3))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\Omega_{a+1}a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\Omega_{a+1}a))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)(3,2)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_4^2))</math>
|<math>\psi(a+\psi_a(\Omega_{a+1}^2))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_4^2))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\Omega_{a+1}^2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\Omega_{a+1}^2))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)(3,2,1)
|-
|<math>\psi(\Omega_3+\psi_2(\psi_4(\Omega_5)))</math>
|<math>\psi(a+\psi_a(\varepsilon_{\Omega_{a+1}+1}))</math>
|<math>\psi(\Omega_\omega+\psi_2(\psi_4(\Omega_5)))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\varepsilon_{\Omega_{a+1}+1}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\varepsilon_{\Omega_{a+1}+1}))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)(3,3)
|-
|<math>\psi(\Omega_3+\psi_2(\psi_4(\Omega_6)))</math>
|<math>\psi(a+\psi_a(\Omega_{a+2}))</math>
|<math>\psi(\Omega_\omega+\psi_2(\psi_4(\Omega_6)))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\Omega_{a+2}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\Omega_{a+2}))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)(3,3,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_5))</math>
|<math>\psi(a+\psi_a(a_2))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_5))</math>
|<math>\psi(\sigma^\omega a+\psi_a(a_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(a_2))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2)
|-
|<math>\psi(\Omega_3+\psi_2(\psi_5(\Omega_8)))</math>
|<math>\psi(a+\psi_a(a_3))</math>
|<math>\psi(\Omega_\omega+\psi_2(\psi_5(\Omega_8)))</math>
|<math>\psi(\sigma^\omega a+\psi_a(a_3))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(a_3))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2)(3,3,2)
|-
|<math>\psi(\Omega_3+\psi_2(\psi_5(\Omega_9)))</math>
|<math>\psi(a+\psi_a(\psi_{\sigma a}(\sigma a_2)))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_6))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\sigma a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\psi_S(\sigma S\times3)))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2)(3,3,3)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6))</math>
|<math>\psi(a+\psi_a(\sigma a))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\Omega_4))</math>
|<math>\psi(a+\psi_a(\sigma a+\Omega_{a+1}))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_\omega+\Omega_4))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\sigma^\omega a+\Omega_{a+1}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\psi_S(\sigma S\times\omega)+\Omega_{a+1}))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_4(\Omega_8)))</math>
|<math>\psi(a+\psi_a(\sigma a+\psi_{a_2}(\sigma a)))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_\omega+\psi_4(\Omega_\omega)))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\sigma^\omega a+\psi_{a_2}(\sigma^\omega a)))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\psi_S(\sigma S\times\omega)+\psi_{a_2}(\psi_S(\sigma S\times\omega))))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,1)(3,3,2,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\Omega_5))</math>
|<math>\psi(a+\psi_a(\sigma a+a_2))</math>
|<math>\psi(\Omega_\omega+\Omega_3)</math>
|<math>\psi(\sigma^\omega a+a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+a)</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_5(\Omega_8)))</math>
|<math>\psi(a+\psi_a(\sigma a+a_3))</math>
|<math>\psi(\Omega_\omega+\psi_3(\Omega_6))</math>
|<math>\psi(\sigma^\omega a+a_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+a_2)</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,2)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_5(\Omega_9)))</math>
|<math>\psi(a+\psi_a(\sigma a+\psi_{\sigma a}(\sigma a_2)))</math>
|<math>\psi(\Omega_\omega+\psi_3(\Omega_7))</math>
|<math>\psi(\sigma^\omega a+\psi_{\sigma a}(\sigma a_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_S(\sigma S\times2+S_2))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,3)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_5(\Omega_{10})))</math>
|<math>\psi(a+\psi_a(\sigma a+\psi_{\sigma a}(\sigma^2a)))</math>
|<math>\psi(\Omega_\omega+\psi_3(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a+\psi_{\sigma a}(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_{\psi_S(\sigma S\times3)}(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,3,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_5(\Omega_{10}+\Omega_9)))</math>
|<math>\psi(a+\psi_a(\sigma a+\psi_{\sigma a}(\sigma^2a+\sigma a_2)))</math>
|<math>\psi(\Omega_\omega+\Omega_4)</math>
|<math>\psi(\sigma^\omega a+\sigma a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_S(\sigma S\times3))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,3,1)(3,3,3)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_5(\Omega_{10}+\psi_9(\Omega_{15}))))</math>
|<math>\psi(a+\psi_a(\sigma a+\psi_{\sigma a}(\sigma^2a+\psi_{\sigma^2a}(\sigma^3a))))</math>
|<math>\psi(\Omega_\omega+\psi_4(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a+\psi_{\sigma^2a}(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_{\psi_S(\sigma S\times4)}(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,3,1)(3,3,3)(4,4,4,1)
|-
|<math>\psi(\Omega_32)</math>
|<math>\psi(a2)</math>
|<math>\psi(\Omega_\omega2)</math>
|<math>\psi(\sigma^\omega a2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times2)</math>
|(0)(1,1,1,1)(1,1,1,1)
|-
|<math>\psi(\Omega_32+\Omega_2)</math>
|<math>\psi(a2+\Omega_2)</math>
|<math>\psi(\Omega_\omega2+\Omega_2)</math>
|<math>\psi(\sigma^\omega a2+\Omega_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times2+\Omega_2)</math>
|(0)(1,1,1,1)(1,1,1,1)(1,1,1)
|-
|<math>\psi(\Omega_32+\psi_2(\Omega_6))</math>
|<math>\psi(a2+\psi_a(\sigma a))</math>
|<math>\psi(\Omega_\omega2+\psi_2(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a2+\psi_a(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times2+\psi_a(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(1,1,1,1)(1,1,1)(2,2,2,1)
|-
|<math>\psi(\Omega_32+\psi_2(\Omega_62))</math>
|<math>\psi(a2+\psi_a(\sigma a2))</math>
|<math>\psi(\Omega_\omega2+\psi_2(\Omega_\omega2))</math>
|<math>\psi(\sigma^\omega a2+\psi_a(\sigma^\omega a2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times2+\psi_a(\psi_S(\sigma S\times\omega)\times2))</math>
|(0)(1,1,1,1)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2,1)
|-
|<math>\psi(\Omega_32+\psi_2(\Omega_62+\Omega_5))</math>
|<math>\psi(a2+\psi_a(\sigma a2+a_2))</math>
|<math>\psi(\Omega_\omega2+\Omega_3)</math>
|<math>\psi(\sigma^\omega a2+a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times2+a)</math>
|(0)(1,1,1,1)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2,1)(2,2,2)
|-
|<math>\psi(\Omega_33)</math>
|<math>\psi(a3)</math>
|<math>\psi(\Omega_\omega3)</math>
|<math>\psi(\sigma^\omega a3)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times3)</math>
|(0)(1,1,1,1)(1,1,1,1)(1,1,1,1)
|-
|<math>\psi(\Omega_3\omega)</math>
|<math>\psi(a\omega)</math>
|<math>\psi(\Omega_\omega\omega)</math>
|<math>\psi(\sigma^\omega a\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\omega)</math>
|(0)(1,1,1,1)(2)
|-
|<math>\psi(\Omega_3\times(\omega+1))</math>
|<math>\psi(a\times(\omega+1))</math>
|<math>\psi(\Omega_\omega\times(\omega+1))</math>
|<math>\psi(\sigma^\omega a\times(\omega+1))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times(\omega+1))</math>
|(0)(1,1,1,1)(2)(1,1,1,1)
|-
|<math>\psi(\Omega_3\times\omega2)</math>
|<math>\psi(a\times\omega2)</math>
|<math>\psi(\Omega_\omega\times\omega2)</math>
|<math>\psi(\sigma^\omega a\times\omega2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\omega2)</math>
|(0)(1,1,1,1)(2)(1,1,1,1)(2)
|-
|<math>\psi(\Omega_3\times\omega^2)</math>
|<math>\psi(a\times\omega^2)</math>
|<math>\psi(\Omega_\omega\times\omega^2)</math>
|<math>\psi(\sigma^\omega a\times\omega^2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\omega^2)</math>
|(0)(1,1,1,1)(2)(2)
|-
|<math>\psi(\Omega_3\times\omega^\omega)</math>
|<math>\psi(a\times\omega^\omega)</math>
|<math>\psi(\Omega_\omega\times\omega^\omega)</math>
|<math>\psi(\sigma^\omega a\times\omega^\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\omega^\omega)</math>
|(0)(1,1,1,1)(2)(3)
|-
|<math>\psi(\Omega_3\times\varepsilon_0)</math>
|<math>\psi(a\times\varepsilon_0)</math>
|<math>\psi(\Omega_\omega\times\varepsilon_0)</math>
|<math>\psi(\sigma^\omega a\times\varepsilon_0)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\varepsilon_0)</math>
|(0)(1,1,1,1)(2)(3,1)
|-
|<math>\psi(\Omega_3\times\psi(\Omega_2))</math>
|<math>\psi(a\times\psi(\Omega_2))</math>
|<math>\psi(\Omega_\omega\times\psi(\Omega_2))</math>
|<math>\psi(\sigma^\omega a\times\psi(\Omega_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi(\Omega_2))</math>
|(0)(1,1,1,1)(2)(3,1,1)
|-
|<math>\psi(\Omega_3\times\psi(\Omega_3))</math>
|<math>\psi(a\times\psi(a))</math>
|<math>\psi(\Omega_\omega\times\psi(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a\times\psi(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2)(3,1,1,1)
|-
|<math>\psi(\Omega_3\Omega)</math>
|<math>\psi(a\Omega)</math>
|<math>\psi(\Omega_\omega\Omega)</math>
|<math>\psi(\sigma^\omega a\Omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega)</math>
|(0)(1,1,1,1)(2,1)
|}

== 分析2：(0)(1,1,1,1)(2,1)~(0)(1,1,1,1)(2,1)(1,1,1,1) ==
{| class="wikitable" style="white-space: nowrap;"
|+分析2：(0)(1,1,1,1)(2,1)~(0)(1,1,1,1)(2,1)(1,1,1,1)
!0Yψ
!强LPrSS投影
!拓展HPrSSψ
!弱LPrSS投影
!弱LPrSS向上投影
!BMS
|-
|<math>\psi(\Omega_3\Omega)</math>
|<math>\psi(a\Omega)</math>
|<math>\psi(\Omega_\omega\Omega)</math>
|<math>\psi(\sigma^\omega a\Omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega)</math>
|(0)(1,1,1,1)(2,1)
|-
|<math>\psi(\Omega_3\Omega+\Omega)</math>
|<math>\psi(a\Omega+\Omega)</math>
|<math>\psi(\Omega_\omega\Omega+\Omega)</math>
|<math>\psi(\sigma^\omega a\Omega+\Omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\Omega)</math>
|(0)(1,1,1,1)(2,1)(1,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_1(\Omega_4))</math>
|<math>\psi(a\Omega+\psi_1(a))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_1(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a\Omega+\psi_1(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_1(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(1,1)(2,2,1,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_1(\Omega_4\Omega))</math>
|<math>\psi(a\Omega+\psi_1(a\Omega))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_1(\Omega_\omega\Omega))</math>
|<math>\psi(\sigma^\omega a\Omega+\psi_1(\sigma^\omega a\Omega))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_1(\psi_S(\sigma S\times\omega)\times\Omega))</math>
|(0)(1,1,1,1)(2,1)(1,1)(2,2,1,1)(3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_1(\Omega_4\Omega_2))</math>
|<math>\psi(a\Omega+\psi_1(a\Omega_2))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_1(\Omega_\omega\Omega_2))</math>
|<math>\psi(\sigma^\omega a\Omega+\psi_1(\sigma^\omega a\Omega_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_1(\psi_S(\sigma S\times\omega)\times\Omega_2))</math>
|(0)(1,1,1,1)(2,1)(1,1)(2,2,1,1)(3,2)
|-
|<math>\psi(\Omega_3\Omega+\Omega_2)</math>
|<math>\psi(a\Omega+\Omega_2)</math>
|<math>\psi(\Omega_\omega\Omega+\Omega_2)</math>
|<math>\psi(\sigma^\omega a\Omega+\Omega_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\Omega_2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_4))</math>
|<math>\psi(a\Omega+\Omega_3)</math>
|<math>\psi(\Omega_\omega\Omega+\psi_2(\Omega_4))</math>
|<math>\psi(\sigma^\omega a\Omega+\Omega_3)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\Omega_3)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_5))</math>
|<math>\psi(a\Omega+\psi_a(a_2))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_2(\Omega_5))</math>
|<math>\psi(\sigma^\omega a\Omega+\psi_a(a_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_a(a_2))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\psi_5(\Omega_9)))</math>
|<math>\psi(a\Omega+\psi_a(\psi_{\sigma a}(\sigma a_2)))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_2(\Omega_6))</math>
|<math>\psi(\sigma^\omega a\Omega+\psi_a(\sigma a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_a(\psi_S(\sigma S\times3)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2)(3,3,3)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_2(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a\Omega+\psi_a(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_a(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\Omega))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_2(\Omega_\omega\Omega))</math>
|<math>\psi(\sigma^\omega a\Omega+\psi_a(\sigma^\omega a\Omega))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_a(\psi_S(\sigma S\times\omega)\times\Omega))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega+\Omega_5))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\Omega+a_2))</math>
|<math>\psi(\Omega_\omega\Omega+\Omega_3)</math>
|<math>\psi(\sigma^\omega a\Omega+a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+a)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(2,2,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega+\psi_5(\Omega_{10}\Omega)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\Omega+\psi_{\sigma a}(\sigma^2 a\Omega)))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_3(\Omega_\omega\Omega))</math>
|<math>\psi(\sigma^\omega a\Omega+\psi_{\sigma a}(\sigma^\omega a\Omega))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_{\psi_S(\sigma S\times3)}(\psi_S(\sigma S\times\omega)\times\Omega))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(2,2,2)(3,3,3,1)(4,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega+\psi_5(\Omega_{10}\Omega+\Omega_9)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\Omega+\psi_{\sigma a}(\sigma^2 a\Omega+\sigma a_2)))</math>
|<math>\psi(\Omega_\omega\Omega+\Omega_4)</math>
|<math>\psi(\sigma^\omega a\Omega+\sigma a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_S(\sigma S\times3))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(2,2,2)(3,3,3,1)(4,1)(3,3,3)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times(\Omega+1)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times(\Omega+1)))</math>
|<math>\psi(\Omega_\omega\times(\Omega+1))</math>
|<math>\psi(\sigma^\omega a\times(\Omega+1))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times(\Omega+1))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times(\Omega+2)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times(\Omega+2)))</math>
|<math>\psi(\Omega_\omega\times(\Omega+2))</math>
|<math>\psi(\sigma^\omega a\times(\Omega+2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times(\Omega+2))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(2,2,2,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\Omega2))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\Omega2))</math>
|<math>\psi(\Omega_\omega\times\Omega2)</math>
|<math>\psi(\sigma^\omega a\times\Omega2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(2,2,2,1)(3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\Omega^2))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\Omega^2))</math>
|<math>\psi(\Omega_\omega\times\Omega^2)</math>
|<math>\psi(\sigma^\omega a\times\Omega^2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega^2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_1(\Omega_2)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_1(\Omega_2)))</math>
|<math>\psi(\Omega_\omega\times\psi_1(\Omega_2))</math>
|<math>\psi(\sigma^\omega a\times\psi_1(\Omega_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_1(\Omega_2))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(4,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_1(\Omega_3)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_1(\Omega_3)))</math>
|<math>\psi(\Omega_\omega\times\psi_1(\Omega_3))</math>
|<math>\psi(\sigma^\omega a\times\psi_1(\Omega_3))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_1(\Omega_3))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(4,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_1(\psi_3(\Omega_5))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_1(\Omega_4)))</math>
|<math>\psi(\Omega_\omega\times\psi_1(\psi_3(\Omega_5)))</math>
|<math>\psi(\sigma^\omega a\times\psi_1(\Omega_4))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_1(\Omega_4))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(4,2,1)(5,3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_1(\psi_3(\Omega_6))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_1(\psi_a(a_2))))</math>
|<math>\psi(\Omega_\omega\times\psi_1(\Omega_4))</math>
|<math>\psi(\sigma^\omega a\times\psi_1(a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_1(a))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(4,2,1)(5,3,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_1(\Omega_4)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_1(a)))</math>
|<math>\psi(\Omega_\omega\times\psi_1(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a\times\psi_1(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_1(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(4,2,1,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_2))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\Omega_2))</math>
|<math>\psi(\Omega_\omega\Omega_2)</math>
|<math>\psi(\sigma^\omega a\Omega_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega_2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times(\Omega_2+1)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times(\Omega_2+1)))</math>
|<math>\psi(\Omega_\omega\times(\Omega_2+1))</math>
|<math>\psi(\sigma^\omega a\times(\Omega_2+1))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times(\Omega_2+1))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\Omega_3)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_2(\Omega_3)))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_3))</math>
|<math>\psi(\sigma^\omega a\times\psi_2(\Omega_3))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_2(\Omega_3))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\Omega_4)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\Omega_3))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_4))</math>
|<math>\psi(\sigma^\omega a\Omega_3)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega_3)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\Omega_4\omega)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\Omega_\omega))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_4\omega))</math>
|<math>\psi(\sigma^\omega a\Omega_\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega_\omega)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,1)(5)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\Omega_4\Omega_3)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_a(\Omega_{a+1}a)))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_4\Omega_3))</math>
|<math>\psi(\sigma^\omega a\times\psi_a(\Omega_{a+1}a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_a(\Omega_{a+1}a))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,1)(5,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\Omega_4^2)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_a(\Omega_{a+1}^2)))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_4^2))</math>
|<math>\psi(\sigma^\omega a\times\psi_a(\Omega_{a+1}^2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_a(\Omega_{a+1}^2))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,1)(5,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\psi_4(\Omega_5))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_a(\varepsilon_{\Omega_{a+1}+1})))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\psi_4(\Omega_5)))</math>
|<math>\psi(\sigma^\omega a\times\psi_a(\varepsilon_{\Omega_{a+1}+1}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_a(\varepsilon_{\Omega_{a+1}+1}))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,1)(5,3)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\psi_4(\Omega_6))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_a(\Omega_{a+2})))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\psi_4(\Omega_6)))</math>
|<math>\psi(\sigma^\omega a\times\psi_a(\Omega_{a+2}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_a(\Omega_{a+2}))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,1)(5,3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\Omega_5)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_a(a_2)))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_5))</math>
|<math>\psi(\sigma^\omega a\times\psi_a(a_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_a(a_2))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\psi_5(\Omega_9))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_a(\psi_{\sigma a}(\sigma a_2))))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_6))</math>
|<math>\psi(\sigma^\omega a\times\psi_a(\sigma a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_a(\psi_S(\sigma S\times3)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,2)(5,3,3)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\Omega_6)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_a(\sigma a)))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a\times\psi_a(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_a(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa))</math>
|<math>\psi(\Omega_\omega\Omega_3)</math>
|<math>\psi(\sigma^\omega aa)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times a)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\Omega_5))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+a_2))</math>
|<math>\psi(\Omega_\omega\Omega_3+\Omega_3)</math>
|<math>\psi(\sigma^\omega aa+a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times a+a)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10})))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2a)))</math>
|<math>\psi(\Omega_\omega\Omega_3+\psi_3(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega aa+\psi_{\sigma a}(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times a+\psi_{\psi_S(\sigma S\times3)}(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\Omega_3)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2aa)))</math>
|<math>\psi(\Omega_\omega\Omega_3+\psi_3(\Omega_\omega\Omega_3))</math>
|<math>\psi(\sigma^\omega aa+\psi_{\sigma a}(\sigma^\omega aa))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times a+\psi_{\psi_S(\sigma S\times3)}(\psi_S(\sigma S\times\omega)\times a))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\Omega_3+\Omega_9)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2aa+\sigma a)))</math>
|<math>\psi(\Omega_\omega\Omega_3+\Omega_4)</math>
|<math>\psi(\sigma^\omega aa+\sigma a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times a+\psi_S(\sigma S\times3))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,2)(3,3,3)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\times(\Omega_3+1))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2a\times(a+1))))</math>
|<math>\psi(\Omega_\omega\times(\Omega_3+1))</math>
|<math>\psi(\sigma^\omega a\times(a+1))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times(a+1))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,2)(3,3,3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\times\psi_3(\Omega_4))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2a\times\varepsilon_{a+1})))</math>
|<math>\psi(\Omega_\omega\times\psi_3(\Omega_4))</math>
|<math>\psi(\sigma^\omega a\times\varepsilon_{a+1})</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\varepsilon_{a+1})</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,2)(5,3)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\Omega_4)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2a\times\Omega_{a+1})))</math>
|<math>\psi(\Omega_\omega\times\psi_3(\Omega_5))</math>
|<math>\psi(\sigma^\omega a\times\Omega_{a+1})</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega_{a+1})</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\Omega_5)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2a\times a_2)))</math>
|<math>\psi(\Omega_\omega\times\psi_3(\Omega_6))</math>
|<math>\psi(\sigma^\omega a\times a_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times a_2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,2,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\times\psi_5(\Omega_{10}))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2a\times\psi_{\sigma a}(\sigma^2a))))</math>
|<math>\psi(\Omega_\omega\times\psi_3(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a\times\psi_{\sigma a}(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_{\psi_S(\sigma S\times3)}(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,2,2)(5,3,3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\Omega_6)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2a\sigma a)))</math>
|<math>\psi(\Omega_\omega\Omega_4)</math>
|<math>\psi(\sigma^\omega a\sigma a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times \psi_S(\sigma S\times3))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,3)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\Omega_6+\psi_9(\Omega_{15}\Omega_{10}))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2 a\sigma a+\psi_{\sigma^2a}(\sigma^3a\sigma^2a))))</math>
|<math>\psi(\Omega_\omega\Omega_5)</math>
|<math>\psi(\sigma^\omega a\sigma^2a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times \psi_S(\sigma S\times4))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,3)(3,3,3)(4,4,4,1)(5,4)
|-
|<math>\psi(\Omega_3\times(\Omega+1))</math>
|<math>\psi(a\times(\Omega+1))</math>
|<math>\psi(\Omega_\omega^2)</math>
|<math>\psi(\sigma^\omega a^2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)
|}

== 分析3：(0)(1,1,1,1)(2,1)(1,1,1,1)~(0)(1,1,1,1)(2,1)(3,2) ==
{| class="wikitable" style="white-space: nowrap;"
|+分析3：(0)(1,1,1,1)(2,1)(1,1,1,1)~(0)(1,1,1,1)(2,1)(3,2)
!0Yψ
!强LPrSS投影
!拓展HPrSSψ
!弱LPrSS投影
!弱LPrSS向上投影
!BMS
|-
|<math>\psi(\Omega_3\times(\Omega+1))</math>
|<math>\psi(a\times(\Omega+1))</math>
|<math>\psi(\Omega_\omega^2)</math>
|<math>\psi(\sigma^\omega a^2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)
|-
|<math>\psi(\Omega_3\times(\Omega+2))</math>
|<math>\psi(a\times(\Omega+2))</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega)</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega))</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(1,1,1,1)
|-
|<math>\psi(\Omega_3\times(\Omega+\omega))</math>
|<math>\psi(a\times(\Omega+\omega))</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\omega)</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times\omega)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2)
|-
|<math>\psi(\Omega_3\times\Omega2)</math>
|<math>\psi(a\times\Omega2)</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega)</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a\Omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times\Omega)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)
|-
|<math>\psi(\Omega_3\times\Omega2+\Omega_2)</math>
|<math>\psi(a\times\Omega2+\Omega_2)</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega+\Omega_2)</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a\Omega+\Omega_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times\Omega+\Omega_2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)(1,1,1)
|-
|<math>\psi(\Omega_3\times\Omega2+\psi_2(\Omega_6))</math>
|<math>\psi(a\times\Omega2+\psi_a(\sigma a))</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega+\psi_2(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a\Omega+\psi_a(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times\Omega+\psi_a(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3\times\Omega2+\psi_2(\Omega_6\times(\Omega_3+\Omega)))</math>
|<math>\psi(a\times\Omega2+\psi_a(\sigma a\times(a+\Omega)))</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega+\psi_2(\Omega_\omega^2+\Omega_\omega\Omega))</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a\Omega+\psi_a(\sigma^\omega a^2+\sigma^\omega a\Omega))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times\Omega+\psi_a(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2,1)(3,1)
|-
|<math>\psi(\Omega_3\times\Omega2+\psi_2(\Omega_6\times(\Omega_3+\Omega)+\Omega_5))</math>
|<math>\psi(a\times\Omega2+\psi_a(\sigma a\times(a+\Omega)+a_2))</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega+\Omega_3)</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a\Omega+a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times\Omega+a)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2,1)(3,1)(2,2,2)
|-
|<math>\psi(\Omega_3\times\Omega2+\psi_2(\Omega_6\times(\Omega_3+\Omega+1)))</math>
|<math>\psi(a\times\Omega2+\psi_a(\sigma a\times(a+\Omega+1)))</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\times(\Omega+1))</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a\times(\Omega+1))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times(\Omega+1))</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2,1)(3,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3\times\Omega2+\psi_2(\Omega_6\times(\Omega_3+\Omega_2)))</math>
|<math>\psi(a\times\Omega2+\psi_a(\sigma a\times(a+\Omega_2)))</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega_2)</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a\Omega_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times\Omega_2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2,1)(3,1,1)
|-
|<math>\psi(\Omega_3\times\Omega2+\psi_2(\Omega_6\times\Omega_32))</math>
|<math>\psi(a\times\Omega2+\psi_a(\sigma a\times a2))</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega_3)</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega aa)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times a)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2,1)(3,2)
|-
|<math>\psi(\Omega_3\times(\Omega2+1))</math>
|<math>\psi(a\times(\Omega2+1))</math>
|<math>\psi(\Omega_\omega^22)</math>
|<math>\psi(\sigma^\omega a^22)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2\times2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)(1,1,1,1)
|-
|<math>\psi(\Omega_3\times\Omega\omega)</math>
|<math>\psi(a\times\Omega\omega)</math>
|<math>\psi(\Omega_\omega^2\omega)</math>
|<math>\psi(\sigma^\omega a^2\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2\times\omega)</math>
|(0)(1,1,1,1)(2,1)(2)
|-
|<math>\psi(\Omega_3\times\Omega^2)</math>
|<math>\psi(a\times\Omega^2)</math>
|<math>\psi(\Omega_\omega^2\Omega)</math>
|<math>\psi(\sigma^\omega a^2\Omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2\times\Omega)</math>
|(0)(1,1,1,1)(2,1)(2,1)
|-
|<math>\psi(\Omega_3\times\Omega^2+\psi_2(\Omega_6\times(\Omega_3\Omega+1)))</math>
|<math>\psi(a\times\Omega^2+\psi_a(\sigma a\times(a\Omega+1)))</math>
|<math>\psi(\Omega_\omega^2\Omega+\Omega_\omega)</math>
|<math>\psi(\sigma^\omega a^2\Omega+\sigma^\omega a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2\times\Omega+\psi_S(\sigma S\times\omega))</math>
|(0)(1,1,1,1)(2,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(3,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3\times\Omega^2+\psi_2(\Omega_6\times\Omega_3\Omega_2))</math>
|<math>\psi(a\times\Omega^2+\psi_a(\sigma a\times a\Omega_2))</math>
|<math>\psi(\Omega_\omega^2\Omega_2)</math>
|<math>\psi(\sigma^\omega a^2\Omega_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2\times\Omega_2)</math>
|(0)(1,1,1,1)(2,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(3,1,1)
|-
|<math>\psi(\Omega_3\times\Omega^2+\psi_2(\Omega_6\times\Omega_3^2))</math>
|<math>\psi(a\times\Omega^2+\psi_a(\sigma a\times a^2))</math>
|<math>\psi(\Omega_\omega^2\Omega_3)</math>
|<math>\psi(\sigma^\omega a^2a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2\times a)</math>
|(0)(1,1,1,1)(2,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(3,2)
|-
|<math>\psi(\Omega_3\times(\Omega^2+1))</math>
|<math>\psi(a\times(\Omega^2+1))</math>
|<math>\psi(\Omega_\omega^3)</math>
|<math>\psi(\sigma^\omega a^3)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^3)</math>
|(0)(1,1,1,1)(2,1)(2,1)(1,1,1,1)
|-
|<math>\psi(\Omega_3\times\Omega^\omega)</math>
|<math>\psi(a\times\Omega^\omega)</math>
|<math>\psi(\Omega_\omega^\omega)</math>
|<math>\psi(\sigma^\omega a^\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^\omega)</math>
|(0)(1,1,1,1)(2,1)(3)
|-
|<math>\psi(\Omega_3\times\Omega^\Omega)</math>
|<math>\psi(a\times\Omega^\Omega)</math>
|<math>\psi(\Omega_\omega^\Omega)</math>
|<math>\psi(\sigma^\omega a^\Omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^\Omega)</math>
|(0)(1,1,1,1)(2,1)(3,1)
|-
|<math>\psi(\Omega_3\times\Omega^\Omega+\psi_2(\Omega_6\times(\Omega_3^\Omega+1)))</math>
|<math>\psi(a\times\Omega^\Omega+\psi_a(\sigma a\times(a^\Omega+1)))</math>
|<math>\psi(\Omega_\omega^\Omega+\Omega_\omega)</math>
|<math>\psi(\sigma^\omega a^\Omega+\sigma^\omega a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^\Omega+\psi_S(\sigma S\times\omega))</math>
|(0)(1,1,1,1)(2,1)(3,1)(1,1,1)(2,2,2,1)(3,2)(4,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3\times\Omega^\Omega+\psi_2(\Omega_6\times\Omega_3^{\Omega_2}))</math>
|<math>\psi(a\times\Omega^\Omega+\psi_a(\sigma a\times a^{\Omega_2}))</math>
|<math>\psi(\Omega_\omega^{\Omega_2})</math>
|<math>\psi(\sigma^\omega a^{\Omega_2})</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^{\Omega_2})</math>
|(0)(1,1,1,1)(2,1)(3,1)(1,1,1)(2,2,2,1)(3,2)(4,1,1)
|-
|<math>\psi(\Omega_3\times\Omega^\Omega+\psi_2(\Omega_6\times\Omega_3^{\Omega_3}))</math>
|<math>\psi(a\times\Omega^\Omega+\psi_a(\sigma a\times a^a))</math>
|<math>\psi(\Omega_\omega^{\Omega_3})</math>
|<math>\psi(\sigma^\omega a^a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^a)</math>
|(0)(1,1,1,1)(2,1)(3,1)(1,1,1)(2,2,2,1)(3,2)(4,2)
|-
|<math>\psi(\Omega_3\times(\Omega^\Omega+1))</math>
|<math>\psi(a\times(\Omega^\Omega+1))</math>
|<math>\psi(\Omega_\omega^{\Omega_\omega})</math>
|<math>\psi(\sigma^\omega a^{\sigma^\omega a})</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^{\psi_S(\sigma S\times\omega)})</math>
|(0)(1,1,1,1)(2,1)(3,1)(1,1,1,1)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_2))</math>
|<math>\psi(a\times\psi_1(\Omega_2))</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1}))=\psi(\varepsilon_{\Omega_\omega+1})</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}))=\psi(\varepsilon_{\sigma^\omega a+1})</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S))</math>
|(0)(1,1,1,1)(2,1)(3,2)
|}

== 分析4：(0)(1,1,1,1)(2,1)(3,2)~(0)(1,1,1,1)(2,1,1) ==
{| class="wikitable" style="white-space: nowrap;"
|+分析4：(0)(1,1,1,1)(2,1)(3,2)~(0)(1,1,1,1)(2,1,1)
!0Yψ
!强LPrSS投影
!拓展HPrSSψ
!弱LPrSS投影
!弱LPrSS向上投影
!BMS
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_2))</math>
|<math>\psi(a\times\psi_1(\Omega_2))</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1}))=\psi(\varepsilon_{\Omega_\omega+1})</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}))=\psi(\varepsilon_{\sigma^\omega a+1})</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S))</math>
|(0)(1,1,1,1)(2,1)(3,2)
|-
|<math>\psi(\Omega_3\times(\psi_1(\Omega_2)+1))</math>
|<math>\psi(a\times(\psi_1(\Omega_2)+1))</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1})+\Omega_\omega)</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1})+\sigma^\omega a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S)+\psi_S(\sigma S\times\omega))</math>
|(0)(1,1,1,1)(2,1)(3,2)(1,1,1,1)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_2)\times2)</math>
|<math>\psi(a\times\psi_1(\Omega_2)\times2)</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1})\times2)</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1})\times2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S)\times2)</math>
|(0)(1,1,1,1)(2,1)(3,2)(1,1,1,1)(2,1)(3,2)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_2+1))</math>
|<math>\psi(a\times\psi_1(\Omega_2+1))</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1}+1))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}+1))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S+1))</math>
|(0)(1,1,1,1)(2,1)(3,2)(2)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_2+\Omega))</math>
|<math>\psi(a\times\psi_1(\Omega_2+\Omega))</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1}+\Omega))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}+\Omega))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S+\Omega))</math>
|(0)(1,1,1,1)(2,1)(3,2)(2,1)
|-
|<math>\psi(\Omega_3\times(\psi_1(\Omega_2+\Omega)+1))</math>
|<math>\psi(a\times(\psi_1(\Omega_2+\Omega)+1))</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1}+\Omega_\omega))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}+\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S+\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(3,2)(2,1)(1,1,1,1)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_2+\psi_1(\Omega_2)))</math>
|<math>\psi(a\times\psi_1(\Omega_2+\psi_1(\Omega_2)))</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1}+\psi_\omega(\Omega_{\omega+1})))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}+\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1})))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S+\psi_S(\sigma S\times\omega+S)))</math>
|(0)(1,1,1,1)(2,1)(3,2)(2,1)(3,2)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_2+\psi_1(\Omega_2+1)))</math>
|<math>\psi(a\times\psi_1(\Omega_2+\psi_1(\Omega_2+1)))</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1}+\psi_\omega(\Omega_{\omega+1}+1)))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}+\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}+1)))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S+\psi_S(\sigma S\times\omega+S+1)))</math>
|(0)(1,1,1,1)(2,1)(3,2)(3)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2))))</math>
|<math>\psi(a\times\psi_1(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2))))</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1}+\psi_\omega(\Omega_{\omega+1}+\psi_\omega(\Omega_{\omega+1}))))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}+\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}+\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}))))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S+\psi_S(\sigma S\times\omega+S+\psi_S(\sigma S\times\omega+S))))</math>
|(0)(1,1,1,1)(2,1)(3,2)(3,1)(4,2)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_22))</math>
|<math>\psi(a\times\psi_1(\Omega_22))</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1}2))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S2))</math>
|(0)(1,1,1,1)(2,1)(3,2)(3,2)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_2\omega))</math>
|<math>\psi(a\times\psi_1(\Omega_2\omega))</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1}\omega))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}\omega))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S\omega))</math>
|(0)(1,1,1,1)(2,1)(3,2)(4)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_2\Omega))</math>
|<math>\psi(a\times\psi_1(\Omega_2\Omega))</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1}\Omega))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}\Omega))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S\Omega))</math>
|(0)(1,1,1,1)(2,1)(3,2)(4,1)
|-
|<math>\psi(\Omega_3\times(\psi_1(\Omega_2\Omega)+1))</math>
|<math>\psi(a\times(\psi_1(\Omega_2\Omega)+1))</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1}\Omega\omega))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S\times\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(3,2)(4,1)(1,1,1,1)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_2^2))</math>
|<math>\psi(a\times\psi_1(\Omega_2^2))</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1}^2))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}^2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S^2))</math>
|(0)(1,1,1,1)(2,1)(3,2)(4,2)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_2^{\Omega_2}))</math>
|<math>\psi(a\times\psi_1(\Omega_2^{\Omega_2}))</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1}^{\Omega_{\omega+1}}))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}^{\Omega_{\sigma^\omega a+1}}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S^S))</math>
|(0)(1,1,1,1)(2,1)(3,2)(4,2)(5,2)
|-
|<math>\psi(\Omega_3\times\psi_1(\psi_2(\Omega_3)))</math>
|<math>\psi(a\times\psi_1(\psi_2(\Omega_3)))</math>
|<math>\psi(\psi_\omega(\psi_{\omega+1}(\Omega_{\omega+2}))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\psi_{\sigma^\omega a+2}(\Omega_{\sigma^\omega a+2})))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+\varepsilon_{S+1}))</math>
|(0)(1,1,1,1)(2,1)(3,2)(4,3)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_3))</math>
|<math>\psi(a\times\psi_1(\Omega_3))</math>
|<math>\psi(\psi_\omega(\psi_{\omega+1}(\Omega_{\omega+3}))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+2}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+\psi_{S+1}(\Omega_{S+2})))</math>
|(0)(1,1,1,1)(2,1)(3,2,1)
|-
|<math>\psi(\Omega_3\times\psi_1(\psi_3(\Omega_5)))</math>
|<math>\psi(a\times\psi_1(\Omega_4))</math>
|<math>\psi(\psi_\omega(\psi_{\omega+1}(\Omega_{\omega+3}2))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+3}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+\psi_{S+1}(\Omega_{S+3})))</math>
|(0)(1,1,1,1)(2,1)(3,2,1)(4,3,1)
|-
|<math>\psi(\Omega_3\times\psi_1(\psi_3(\Omega_6)))</math>
|<math>\psi(a\times\psi_1(\psi_a(\sigma a)))</math>
|<math>\psi(\psi_\omega(\psi_{\omega+1}(\Omega_{\omega+4}))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+a}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+\psi_{S+1}(\Omega_{S+a})))</math>
|(0)(1,1,1,1)(2,1)(3,2,1)(4,3,2)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_4))</math>
|<math>\psi(a\times\psi_1(a))</math>
|<math>\psi(\psi_\omega(\psi_{\omega+1}(\Omega_{\omega2}))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a2}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+\psi_{S+1}(\Omega_{S+\psi_S(\sigma S\times\omega)})))</math>
|(0)(1,1,1,1)(2,1)(3,2,1,1)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_4\Omega_2))</math>
|<math>\psi(a\times\psi_1(a\Omega_2))</math>
|<math>\psi(\psi_\omega(\psi_{\omega+1}(\Omega_{\omega2}\Omega_2))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a2}\Omega_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+\psi_{S+1}(\Omega_{S+\psi_S(\sigma S\times\omega)\times\Omega_2})))</math>
|(0)(1,1,1,1)(2,1)(3,2,1,1)(4,2)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_4\times(\Omega_2+1)))</math>
|<math>\psi(a\times\psi_1(a\times(\Omega_2+1)))</math>
|<math>\psi(\psi_\omega(\psi_{\omega+1}(\Omega_{\omega2}^2))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a2}^2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+\psi_{S+1}(\Omega_{S+\psi_S(\sigma S\times\omega)^2})))</math>
|(0)(1,1,1,1)(2,1)(3,2,1,1)(4,2)(3,2,1,1)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_4\times\psi_2(\Omega_3)))</math>
|<math>\psi(a\times\psi_1(a\times\psi_2(\Omega_3)))</math>
|<math>\psi(\psi_\omega(\psi_{\omega+1}(\psi_{\omega2}(\Omega_{\omega2+1})))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\psi_{\sigma^\omega a2+1}(\Omega_{\sigma^\omega a2+1})))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+\psi_{S+1}(\Omega_{S+\psi_S(\sigma S\times\omega+S)})))</math>
|(0)(1,1,1,1)(2,1)(3,2,1,1)(4,2)(5,3)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_4\times\psi_2(\Omega_4)))</math>
|<math>\psi(a\times\psi_1(a\times\psi_2(\Omega_4)))</math>
|<math>\psi(\psi_\omega(\psi_{\omega+1}(\psi_{\omega2}(\psi_{\omega2+1}(\Omega_{\omega2+3}))))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\psi_{\sigma^\omega a2+1}(\Omega_{\sigma^\omega a2+2})))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+\psi_{S+1}(\Omega_{S+\psi_S(\sigma S\times\omega+\psi_{S+1}(\Omega_{S+2}))})))</math>
|(0)(1,1,1,1)(2,1)(3,2,1,1)(4,2)(5,3,1)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_4\times\psi_2(\Omega_5)))</math>
|<math>\psi(a\times\psi_1(a\times\psi_2(a)))</math>
|<math>\psi(\psi_\omega(\psi_{\omega+1}(\psi_{\omega2}(\psi_{\omega2+1}(\Omega_{\omega3}))))</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\psi_{\sigma^\omega a2+1}(\Omega_{\sigma^\omega a3})))</math>
|<math>\psi(\psi_S(\sigma S\times\omega+\psi_{S+1}(\Omega_{S+\psi_S(\sigma S\times\omega+\psi_{S+1}(\Omega_{S+\psi_S(\sigma S\times\omega)}))})))</math>
|(0)(1,1,1,1)(2,1)(3,2,1,1)(4,2)(5,3,1,1)
|-
|<math>\psi(\Omega_3\Omega_2)</math>
|<math>\psi(a\Omega_2)</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+2}))</math>
|<math>\psi(\Omega_{\sigma^\omega a+1})</math>
|<math>\psi(\psi_S(\sigma S\times\omega+\psi_{S_2}(\sigma S)))</math>
|(0)(1,1,1,1)(2,1,1)
|}
未完待续
[[分类:分析]]

HPrSSψ vs LPrSS投影 vs LPrSS反射分析

2026-08-06T02:49:48Z

量子杰克：

上篇：[[HPrSSψ vs 拓展LPrSSψ分析]]

== 分析1：LDO~(0)(1,1,1)(2,2,1)(3,2)(2,2,1) ==
{| class="wikitable" style="white-space: nowrap;"
|+分析1：LDO~(0)(1,1,1)(2,2,1)(3,2)(2,2,1)
!HPrSSψ
!LPrSS投影
!LPrSS反射
!BMS
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a))</math>
|<math>\psi(\psi_I(I))=\psi(\Phi(1,0))</math>
|(0)(1,1,1)(2,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3)+\Omega)</math>
|<math>\psi(\psi_a(\Omega_{a+1}a)+\Omega)</math>
|<math>\psi(\psi_I(I)+\Omega)</math>
|(0)(1,1,1)(2,2,1)(3,2)(1,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3)+\psi_1(\psi_3(\Omega_5\Omega_4)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a)+\psi_1(\psi_a(\Omega_{a+1}a)))</math>
|<math>\psi(\psi_I(I)+\psi_1(\psi_I(I)))</math>
|(0)(1,1,1)(2,2,1)(3,2)(1,1)(2,2,1)(3,3,1)(4,3)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3)+\Omega_2)</math>
|<math>\psi(\psi_a(\Omega_{a+1}a)+\Omega_2)</math>
|<math>\psi(\psi_I(I)+\Omega_2)</math>
|(0)(1,1,1)(2,2,1)(3,2)(1,1,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3)+\psi_2(\Omega_4))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a)+\Omega_3)</math>
|<math>\psi(\psi_I(I)+\Omega_3)</math>
|(0)(1,1,1)(2,2,1)(3,2)(1,1,1)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3)+\psi_2(\Omega_4\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a)+\Omega_\omega)</math>
|<math>\psi(\psi_I(I)+\Omega_\omega)</math>
|(0)(1,1,1)(2,2,1)(3,2)(1,1,1)(2,2,1)(3)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3)+\psi_2(\Omega_4\Omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a)+\Omega_\Omega)</math>
|<math>\psi(\psi_I(I)+\Omega_\Omega)</math>
|(0)(1,1,1)(2,2,1)(3,2)(1,1,1)(2,2,1)(3,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3)+\psi_2(\Omega_4\Omega_2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a)+\Omega_{\Omega_2})</math>
|<math>\psi(\psi_I(I)+\Omega_{\Omega_2})</math>
|(0)(1,1,1)(2,2,1)(3,2)(1,1,1)(2,2,1)(3,1,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3)\times2)</math>
|<math>\psi(\psi_a(\Omega_{a+1}a)\times2)</math>
|<math>\psi(\psi_I(I)\times2)</math>
|(0)(1,1,1)(2,2,1)(3,2)(1,1,1)(2,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+1))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+1))</math>
|<math>\psi(\psi_I(I)\times\omega)</math>
|(0)(1,1,1)(2,2,1)(3,2)(2)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\Omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\Omega))</math>
|<math>\psi(\psi_I(I)\times\Omega)</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\Omega_2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\Omega_2))</math>
|<math>\psi(\psi_I(I)\times\Omega_2)</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,1,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_2(\Omega_4)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\Omega_3))</math>
|<math>\psi(\psi_I(I)\times\Omega_3)</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,1,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_2(\Omega_4\omega)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\Omega_\omega))</math>
|<math>\psi(\psi_I(I)\times\Omega_\omega)</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,1,1)(3,2,1)(4)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_2(\Omega_4\Omega)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\Omega_\Omega))</math>
|<math>\psi(\psi_I(I)\times\Omega_\Omega)</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,1,1)(3,2,1)(4,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_2(\Omega_4\Omega_2)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\Omega_{\Omega_2}))</math>
|<math>\psi(\psi_I(I)\times\Omega_{\Omega_2})</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,1,1)(3,2,1)(4,1,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_2(\Omega_4\Omega_3)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_a(\Omega_{a+1}a)))</math>
|<math>\psi(\psi_I(I)^2)</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,1,1)(3,2,1)(4,2)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_2(\Omega_4\Omega_3+1)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_a(\Omega_{a+1}a+1)))</math>
|<math>\psi(\psi_I(I)^\omega)</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,1,1)(3,2,1)(4,2)(3)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_2(\Omega_4\Omega_3+\psi_2(\Omega_4\Omega_3))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_a(\Omega_{a+1}a+\psi_a(\Omega_{a+1}a))))</math>
|<math>\psi(\psi_I(I)^{\psi_I(I)})</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,1,1)(3,2,1)(4,2)(3,1,1)(4,2,1)(5,2)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+a))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+1)))=\psi(\varepsilon_{\Phi(1,0)+1})</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\Omega_3+1))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+a+1))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+1)+1))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(2)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\Omega_32))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+a2))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+1)\times2))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(2,2)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\Omega_3\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+a\omega))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+1)\times\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\Omega_3^2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+a^2))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+1)^2))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\Omega_3^\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+a^\omega))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+1)^\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,2)(4)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\Omega_3^{\Omega_3}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+a^a))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+1)^{\psi_I(I+1)}))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,2)(4,2)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_3(\Omega_4)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_{a+1}(\Omega_{a+1})))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_{\psi_I(I+1)}(\psi_I(I+2))))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,3)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_3(\Omega_5)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_{a+1}(\Omega_{a+2})))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+2)))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,3,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_3(\psi_5(\Omega_7))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_{a+1}(\Omega_{a+3})))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+3)))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,4,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_3(\psi_5(\Omega_7\omega))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_{a+1}(\Omega_{a+\omega})))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+\omega)))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,4,1)(5)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_3(\psi_5(\Omega_7\Omega))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_{a+1}(\Omega_{a+\Omega})))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+\Omega)))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,4,1)(5,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_3(\psi_5(\Omega_7\Omega_2))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_{a+1}(\Omega_{a+\Omega_2})))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+\Omega_2)))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,4,1)(5,1,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_3(\psi_5(\Omega_7\times\psi_2(\Omega_4)))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_{a+1}(\Omega_{a+\Omega_3})))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+\Omega_3)))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,4,1)(5,1,1)(6,2,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_3(\psi_5(\Omega_7\times\psi_2(\Omega_4\omega)))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_{a+1}(\Omega_{a+\Omega_\omega})))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+\Omega_\omega)))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,4,1)(5,1,1)(6,2,1)(7)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_3(\psi_5(\Omega_7\times\psi_2(\Omega_4\Omega_3)))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_{a+1}(\Omega_{a+\psi_a(\Omega_{a+1}a)})))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+\psi_I(I))))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,4,1)(5,1,1)(6,2,1)(7,2)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_3(\psi_5(\Omega_7\Omega_3))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_{a+1}(\Omega_{a2})))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+\psi_I(I+1))))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,4,1)(5,2)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_3(\psi_5(\Omega_7\Omega_4))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_{a+1}(\Omega_{\Omega_{a+1}})))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+\psi_{\psi_I(I+1)}(\psi_I(I+2)))))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,4,1)(5,3)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_3(\psi_5(\Omega_7\Omega_5))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_{a+1}(\Omega_{\Omega_{a+2}})))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I+\psi_I(I+2))))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,4,1)(5,3,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_3(\psi_5(\Omega_7\Omega_6))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}a_2))))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_I(I2)))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,4,1)(5,4)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_3(\psi_5(\Omega_7\Omega_6+\Omega_6))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}a_2+a_2))))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_{\psi_I(I2)}(\psi_I(I2+1))))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,4,1)(5,4)(4,4)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_3(\psi_5(\Omega_7\Omega_6+\psi_6(\Omega_8)))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}a_2+\psi_{a_2+1}(\Omega_{a_2+2})))))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_{\psi_I(I2)}(\psi_I(I2+2))))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,4,1)(5,4)(4,4)(5,5,1)
|-
|<math>\psi(\psi_2(\Omega_4\Omega_3+\psi_3(\psi_5(\Omega_7\Omega_6+\psi_6(\psi_8(\Omega_{10}\Omega_9))))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}a+\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}a_2+\psi_{a_2+1}(\psi_{a_3}(\Omega_{a_3+1}a_3))))))</math>
|<math>\psi(\psi_{\psi_I(I)}(\psi_{\psi_I(I2)}(\psi_I(I3))))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,4,1)(5,4)(4,4)(5,5,1)(6,6,1)(7,6)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3+1)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times(a+1)))</math>
|<math>\psi(\psi_I(I+1))=\psi(\Omega_{\Phi(1,0)+1})</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2,1)
|}

== 分析2：(0)(1,1,1)(2,2,1)(3,2)(2,2,1)~(0)(1,1,1)(2,2,1)(3,2,1) ==
{| class="wikitable" style="white-space: nowrap;"
|+分析2：(0)(1,1,1)(2,2,1)(3,2)(2,2,1)~(0)(1,1,1)(2,2,1)(3,2,1)
!HPrSSψ
!LPrSS投影
!LPrSS反射
!BMS
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3+1)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times(a+1)))</math>
|<math>\psi(\psi_I(I+1))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3+1)+1))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times(a+1)+1))</math>
|<math>\psi(\psi_I(I+1)\times\omega)</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2,1)(2)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3+1)+\psi_2(\Omega_4\times(\Omega_3+1))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times(a+1)+\psi_a(\Omega_{a+1}\times(a+1))))</math>
|<math>\psi(\psi_I(I+1)^2)</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2,1)(2,1,1)(3,2,1)(4,2)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3+1)+\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times(a+1)+a))</math>
|<math>\psi(\varepsilon_{\psi_I(I+1)+1})</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2,1)(2,2)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3+1)+\psi_3(\psi_5(\Omega_7\Omega_6))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times(a+1)+\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}a_2))))</math>
|<math>\psi(\psi_{\psi_I(I+1)}(\psi_I(I2)))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2,1)(2,2)(3,3,1)(4,4,1)(5,4)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3+1)+\psi_3(\psi_5(\Omega_7\times(\Omega_6+1)))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times(a+1)+\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}\times(a_2+1)))))</math>
|<math>\psi(\psi_{\psi_I(I+1)}(\psi_I(I2+1)))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2,1)(2,2)(3,3,1)(4,4,1)(5,4)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3+2)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times(a+2)))</math>
|<math>\psi(\psi_I(I+2))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2,1)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3+\omega)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times(a+\omega)))</math>
|<math>\psi(\psi_I(I+\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2,1)(3)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3+\Omega)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times(a+\Omega)))</math>
|<math>\psi(\psi_I(I+\Omega))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2,1)(3,1)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3+\Omega_2)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times(a+\Omega_2)))</math>
|<math>\psi(\psi_I(I+\Omega_2))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2,1)(3,1,1)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3+\psi_2(\Omega_4\Omega_3))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times(a+\psi_a(\Omega_{a+1}a))))</math>
|<math>\psi(\psi_I(I+\psi_I(I)))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2,1)(3,1,1)(4,2,1)(5,2)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3+\psi_2(\Omega_4\times(\Omega_3+1)))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times(a+\psi_a(\Omega_{a+1}\times(a+1)))))</math>
|<math>\psi(\psi_I(I+\psi_I(I+1)))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2,1)(3,1,1)(4,2,1)(5,2)(4,2,1)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3+\psi_2(\Omega_4\times(\Omega_3+\psi_2(\Omega_4\Omega_3))))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times(a+\psi_a(\Omega_{a+1}\times(a+\psi_a(\Omega_{a+1}a))))))</math>
|<math>\psi(\psi_I(I+\psi_I(I+\psi_I(I))))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2,1)(3,1,1)(4,2,1)(5,2)(4,2,1)(5,1,1)(6,2,1)(7,2)
|-
|<math>\psi(\psi_2(\Omega_4\times\Omega_32))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times a2))</math>
|<math>\psi(\psi_I(I2))=\psi(\Phi(1,1))</math>
|(0)(1,1,1)(2,2,1)(3,2)(2,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4\times\Omega_3\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times a\omega))</math>
|<math>\psi(\psi_I(I\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2)(3)
|-
|<math>\psi(\psi_2(\Omega_4\times\Omega_3\Omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times a\Omega))</math>
|<math>\psi(\psi_I(I\Omega))</math>
|(0)(1,1,1)(2,2,1)(3,2)(3,1)
|-
|<math>\psi(\psi_2(\Omega_4\times\Omega_3\Omega_2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times a\Omega_2))</math>
|<math>\psi(\psi_I(I\Omega_2))</math>
|(0)(1,1,1)(2,2,1)(3,2)(3,1,1)
|-
|<math>\psi(\psi_2(\Omega_4\times\Omega_3\times\psi_2(\Omega_4\Omega_3)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times a\times\psi_a(\Omega_{a+1}a)))</math>
|<math>\psi(\psi_I(I\times\psi_I(I)))</math>
|(0)(1,1,1)(2,2,1)(3,2)(3,1,1)(4,2,1)(5,2)
|-
|<math>\psi(\psi_2(\Omega_4\times\Omega_3^2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times a^2))</math>
|<math>\psi(\psi_I(I^2))=\psi(\Phi(2,0))</math>
|(0)(1,1,1)(2,2,1)(3,2)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3^2+1)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times (a^2+1)))</math>
|<math>\psi(\psi_I(I^2+1))</math>
|(0)(1,1,1)(2,2,1)(3,2)(3,2)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3^2+\Omega_3)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times (a^2+a)))</math>
|<math>\psi(\psi_I(I^2+I))</math>
|(0)(1,1,1)(2,2,1)(3,2)(3,2)(2,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3^22)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times (a^22)))</math>
|<math>\psi(\psi_I(I^22))</math>
|(0)(1,1,1)(2,2,1)(3,2)(3,2)(2,2,1)(3,2)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4\times(\Omega_3^2\omega)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times (a^2\omega)))</math>
|<math>\psi(\psi_I(I^2\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2)(3,2)(3)
|-
|<math>\psi(\psi_2(\Omega_4\times\Omega_3^3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times a^3))</math>
|<math>\psi(\psi_I(I^3))</math>
|(0)(1,1,1)(2,2,1)(3,2)(3,2)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4\times\Omega_3^\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times a^\omega))</math>
|<math>\psi(\psi_I(I^\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4)
|-
|<math>\psi(\psi_2(\Omega_4\times\Omega_3^\Omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times a^\Omega))</math>
|<math>\psi(\psi_I(I^\Omega))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,1)
|-
|<math>\psi(\psi_2(\Omega_4\times\Omega_3^{\Omega_2}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times a^{\Omega_2}))</math>
|<math>\psi(\psi_I(I^{\Omega_2}))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,1,1)
|-
|<math>\psi(\psi_2(\Omega_4\times\Omega_3^{\psi_2(\Omega_4\Omega_3)}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times a^{\psi_a(\Omega_{a+1}a)}))</math>
|<math>\psi(\psi_I(I^{\psi_I(I)}))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,1,1)(5,2,1)(6,2)
|-
|<math>\psi(\psi_2(\Omega_4\times\Omega_3^{\Omega_3}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times a^a))</math>
|<math>\psi(\psi_I(I^I))=\psi(\Phi(1,0,0))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,2)
|-
|<math>\psi(\psi_2(\Omega_4\times\Omega_3^{\Omega_3^\omega}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times a^{a^\omega}))</math>
|<math>\psi(\psi_I(I^{I^\omega}))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,2)(5)
|-
|<math>\psi(\psi_2(\Omega_4\times\Omega_3^{\Omega_3^{\Omega_3}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times a^{a^a}))</math>
|<math>\psi(\psi_I(I^{I^I}))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,2)(5,2)
|-
|<math>\psi(\psi_2(\Omega_4\times\psi_3(\Omega_4)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times\psi_{a+1}(\Omega_{a+1})))=\psi(\psi_a(\Omega_{a+1}\times\varepsilon_{a+1}))</math>
|<math>\psi(\psi_I(\psi_{I+1}(\Omega_{I+1})))=\psi(\psi_I(\varepsilon_{I+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,3)
|-
|<math>\psi(\psi_2(\Omega_4\times\psi_3(\Omega_5)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times\psi_{a+1}(\Omega_{a+2})))</math>
|<math>\psi(\psi_I(\Omega_{I+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,3,1)
|-
|<math>\psi(\psi_2(\Omega_4\times\psi_3(\psi_5(\Omega_7))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times\psi_{a+1}(\Omega_{a+3})))</math>
|<math>\psi(\psi_I(\Omega_{I+2}))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,3,1)(5,4,1)
|-
|<math>\psi(\psi_2(\Omega_4\times\psi_3(\psi_5(\Omega_7\omega))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times\psi_{a+1}(\Omega_{a+\omega})))</math>
|<math>\psi(\psi_I(\Omega_{I+\omega}))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,3,1)(5,4,1)(6)
|-
|<math>\psi(\psi_2(\Omega_4\times\psi_3(\psi_5(\Omega_7\Omega))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times\psi_{a+1}(\Omega_{a+\Omega})))</math>
|<math>\psi(\psi_I(\Omega_{I+\Omega}))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,3,1)(5,4,1)(6,1)
|-
|<math>\psi(\psi_2(\Omega_4\times\psi_3(\psi_5(\Omega_7\Omega_2))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times\psi_{a+1}(\Omega_{a+\Omega_2})))</math>
|<math>\psi(\psi_I(\Omega_{I+\Omega_2}))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,3,1)(5,4,1)(6,1,1)
|-
|<math>\psi(\psi_2(\Omega_4\times\psi_3(\psi_5(\Omega_7\Omega_3))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times\psi_{a+1}(\Omega_{a2})))</math>
|<math>\psi(\psi_I(\Omega_{I2}))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,3,1)(5,4,1)(6,2)
|-
|<math>\psi(\psi_2(\Omega_4\times\psi_3(\psi_5(\Omega_7\Omega_4))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times\psi_{a+1}(\Omega_{\Omega_{a+1}})))</math>
|<math>\psi(\psi_I(\Omega_{\Omega_{I+1}}))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,3,1)(5,4,1)(6,3)
|-
|<math>\psi(\psi_2(\Omega_4\times\psi_3(\psi_5(\Omega_7\Omega_5))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times\psi_{a+1}(\Omega_{\Omega_{a+2}})))</math>
|<math>\psi(\psi_I(\Omega_{\Omega_{I+2}}))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,3,1)(5,4,1)(6,3,1)
|-
|<math>\psi(\psi_2(\Omega_4\times\psi_3(\psi_5(\Omega_7\Omega_6))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}a_2))))</math>
|<math>\psi(\psi_I(\psi_{I_2}(I_2)))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,3,1)(5,4,1)(6,4)
|-
|<math>\psi(\psi_2(\Omega_4\times\psi_3(\psi_5(\Omega_7\times\psi_6(\psi_8(\Omega_{10}\Omega_9))))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}\times\psi_{a_2+1}(\psi_{a_3}(\Omega_{a_3+1}a_3))))))</math>
|<math>\psi(\psi_I(\psi_{I_2}(\psi_{I_3}(I_3))))</math>
|(0)(1,1,1)(2,2,1)(3,2)(4,3,1)(5,4,1)(6,4)(7,5,1)(8,6,1)(9,6)
|-
|<math>\psi(\psi_2(\Omega_4^2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2))</math>
|<math>\psi(I)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)
|}

== 分析3：(0)(1,1,1)(2,2,1)(3,2,1)~(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1) ==
{| class="wikitable" style="white-space: nowrap;"
|+分析3：(0)(1,1,1)(2,2,1)(3,2,1)~(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)
!HPrSSψ
!LPrSS投影
!LPrSS反射
!BMS
|-
|<math>\psi(\psi_2(\Omega_4^2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2))</math>
|<math>\psi(I)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2)+\Omega)</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2)+\Omega)</math>
|<math>\psi(I+\Omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(1,1)
|-
|<math>\psi(\psi_2(\Omega_4^2)+\psi_1(\psi_3(\Omega_5^2)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2)+\psi_1(\psi_a(\Omega_{a+1}^2)))</math>
|<math>\psi(I+\psi_1(I))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(1,1)(2,2,1)(3,3,1)(4,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^2)+\Omega_2)</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2)+\Omega_2)</math>
|<math>\psi(I+\Omega_2)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(1,1,1)
|-
|<math>\psi(\psi_2(\Omega_4^2)+\psi_2(\Omega_4))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2)+\Omega_3)</math>
|<math>\psi(I+\Omega_3)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(1,1,1)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2)+\psi_2(\Omega_4\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2)+\Omega_\omega)</math>
|<math>\psi(I+\Omega_\omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(1,1,1)(2,2,1)(3)
|-
|<math>\psi(\psi_2(\Omega_4^2)+\psi_2(\Omega_4\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2)+\psi_a(\Omega_{a+1}a))</math>
|<math>\psi(I+\psi_I(I))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(1,1,1)(2,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^2)+\psi_2(\Omega_4\times\psi_3(\Omega_5)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2)+\psi_a(\Omega_{a+1}\times\psi_{a+1}(\Omega_{a+2})))</math>
|<math>\psi(I+\psi_I(\Omega_{I+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(1,1,1)(2,2,1)(3,2)(4,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^2)+\psi_2(\Omega_4\times\psi_3(\psi_5(\Omega_7\Omega_6))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2)+\psi_a(\Omega_{a+1}\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}a_2))))</math>
|<math>\psi(I+\psi_I(\psi_{I_2}(I_2)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(1,1,1)(2,2,1)(3,2)(4,3,1)(5,4,1)(6,4)
|-
|<math>\psi(\psi_2(\Omega_4^2)+\psi_2(\Omega_4\times\psi_3(\psi_5(\Omega_7^2))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2)+\psi_a(\Omega_{a+1}\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2))))</math>
|<math>\psi(I+\psi_I(I_2))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(1,1,1)(2,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^2)+\psi_2(\Omega_4\times\psi_3(\psi_5(\Omega_7^2)+\psi_5(\Omega_7\Omega_6))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2)+\psi_a(\Omega_{a+1}\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2)+\psi_{a_2}(\Omega_{a_2+1}a_2))))</math>
|<math>\psi(I+\psi_I(I_2+\psi_{I_2}(I_2)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(1,1,1)(2,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)(4,3,1)(5,4,1)(6,4)
|-
|<math>\psi(\psi_2(\Omega_4^2)\times2)</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2)\times2)</math>
|<math>\psi(I2)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(1,1,1)(2,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+1))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+1))</math>
|<math>\psi(I\omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega))</math>
|<math>\psi(I\Omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_2))</math>
|<math>\psi(I\Omega_2)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,1,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_2(\Omega_4)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_3))</math>
|<math>\psi(I\Omega_3)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,1,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_2(\Omega_4\omega)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_\omega))</math>
|<math>\psi(I\Omega_\omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,1,1)(3,2,1)(4)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_2(\Omega_4\Omega_3)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\psi_a(\Omega_{a+1}a)))</math>
|<math>\psi(I\times\psi_I(I))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,1,1)(3,2,1)(4,2)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_2(\Omega_4^2)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\psi_a(\Omega_{a+1}^2)))</math>
|<math>\psi(I^2)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,1,1)(3,2,1)(4,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_2(\Omega_4^2+1)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\psi_a(\Omega_{a+1}^2+1)))</math>
|<math>\psi(I^\omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,1,1)(3,2,1)(4,2,1)(3)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_2(\Omega_4^2+\psi_2(\Omega_4^2))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\psi_a(\Omega_{a+1}^2+\psi_a(\Omega_{a+1}^2))))</math>
|<math>\psi(I^I)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,1,1)(3,2,1)(4,2,1)(3,1,1)(4,2,1)(5,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+a))</math>
|<math>\psi(\psi_{I+1}(\Omega_{I+1}))=\psi(\varepsilon_{I+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_3+1))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+a+1))</math>
|<math>\psi(\psi_{I+1}(\Omega_{I+1}+1))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2)(2)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_32))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+a2))</math>
|<math>\psi(\psi_{I+1}(\Omega_{I+1}2))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2)(2,2)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_3^2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+a^2))</math>
|<math>\psi(\psi_{I+1}(\Omega_{I+1}^2))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_3(\Omega_4)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\psi_{a+1}(\Omega_{a+1})))</math>
|<math>\psi(\psi_{I+1}(\psi_{I+2}(\Omega_{I+2})))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2)(3,3)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_3(\Omega_5)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\psi_{a+1}(\Omega_{a+2})))</math>
|<math>\psi(\psi_{I+1}(\Omega_{I+2}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2)(3,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_3(\psi_5(\Omega_7))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\psi_{a+1}(\Omega_{a+3})))</math>
|<math>\psi(\psi_{I+1}(\Omega_{I+3}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2)(3,3,1)(4,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_3(\psi_5(\Omega_7\omega))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\psi_{a+1}(\Omega_{a+\omega})))</math>
|<math>\psi(\psi_{I+1}(\Omega_{I+\omega}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2)(3,3,1)(4,4,1)(5)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_3(\psi_5(\Omega_7\Omega))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\psi_{a+1}(\Omega_{a+\Omega})))</math>
|<math>\psi(\psi_{I+1}(\Omega_{I+\Omega}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2)(3,3,1)(4,4,1)(5,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_3(\psi_5(\Omega_7\Omega_2))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\psi_{a+1}(\Omega_{a+\Omega_2})))</math>
|<math>\psi(\psi_{I+1}(\Omega_{I+\Omega_2}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2)(3,3,1)(4,4,1)(5,1,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_3(\psi_5(\Omega_7\Omega_3))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\psi_{a+1}(\Omega_{a2})))</math>
|<math>\psi(\psi_{I+1}(\Omega_{I2}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2)(3,3,1)(4,4,1)(5,2)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_3(\psi_5(\Omega_7\Omega_4))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\psi_{a+1}(\Omega_{\Omega_{a+1}})))</math>
|<math>\psi(\psi_{I+1}(\Omega_{\Omega_{I+1}}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2)(3,3,1)(4,4,1)(5,3)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_3(\psi_5(\Omega_7\Omega_5))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\psi_{a+1}(\Omega_{\Omega_{a+2}})))</math>
|<math>\psi(\psi_{I+1}(\Omega_{\Omega_{I+2}}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2)(3,3,1)(4,4,1)(5,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_3(\psi_5(\Omega_7\Omega_6))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}a_2))))</math>
|<math>\psi(\psi_{I+1}(\psi_{I_2}(I_2)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2)(3,3,1)(4,4,1)(5,4)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_3(\psi_5(\Omega_7^2))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2))))</math>
|<math>\psi(\psi_{I+1}(I_2))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2)(3,3,1)(4,4,1)(5,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\psi_3(\psi_5(\Omega_7^2+\psi_6(\psi_8(\Omega_{10}^2))))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2+\psi_{a_2+1}(\psi_{a_3}(\Omega_{a_3+1}^2))))))</math>
|<math>\psi(\psi_{I+1}(\psi_{I_2+1}(I_3)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2)(3,3,1)(4,4,1)(5,4,1)(4,4)(5,5,1)(6,6,1)(7,6,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}))</math>
|<math>\psi(\Omega_{I+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_42))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}2))</math>
|<math>\psi(\Omega_{I+2})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\omega))</math>
|<math>\psi(\Omega_{I+\omega})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\Omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\Omega))</math>
|<math>\psi(\Omega_{I+\Omega})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\Omega_2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\Omega_2))</math>
|<math>\psi(\Omega_{I+\Omega_2})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,1,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\times\psi_2(\Omega_4)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\Omega_3))</math>
|<math>\psi(\Omega_{I+\Omega_3})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,1,1)(4,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\times\psi_2(\Omega_4\omega)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\Omega_\omega))</math>
|<math>\psi(\Omega_{I+\Omega_\omega})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,1,1)(4,2,1)(5)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\times\psi_2(\Omega_4\Omega_3)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\psi_a(\Omega_{a+1}a)))</math>
|<math>\psi(\Omega_{I+\psi_I(I)})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,1,1)(4,2,1)(5,2)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\times\psi_2(\Omega_4^2)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\psi_a(\Omega_{a+1}^2)))</math>
|<math>\psi(\Omega_{I2})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,1,1)(4,2,1)(5,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\times\psi_2(\Omega_4^2+\Omega_4)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\psi_a(\Omega_{a+1}^2+\Omega_{a+1})))</math>
|<math>\psi(\Omega_{\Omega_{I+1}})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,1,1)(4,2,1)(5,2,1)(4,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\times\psi_2(\Omega_4^2+\Omega_4\times\psi_2(\Omega_4^2))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\psi_a(\Omega_{a+1}^2))))</math>
|<math>\psi(\Omega_{\Omega_{I2}})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,1,1)(4,2,1)(5,2,1)(4,2,1)(5,1,1)(6,2,1)(7,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}a))</math>
|<math>\psi(\psi_{I_2}(I_2))=\psi(\Phi(1,I+1))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\times(\Omega_3+1)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times(a+1)))</math>
|<math>\psi(\psi_{I_2}(I_2+1))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\times\Omega_32))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times a2))</math>
|<math>\psi(\psi_{I_2}(I_22))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2)(2,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\times\Omega_3^2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times a^2))</math>
|<math>\psi(\psi_{I_2}(I_2^2))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\times\psi_3(\Omega_4)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\psi_{a+1}(\Omega_{a+1})))</math>
|<math>\psi(\psi_{I_2}(\psi_{I_2+1}(\Omega_{I_2+1})))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2)(4,3)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\times\psi_3(\Omega_5)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\psi_{a+1}(\Omega_{a+2})))</math>
|<math>\psi(\psi_{I_2}(\Omega_{I_2+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2)(4,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\times\psi_3(\psi_5(\Omega_7))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\psi_{a+1}(\Omega_{a+3})))</math>
|<math>\psi(\psi_{I_2}(\Omega_{I_2+2}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2)(4,3,1)(5,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\times\psi_3(\psi_5(\Omega_7\Omega_6))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}a_2))))</math>
|<math>\psi(\psi_{I_2}(\psi_{I_3}(I_3)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2)(4,3,1)(5,4,1)(6,4)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\times\psi_3(\psi_5(\Omega_7^2))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2))))</math>
|<math>\psi(\psi_{I_2}(I_3))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\times\psi_3(\psi_5(\Omega_7^2+\Omega_7))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2+\Omega_{a_2+1}))))</math>
|<math>\psi(\psi_{I_2}(\Omega_{I_3+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)(5,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^2+\Omega_4\times\psi_3(\psi_5(\Omega_7^2+\Omega_7\Omega_6))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2+\Omega_{a+1}\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2+\Omega_{a_2+1}a_2))))</math>
|<math>\psi(\psi_{I_2}(\psi_{I_4}(I_4)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)(5,4,1)(6,4)
|-
|<math>\psi(\psi_2(\Omega_4^22))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^22))</math>
|<math>\psi(I_2)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^22+\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^22+a))</math>
|<math>\psi(\varepsilon_{I_2+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2,1)(2,2)
|-
|<math>\psi(\psi_2(\Omega_4^22+\Omega_4))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^22+\Omega_{a+1}))</math>
|<math>\psi(\Omega_{I_2+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2,1)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^22+\Omega_4\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^22+\Omega_{a+1}a))</math>
|<math>\psi(\psi_{I_3}(I_3))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2,1)(2,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^23))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^23))</math>
|<math>\psi(I_3)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2,1)(2,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\omega))</math>
|<math>\psi(I_\omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3)
|-
|<math>\psi(\psi_2(\Omega_4^2\omega+\Omega_4))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\omega+\Omega_{a+1}))</math>
|<math>\psi(\Omega_{I_\omega+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\times(\omega+1)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times(\omega+1)))</math>
|<math>\psi(I_{\omega+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3)(2,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\Omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\Omega))</math>
|<math>\psi(I_\Omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\Omega_2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\Omega_2))</math>
|<math>\psi(I_{\Omega_2})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,1,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_2(\Omega_4)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\Omega_3))</math>
|<math>\psi(I_{\Omega_3})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,1,1)(4,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_2(\Omega_4\omega)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\Omega_\omega))</math>
|<math>\psi(I_{\Omega_\omega})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,1,1)(4,2,1)(5)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_2(\Omega_4\Omega_3)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_a(\Omega_{a+1}a)))</math>
|<math>\psi(I_{\psi_I(I)})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,1,1)(4,2,1)(5,2)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_2(\Omega_4^2)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_a(\Omega_{a+1}^2)))</math>
|<math>\psi(I_I)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,1,1)(4,2,1)(5,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_2(\Omega_4^2\times\psi_2(\Omega_4^2))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_a(\Omega_{a+1}^2\times\psi_a(\Omega_{a+1}^2))))</math>
|<math>\psi(I_{I_I})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,1,1)(4,2,1)(5,2,1)(5,1,1)(6,2,1)(7,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2a))</math>
|<math>\psi(\psi_{I(1,0)}(I(1,0)))=\psi(I-\Phi(1,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^2\Omega_3+\Omega_4))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2a+\Omega_{a+1}))</math>
|<math>\psi(\Omega_{\psi_{I(1,0)}(I(1,0))+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\times(\Omega_3+1)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times(a+1)))</math>
|<math>\psi(\psi_{I(1,0)}(I(1,0)+1))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(2,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\Omega_32))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times a2))</math>
|<math>\psi(\psi_{I(1,0)}(I(1,0)\times2))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(2,2,1)(3,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\Omega_3\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times a\omega))</math>
|<math>\psi(\psi_{I(1,0)}(I(1,0)\times\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(3)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\Omega_3^2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times a^2))</math>
|<math>\psi(\psi_{I(1,0)}(I(1,0)^2))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\Omega_3^\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times a^\omega))</math>
|<math>\psi(\psi_{I(1,0)}(I(1,0)^\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\Omega_3^{\Omega_3}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times a^a))</math>
|<math>\psi(\psi_{I(1,0)}(I(1,0)^{I(1,0)}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,2)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\Omega_4)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\Omega_{a+1})))</math>
|<math>\psi(\psi_{I(1,0)}(\varepsilon_{I(1,0)+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\Omega_5)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\Omega_{a+2})))</math>
|<math>\psi(\psi_{I(1,0)}(\Omega_{I(1,0)+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\Omega_{a+3})))</math>
|<math>\psi(\psi_{I(1,0)}(\Omega_{I(1,0)+2}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7\omega))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\Omega_{a+\omega})))</math>
|<math>\psi(\psi_{I(1,0)}(\Omega_{I(1,0)+\omega}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7\Omega))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\Omega_{a+\Omega})))</math>
|<math>\psi(\psi_{I(1,0)}(\Omega_{I(1,0)+\Omega}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7\Omega_2))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\Omega_{a+\Omega_2})))</math>
|<math>\psi(\psi_{I(1,0)}(\Omega_{I(1,0)+\Omega_2}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,1,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7\Omega_3))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\Omega_{a2})))</math>
|<math>\psi(\psi_{I(1,0)}(\Omega_{I(1,0)\times2}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,2)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7\Omega_4))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\Omega_{\Omega_{a+1}})))</math>
|<math>\psi(\psi_{I(1,0)}(\Omega_{\Omega_{I(1,0)+1}}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,3)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7\Omega_5))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\Omega_{\Omega_{a+2}})))</math>
|<math>\psi(\psi_{I(1,0)}(\Omega_{\Omega_{I(1,0)+1}}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7\Omega_6))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}a_2))))</math>
|<math>\psi(\psi_{I(1,0)}(\Phi(1,I(1,0)+1)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7^2))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2))))</math>
|<math>\psi(\psi_{I(1,0)}(I_{I(1,0)+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7^22))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^22))))</math>
|<math>\psi(\psi_{I(1,0)}(I_{I(1,0)+2}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)(5,4,1)(6,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7^2\omega))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2\omega))))</math>
|<math>\psi(\psi_{I(1,0)}(I_{I(1,0)+\omega}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)(6)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7^2\Omega))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2\Omega))))</math>
|<math>\psi(\psi_{I(1,0)}(I_{I(1,0)+\Omega}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)(6,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7^2\Omega_2))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2\Omega_2))))</math>
|<math>\psi(\psi_{I(1,0)}(I_{I(1,0)+\Omega_2}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)(6,1,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7^2\Omega_3))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2a))))</math>
|<math>\psi(\psi_{I(1,0)}(I_{I(1,0)\times2}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)(6,2)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7^2\Omega_4))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2\times\psi_{a_2}(\Omega_{a_2+1}^2)))))</math>
|<math>\psi(\psi_{I(1,0)}(I_{I_{I(1,0)+1}}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)(6,3)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7^2\Omega_5))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2\times\psi_{a_2}(\Omega_{a_2+1}^22)))))</math>
|<math>\psi(\psi_{I(1,0)}(I_{I_{I(1,0)+2}}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)(6,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7^2\Omega_6))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2a_2))))</math>
|<math>\psi(\psi_{I(1,0)}(\psi_{I(1,1)}(I(1,1))))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)(6,4)
|-
|<math>\psi(\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7^2\Omega_6\times\psi_6(\psi_8(\Omega_{10}^2\Omega_9))))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2\times\psi_{a_2+1}(\psi_{a_3}(\Omega_{a_3+1}^2a_3))))))</math>
|<math>\psi(\psi_{I(1,0)}(\psi_{I(1,1)}(\psi_{I(1,2)}(I(1,2)))))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)(6,4)(7,5,1)(8,6,1)(9,6,1)(9,6)
|-
|<math>\psi(\psi_2(\Omega_4^3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3))</math>
|<math>\psi(I(1,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)
|}

== 分析4：(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)~(0)(1,1,1)(2,2,1)(3,2,1)(4,2) ==
{| class="wikitable" style="white-space: nowrap;"
|+分析4：(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)~(0)(1,1,1)(2,2,1)(3,2,1)(4,2)
!HPrSSψ
!LPrSS投影
!LPrSS反射
!BMS
|-
|<math>\psi(\psi_2(\Omega_4^3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3))</math>
|<math>\psi(I(1,0))=\psi(\psi_M(3))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^3)+\Omega)</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3)+\Omega)</math>
|<math>\psi(I(1,0)+\Omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(1,1)
|-
|<math>\psi(\psi_2(\Omega_4^3)+\psi_1(\psi_3(\Omega_5^3)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3)+\psi_1(\psi_a(\Omega_{a+1}^3)))</math>
|<math>\psi(I(1,0)+\psi_1(I(1,0)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(1,1)(2,2,1)(3,3,1)(4,3,1)(4,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^3)+\Omega_2)</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3)+\Omega_2)</math>
|<math>\psi(I(1,0)+\Omega_2)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(1,1,1)
|-
|<math>\psi(\psi_2(\Omega_4^3)+\psi_2(\Omega_4^2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3)+\psi_a(\Omega_{a+1}^2))</math>
|<math>\psi(I(1,0)+I)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(1,1,1)(2,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^3)+\psi_2(\Omega_4^2\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3)+\psi_a(\Omega_{a+1}^2a))</math>
|<math>\psi(I(1,0)+\psi_{I(1,0)}(I(1,0)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(1,1,1)(2,2,1)(3,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^3)+\psi_2(\Omega_4^2\times\psi_3(\psi_5(\Omega_7^3))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3)+\psi_a(\Omega_{a+1}^2\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^3))))</math>
|<math>\psi(I(1,0)+\psi_{I(1,0)}(I(1,1)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)(6,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^3)\times2)</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3)\times2)</math>
|<math>\psi(I(1,0)\times2)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(1,1,1)(2,2,1)(3,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^3+1))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3+1))</math>
|<math>\psi(I(1,0)\times\omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2)
|-
|<math>\psi(\psi_2(\Omega_4^3+\psi_2(\Omega_4^3)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3+\psi_a(\Omega_{a+1}^3)))</math>
|<math>\psi(I(1,0)^2)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,1,1)(3,2,1)(4,2,1)(4,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^3+\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3+a))</math>
|<math>\psi(\varepsilon_{I(1,0)+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,2)
|-
|<math>\psi(\psi_2(\Omega_4^3+\Omega_4))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3+\Omega_{a+1}))</math>
|<math>\psi(\Omega_{I(1,0)+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^3+\Omega_4\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3+\Omega_{a+1}a))</math>
|<math>\psi(\Phi(1,I(1,0)+1))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^3+\Omega_4^2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3+\Omega_{a+1}^2))</math>
|<math>\psi(I_{I(1,0)+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^3+\Omega_4^2\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3+\Omega_{a+1}^2\omega))</math>
|<math>\psi(I_{I(1,0)+\omega})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)(3)
|-
|<math>\psi(\psi_2(\Omega_4^3+\Omega_4^2\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3+\Omega_{a+1}^2a))</math>
|<math>\psi(\psi_{I(1,1)}(I(1,1)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^3+\Omega_4^2\times\psi_3(\Omega_5)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3+\Omega_{a+1}^2\times\psi_{a+1}(\Omega_{a+2})))</math>
|<math>\psi(\psi_{I(1,1)}(\Omega_{I(1,1)+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)(3,2)(4,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^3+\Omega_4^2\times\psi_3(\psi_5(\Omega_7^2))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3+\Omega_{a+1}^2\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2))))</math>
|<math>\psi(\psi_{I(1,1)}(I_{I(1,1)+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^3+\Omega_4^2\times\psi_3(\psi_5(\Omega_7^3))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3+\Omega_{a+1}^2\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^3))))</math>
|<math>\psi(\psi_{I(1,1)}(I(1,2)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)(6,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^3+\Omega_4^2\times\psi_3(\psi_5(\Omega_7^3+\Omega_7^2\Omega_6))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3+\Omega_{a+1}^2\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^3+\Omega_{a_2+1}^2a_2))))</math>
|<math>\psi(\psi_{I(1,1)}(\psi_{I(1,3)}(I(1,3))))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)(6,4,1)(5,4,1)(6,4,1)(6,4)
|-
|<math>\psi(\psi_2(\Omega_4^32))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^32))</math>
|<math>\psi(I(1,1))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^3\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3\omega))</math>
|<math>\psi(I(1,\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3)
|-
|<math>\psi(\psi_2(\Omega_4^3\Omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3\Omega))</math>
|<math>\psi(I(1,\Omega))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,1)
|-
|<math>\psi(\psi_2(\Omega_4^3\times\psi_2(\Omega_4^2)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3\times\psi_a(\Omega_{a+1}^2)))</math>
|<math>\psi(I(1,I))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,1,1)(4,2,1)(5,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^3\times\psi_2(\Omega_4^3)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3\times\psi_a(\Omega_{a+1}^3)))</math>
|<math>\psi(I(1,I(1,0)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,1,1)(4,2,1)(5,2,1)(5,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^3\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3a))</math>
|<math>\psi(\psi_{I(2,0)}(I(2,0)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^3\times\psi_3(\Omega_5)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3\times\psi_{a+1}(\Omega_{a+2})))</math>
|<math>\psi(\psi_{I(2,0)}(\Omega_{I(2,0)+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2)(4,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^3\times\psi_3(\psi_5(\Omega_7^2))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2))))</math>
|<math>\psi(\psi_{I(2,0)}(I_{I(2,0)+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^3\times\psi_3(\psi_5(\Omega_7^3))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^3\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^3))))</math>
|<math>\psi(\psi_{I(2,0)}(\psi_{I(2,1)}(I(2,1))))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2)(4,3,1)(5,4,1)(6,4,1)(6,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^4))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^4))</math>
|<math>\psi(I(2,0))=\psi(\psi_M(4))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^4+1))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^4+1))</math>
|<math>\psi(I(2,0)\times\omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1)(2)
|-
|<math>\psi(\psi_2(\Omega_4^4+\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^4+a))</math>
|<math>\psi(\varepsilon_{I(2,0)+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1)(2,2)
|-
|<math>\psi(\psi_2(\Omega_4^4+\Omega_4))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^4+\Omega_{a+1}))</math>
|<math>\psi(\Omega_{I(2,0)+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^4+\Omega_4^2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^4+\Omega_{a+1}^2))</math>
|<math>\psi(I_{I(2,0)+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^4+\Omega_4^3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^4+\Omega_{a+1}^3))</math>
|<math>\psi(I(1,I(2,0)+1))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^4+\Omega_4^3\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^4+\Omega_{a+1}^3a))</math>
|<math>\psi(\psi_{I(2,1)}(I(2,1)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)(3,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^42))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^42))</math>
|<math>\psi(I(2,1))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^4\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^4\omega))</math>
|<math>\psi(I(2,\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1)(3)
|-
|<math>\psi(\psi_2(\Omega_4^4\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^4a))</math>
|<math>\psi(\psi_{I(3,0)}(I(3,0)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^5))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^5))</math>
|<math>\psi(I(3,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^\omega))</math>
|<math>\psi(I(\omega,0))=\psi(\psi_M(\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4)
|-
|<math>\psi(\psi_2(\Omega_4^\omega+\Omega_4))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^\omega+\Omega_{a+1}))</math>
|<math>\psi(\Omega_{I(\omega,0)+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^\omega2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^\omega2))</math>
|<math>\psi(I(\omega,1))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4)(2,2,1)(3,2,1)(4)
|-
|<math>\psi(\psi_2(\Omega_4^\omega\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^\omega\omega))</math>
|<math>\psi(I(\omega,\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4)(3)
|-
|<math>\psi(\psi_2(\Omega_4^\omega\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^\omega a))</math>
|<math>\psi(\psi_{I(\omega+1,0)}(I(\omega+1,0)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\omega+1}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\omega+1}))</math>
|<math>\psi(I(\omega+1,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^\Omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^\Omega))</math>
|<math>\psi(I(\Omega,0))=\psi(\psi_M(\Omega))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_2}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_2}))</math>
|<math>\psi(I(\Omega_2,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,1,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_2(\Omega_4)}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_3}))</math>
|<math>\psi(I(\Omega_3,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,1,1)(5,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_2(\Omega_4\omega)}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_\omega}))</math>
|<math>\psi(I(\Omega_\omega,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,1,1)(5,2,1)(6)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_2(\Omega_4^2)}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_a(\Omega_{a+1}^2)}))</math>
|<math>\psi(I(I,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,1,1)(5,2,1)(6,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_2(\Omega_4^\omega)}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_a(\Omega_{a+1}^\omega)}))</math>
|<math>\psi(I(I(\omega,0),0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,1,1)(5,2,1)(6,2,1)(7)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_2(\Omega_4^{\psi_2(\Omega_4^2)})}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_a(\Omega_{a+1}^{\psi_a(\Omega_{a+1}^2)})}))</math>
|<math>\psi(I(I(I,0),0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,1,1)(5,2,1)(6,2,1)(7,1,1)(8,2,1)(9,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^a))</math>
|<math>\psi(\psi_{I(1,0,0)}(1))=\psi(I(x,0)-\Phi(1,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)
|}

== 分析5：(0)(1,1,1)(2,2,1)(3,2,1)(4,2)~(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1) ==
{| class="wikitable" style="white-space: nowrap;"
|+分析5：(0)(1,1,1)(2,2,1)(3,2,1)(4,2)~(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)
!HPrSSψ
!LPrSS投影
!LPrSS反射
!BMS
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^a))</math>
|<math>\psi(\psi_{I(1,0,0)}(1))=\psi(\psi_M(M))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3}+\Omega_4))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^a+\Omega_{a+1}))</math>
|<math>\psi(\Omega_{\psi_{I(1,0,0)}(1)+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3}2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^a2))</math>
|<math>\psi(\psi_{I(1,0,0)}(2))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(2,2,1)(3,2,1)(4,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3}\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^a\omega))</math>
|<math>\psi(\psi_{I(1,0,0)}(\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(3)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3}\Omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^a\Omega))</math>
|<math>\psi(\psi_{I(1,0,0)}(\Omega))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(3,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3}\times\psi_2(\Omega_4^{\Omega_3})))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^a\times\psi_a(\Omega_{a+1}^a)))</math>
|<math>\psi(\psi_{I(1,0,0)}(\psi_{I(1,0,0)}(1)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(3,1,1)(4,2,1)(5,2,1)(6,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3}\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^aa))</math>
|<math>\psi(\psi_{I(1,0,0)}(I(1,0,0)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3}\times\psi_3(\Omega_5)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^a\times\psi_{a+1}(\Omega_{a+2})))</math>
|<math>\psi(\psi_{I(1,0,0)}(\Omega_{I(1,0,0)+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(3,2)(4,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3}\times\psi_3(\psi_5(\Omega_7^2))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^a\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2))))</math>
|<math>\psi(\psi_{I(1,0,0)}(I_{I(1,0,0)+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(3,2)(4,3,1)(5,4,1)(6,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3}\times\psi_3(\psi_5(\Omega_7^\omega))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^a\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^\omega))))</math>
|<math>\psi(\psi_{I(1,0,0)}(I(\omega,I(1,0,0)+1)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(3,2)(4,3,1)(5,4,1)(6,4,1)(7)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3}\times\psi_3(\psi_5(\Omega_7^{\Omega_6}))))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^a\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^{a_2}))))</math>
|<math>\psi(\psi_{I(1,0,0)}(\psi_{I(1,0,1)}(1)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(3,2)(4,3,1)(5,4,1)(6,4,1)(7,6)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3+1}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{a+1}))</math>
|<math>\psi(I(1,0,0))=\psi(\psi_M(M+1))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3+1}2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{a+1}2))</math>
|<math>\psi(I(1,0,1))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(3,2,1)(2,2,1)(3,2,1)(4,2)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3+1}\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{a+1}\omega))</math>
|<math>\psi(I(1,0,\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(3,2,1)(3)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3+1}\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{a+1}a))</math>
|<math>\psi(\psi_{I(1,1,0)}(I(1,1,0)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(3,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3+2}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{a+2}))</math>
|<math>\psi(I(1,1,0))=\psi(\psi_M(M+2))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(3,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3+\omega}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{a+\omega}))</math>
|<math>\psi(I(1,\omega,0))=\psi(\psi_M(M+\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(3,2,1)(4)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_32}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{a2}))</math>
|<math>\psi(\psi_{I(2,0,0)}(1))=\psi(\psi_M(M2))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(3,2,1)(4,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_32+1}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{a2+1}))</math>
|<math>\psi(I(2,0,0))=\psi(\psi_M(M2+1))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(3,2,1)(4,2)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3\omega}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{a\omega}))</math>
|<math>\psi(I(\omega,0,0))=\psi(\psi_M(M\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(4)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3^2}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{a^2}))</math>
|<math>\psi(\psi_{I(1,0,0,0)}(I(1,0,0,0)))=\psi(\psi_M(M^2))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(4,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3^2+1}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{a^2+1}))</math>
|<math>\psi(I(1,0,0,0))=\psi(\psi_M(M^2+1))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(4,2)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3^\omega}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{a^\omega}))</math>
|<math>\psi(\psi_M(M^\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3^{\Omega_3}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{a^a}))</math>
|<math>\psi(\psi_M(M^M))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_3^{\Omega_3^{\Omega_3}}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{a^{a^a}}))</math>
|<math>\psi(\psi_M(M^{M^M}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,2)(6,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\Omega_4)}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\Omega_{a+1})}))</math>
|<math>\psi(\psi_M(\psi_{M+1}(\Omega_{M+1})))=\psi(\psi_M(\varepsilon_{M+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\Omega_4+1)}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\Omega_{a+1}+1)}))</math>
|<math>\psi(\psi_M(\psi_{M+1}(\Omega_{M+1}+1)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3)(5)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\Omega_42)}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\Omega_{a+1}2)}))</math>
|<math>\psi(\psi_M(\psi_{M+1}(\Omega_{M+1}2)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3)(5,3)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\Omega_4^2)}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\Omega_{a+1}^2)}))</math>
|<math>\psi(\psi_M(\psi_{M+1}(\Omega_{M+1}^2)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3)(6,3)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_4(\Omega_5))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\psi_{a+2}(\Omega_{a+2}))}))</math>
|<math>\psi(\psi_M(\psi_{M+1}(\psi_{M+2}(\Omega_{M+2}))))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3)(6,4)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\Omega_5)}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\Omega_{a+2})}))</math>
|<math>\psi(\psi_M(\Omega_{M+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\Omega_{a+3})}))</math>
|<math>\psi(\psi_M(\Omega_{M+2}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7\omega))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\Omega_{a+\omega})}))</math>
|<math>\psi(\psi_M(\Omega_{M+\omega}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7\Omega))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\Omega_{a+\Omega})}))</math>
|<math>\psi(\psi_M(\Omega_{M+\Omega}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7\Omega_2))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\Omega_{a+\Omega_2})}))</math>
|<math>\psi(\psi_M(\Omega_{M+\Omega_2}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,1,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7\Omega_3))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\Omega_{a2})}))</math>
|<math>\psi(\psi_M(\Omega_{M2}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7\Omega_4))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\Omega_{\Omega_{a+1}})}))</math>
|<math>\psi(\psi_M(\Omega_{\Omega_{M+1}}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,3)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7\Omega_5))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\Omega_{\Omega_{a+2}})}))</math>
|<math>\psi(\psi_M(\Omega_{\Omega_{M+2}}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7\Omega_6))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}a_2))}))</math>
|<math>\psi(\psi_M(\Phi(1,M+1)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,4)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7^2))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2))}))</math>
|<math>\psi(\psi_M(I_{M+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7^\omega))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^\omega))}))</math>
|<math>\psi(\psi_M(I(\omega,M+1)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,4,1)(8)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7^\Omega))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^\Omega))}))</math>
|<math>\psi(\psi_M(I(\Omega,M+1)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,4,1)(8,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7^{\Omega_2}))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^{\Omega_2}))}))</math>
|<math>\psi(\psi_M(I(\Omega_2,M+1)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,4,1)(8,1,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7^{\Omega_3}))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^a))}))</math>
|<math>\psi(\psi_M(I(M,1)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,4,1)(8,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7^{\Omega_4}))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^{\Omega_{a+1}}))}))</math>
|<math>\psi(\psi_M(I(\Omega_{M+1},0)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,4,1)(8,3)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7^{\Omega_5}))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^{\Omega_{a+2}}))}))</math>
|<math>\psi(\psi_M(I(\Omega_{M+2},0)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,4,1)(8,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7^{\Omega_6}))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^{a_2}))}))</math>
|<math>\psi(\psi_M(\psi_{M_2}(M_2)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,4,1)(8,4)
|-
|<math>\psi(\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7^{\psi_6(\psi_8(\Omega_{10}^{\Omega_9}))}))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^{\psi_{a_2+1}(\psi_{a_3}(\Omega_{a_3+1}^{a_3}))}))}))</math>
|<math>\psi(\psi_M(\psi_{M_2}(\psi_{M_3}(M_3))))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,4,1)(8,4)(9,5,1)(10,6,1)(11,6,1)(12,6)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}}))</math>
|<math>\psi(M)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)
|}

== 分析6：(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)~(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1) ==
{| class="wikitable" style="white-space: nowrap;"
|+分析6：(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)~(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)
!HPrSSψ
!LPrSS投影
!LPrSS反射
!BMS
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}}))</math>
|<math>\psi(M)=\psi(\Pi_2-\Pi_2)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4})+\Omega)</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}})+\Omega)</math>
|<math>\psi(M+\Omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(1,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4})+\psi_1(\psi_3(\Omega_5^{\Omega_5})))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}})+\psi_1(\psi_a(\Omega_{a+1}^{\Omega_{a+1}})))</math>
|<math>\psi(M+\psi_1(M))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(1,1)(2,2,1)(3,3,1)(4,3,1)(5,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4})+\Omega_2)</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}})+\Omega_2)</math>
|<math>\psi(M+\Omega_2)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(1,1,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4})+\psi_2(\Omega_4^2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}})+\psi_a(\Omega_{a+1}^2))</math>
|<math>\psi(M+I)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(1,1,1)(2,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4})+\psi_2(\Omega_4^{\Omega_3}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}})+\psi_a(\Omega_{a+1}^a))</math>
|<math>\psi(M+\psi_M(M))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(1,1,1)(2,2,1)(3,2,1)(4,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4})+\psi_2(\Omega_4^{\psi_3(\psi_5(\Omega_7^{\Omega_7}))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}})+\psi_a(\Omega_{a+1}^{\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^{\Omega_{a_2+1}}))}))</math>
|<math>\psi(M+\psi_M(M_2))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(1,1,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,4,1)(8,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4})\times2)</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}})\times2)</math>
|<math>\psi(M2)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(1,1,1)(2,2,1)(3,2,1)(4,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}+1))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}}+1))</math>
|<math>\psi(M\omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}+\psi_2(\Omega_4^{\Omega_4})))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}}+\psi_a(\Omega_{a+1}^{\Omega_{a+1}})))</math>
|<math>\psi(M^2)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(2,1,1)(3,2,1)(4,2,1)(5,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}+\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}}+a))</math>
|<math>\psi(\varepsilon_{M+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(2,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}+\Omega_4))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}}+\Omega_{a+1}))</math>
|<math>\psi(\Omega_{M+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}+\Omega_4^2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}}+\Omega_{a+1}^2))</math>
|<math>\psi(I_{M+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(2,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}+\Omega_4^{\Omega_3}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}}+\Omega_{a+1}^a))</math>
|<math>\psi(\psi_{M_2}(M_2))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(2,2,1)(3,2,1)(4,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}+\Omega_4^{\psi_3(\psi_5(\Omega_7^{\Omega_7}))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}}+\Omega_{a+1}^{\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^{\Omega_{a_2+1}}))}))</math>
|<math>\psi(\psi_{M_2}(M_3))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(2,2,1)(3,2,1)(4,2)(5,3,1)(6,4,1)(7,4,1)(8,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}}2))</math>
|<math>\psi(M_2)=\psi(2nd\ \Pi_2-\Pi_2)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(2,2,1)(3,2,1)(4,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}}\omega))</math>
|<math>\psi(M_\omega)=\psi(\Pi_1-\Pi_2-\Pi_2)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(3)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}\Omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}}\Omega))</math>
|<math>\psi(M_\Omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(3,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}\Omega_2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}}\Omega_2))</math>
|<math>\psi(M_{\Omega_2})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(3,1,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}\times\psi_2(\Omega_4^2)))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}}\times\psi_a(\Omega_{a+1}^2)))</math>
|<math>\psi(M_I)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(3,1,1)(4,2,1)(5,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}\times\psi_2(\Omega_4^{\Omega_4})))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}}\times\psi_a(\Omega_{a+1}^{\Omega_{a+1}})))</math>
|<math>\psi(M_M)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(3,1,1)(4,2,1)(5,2,1)(6,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4}\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}}a))</math>
|<math>\psi(\Pi_1^a-\Pi_2-\Pi_2)=\psi(M-\Phi(1,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4+1}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}+1}))</math>
|<math>\psi(\Pi_2\ \Pi_1-\Pi_2-\Pi_2)=\psi(M-I(1,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4+2}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}+2}))</math>
|<math>\psi((\Pi_2\ \Pi_1-)^2\Pi_2-\Pi_2)=\psi(M-I(2,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(3,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4+\omega}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}+\omega}))</math>
|<math>\psi((\Pi_2\ \Pi_1-)^\omega\Pi_2-\Pi_2)=\psi(M-I(\omega,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(3,2,1)(4)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4+\Omega_3}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}+a}))</math>
|<math>\psi((\Pi_2\ \Pi_1-)^a\Pi_2-\Pi_2)=\psi(\psi_{M(1,0)}(M(1,0)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(3,2,1)(4,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_42}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}2}))</math>
|<math>\psi(\Pi_2-\Pi_2\ \Pi_1-\Pi_2-\Pi_2)=\psi(M(1,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(3,2,1)(4,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4\omega}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}\omega}))</math>
|<math>\psi((\Pi_2-\Pi_2\ \Pi_1-)^\omega)=\psi(M(\omega,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(4)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4\Omega}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}\Omega}))</math>
|<math>\psi((\Pi_2-\Pi_2\ \Pi_1-)^\Omega)=\psi(M(\Omega,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(4,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4\Omega_2}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}\Omega_2}))</math>
|<math>\psi((\Pi_2-\Pi_2\ \Pi_1-)^{\Omega_2})=\psi(M(\Omega_2,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(4,1,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4\Omega_3}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}a}))</math>
|<math>\psi((\Pi_2-\Pi_2\ \Pi_1-)^a)=\psi(\psi_N(N))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(4,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4\times\psi_3(\Omega_4)}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}\times\psi_{a+1}(\Omega_{a+1})}))</math>
|<math>\psi(\psi_N(\varepsilon_{N+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(4,2)(5,3)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4\times\psi_3(\Omega_5)}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}\times\psi_{a+1}(\Omega_{a+2})}))</math>
|<math>\psi(\psi_N(\Omega_{N+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(4,2)(5,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4\times\psi_3(\psi_5(\Omega_7^{\Omega_7\Omega_6}))}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}\times\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^{\Omega_{a_2+1}\times a_2}))}))</math>
|<math>\psi(\psi_N(\psi_{N_2}(N_2)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(4,2)(5,3,1)(6,4,1)(7,4,1)(8,4,1)(8,4)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^2}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^2}))</math>
|<math>\psi(\Pi_2-^3)=\psi(N)=\psi(\psi_K(2))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(4,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^3}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^3}))</math>
|<math>\psi(\Pi_2-^4)=\psi(\psi_K(3))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(4,2,1)(4,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^\omega}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^\omega}))</math>
|<math>\psi(\Pi_2-^\omega)=\psi(\psi_K(\omega))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^\Omega}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^\Omega}))</math>
|<math>\psi(\Pi_2-^\Omega)=\psi(\psi_K(\Omega))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_2}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_2}}))</math>
|<math>\psi(\Pi_2-^{\Omega_2})=\psi(\psi_K(\Omega_2))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,1,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\psi_2(\Omega_4)}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_3}}))</math>
|<math>\psi(\Pi_2-^{\Omega_3})=\psi(\psi_K(\Omega_3))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,1,1)(6,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\psi_2(\Omega_4^2)}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\psi_a(\Omega_{a+1}^2)}}))</math>
|<math>\psi(\Pi_2-^I)=\psi(\psi_K(I))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,1,1)(6,2,1)(7,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\psi_2(\Omega_4^{\Omega_4})}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\psi_a(\Omega_{a+1}^{\Omega_{a+1}})}}))</math>
|<math>\psi(\Pi_2-^M)=\psi(\psi_K(M))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,1,1)(6,2,1)(7,2,1)(8,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_3}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^a}))</math>
|<math>\psi(\Pi_2-^a)=\psi(\psi_K(K))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\psi_3(\Omega_4)}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\psi_{a+1}(\Omega_{a+1})}}))</math>
|<math>\psi(\psi_K(\varepsilon_{K+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2)(6,3)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\psi_3(\Omega_5)}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\psi_{a+1}(\Omega_{a+2})}}))</math>
|<math>\psi(\psi_K(\Omega_{K+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2)(6,3,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\psi_3(\psi_5(\Omega_7))}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\psi_{a+1}(\Omega_{a+3})}}))</math>
|<math>\psi(\psi_K(\Omega_{K+2}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2)(6,3,1)(7,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\psi_3(\psi_5(\Omega_7^2))}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^2))}}))</math>
|<math>\psi(\psi_K(I_{K+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2)(6,3,1)(7,4,1)(8,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\psi_3(\psi_5(\Omega_7^{\Omega_7}))}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^\Omega_{a_2+1}))}}))</math>
|<math>\psi(\psi_K(M_{K+1}))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2)(6,3,1)(7,4,1)(8,4,1)(9,4,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\psi_3(\psi_5(\Omega_7^{\Omega_7^{\Omega_6}}))}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\psi_{a+1}(\psi_{a_2}(\Omega_{a_2+1}^{\Omega_{a_2+1}^{a_2}}))}}))</math>
|<math>\psi(\psi_K(\psi_{K_2}(K_2)))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2)(6,3,1)(7,4,1)(8,4,1)(9,4,1)(10,4)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}}}))</math>
|<math>\psi(\Pi_3)=\psi(K)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)
|}

== 分析7：(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)~(0)(1,1,1)(2,2,1)(3,3) ==
{| class="wikitable" style="white-space: nowrap;"
|+分析7：(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)~(0)(1,1,1)(2,2,1)(3,3)
!HPrSSψ
!LPrSS投影
!LPrSS反射
!BMS
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}}}))</math>
|<math>\psi(\Pi_3)=\psi(K)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4}}+\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}}}+a))</math>
|<math>\psi(\varepsilon_{K+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(2,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4}}+\Omega_4))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}}}+\Omega_{a+1}))</math>
|<math>\psi(\Pi_2\ aft\ \Pi_3)=\psi(\Omega_{K+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(2,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4}}+\Omega_4^2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}}}+\Omega_{a+1}^2))</math>
|<math>\psi(\Pi_2\ \Pi_1-\Pi_2\ aft\ \Pi_3)=\psi(I_{K+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(2,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4}}+\Omega_4^{\Omega_4}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}}}+\Omega_{a+1}^{\Omega_{a+1}}))</math>
|<math>\psi(\Pi_2-\Pi_2\ aft\ \Pi_3)=\psi(M_{K+1})</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(2,2,1)(3,2,1)(4,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4}}2))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}}}2))</math>
|<math>\psi(2nd\ \Pi_3)=\psi(K_2)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4}}\omega))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}}}\omega))</math>
|<math>\psi(\Pi_1-\Pi_3)=\psi(K_\omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(3)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4}}\Omega_3))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}}}a))</math>
|<math>\psi(\Pi_1^a-\Pi_3)=\psi(K-\Phi(1,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(3,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4}+1}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}}+1}))</math>
|<math>\psi(\Pi_2\ \Pi_1-\Pi_3)=\psi(K-I(1,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(3,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4}+\Omega_4}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}}+\Omega_{a+1}}))</math>
|<math>\psi(\Pi_2-\Pi_2\ \Pi_1-\Pi_3)=\psi(K-M(1,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(3,2,1)(4,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4}2}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}}2}))</math>
|<math>\psi(\Pi_3\ \Pi_1-\Pi_3)=\psi(K(1,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(3,2,1)(4,2,1)(5,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4}\omega}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}}\omega}))</math>
|<math>\psi((\Pi_3\ \Pi_1-)^\omega)=\psi(K(\omega,0))</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(4)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4}\Omega_3}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}}a}))</math>
|<math>\psi((\Pi_3\ \Pi_1-)^a)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(4,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4+1}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}+1}}))</math>
|<math>\psi(\Pi_2-\Pi_3)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(4,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_42}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}2}}))</math>
|<math>\psi(\Pi_3\ \Pi_2-\Pi_3)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(4,2,1)(5,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4\omega}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}\omega}}))</math>
|<math>\psi((\Pi_3\ \Pi_2-)^\omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(5)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4\Omega_3}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}a}}))</math>
|<math>\psi((\Pi_3\ \Pi_2-)^a)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(5,2)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4^2}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}^2}}))</math>
|<math>\psi(\Pi_3-\Pi_3)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(5,2,1)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4^\omega}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}^\omega}}))</math>
|<math>\psi(\Pi_3-^\omega)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(6)
|-
|<math>\psi(\psi_2(\Omega_4^{\Omega_4^{\Omega_4^{\Omega_3}}}))</math>
|<math>\psi(\psi_a(\Omega_{a+1}^{\Omega_{a+1}^{\Omega_{a+1}^a}}))</math>
|<math>\psi(\Pi_3-^a)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(6,2)
|-
|<math>\psi(\psi_2(\Omega_4\uparrow\uparrow4))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\uparrow\uparrow4))</math>
|<math>\psi(\Pi_4)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(6,2,1)
|-
|<math>\psi(\psi_2(\Omega_4\uparrow\uparrow5))</math>
|<math>\psi(\psi_a(\Omega_{a+1}\uparrow\uparrow5))</math>
|<math>\psi(\Pi_5)</math>
|(0)(1,1,1)(2,2,1)(3,2,1)(4,2,1)(5,2,1)(6,2,1)(7,2,1)
|-
|<math>\psi(\psi_2(\psi_4(\Omega_5)))=\psi(\psi_2(\varepsilon_{\Omega_4+1}))</math>
|<math>\psi(\psi_a(\psi_{a+2}(\Omega_{a+2})))=\psi(\psi_a(\varepsilon_{\Omega_{a+1}+1}))</math>
|<math>\psi(\Pi_\omega)=\psi(\lambda a.a+1-\Pi_0)</math>
|(0)(1,1,1)(2,2,1)(3,3)
|}
下篇：[[HPrSSψ vs LPrSS投影分析Part2]]
[[分类:分析]]

0Yψ vs 拓展HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影分析

2026-08-01T19:03:30Z

量子杰克：到0,1111,21,32

上篇：[[0Yψ vs HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影分析]]

== 分析1：(0)(1,1,1,1)~(0)(1,1,1,1)(2,1) ==
{| class="wikitable" style="white-space: nowrap;"
|+分析1：(0)(1,1,1,1)~(0)(1,1,1,1)(2,1)
!0Yψ
!强LPrSS投影
!拓展HPrSSψ
!弱LPrSS投影
!弱LPrSS向上投影
!BMS
|-
|<math>\psi(\Omega_3)</math>
|<math>\psi(a)</math>
|<math>\psi(\Omega_\omega)</math>
|<math>\psi(\sigma^\omega a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega))</math>
|(0)(1,1,1,1)
|-
|<math>\psi(\Omega_3+\Omega)</math>
|<math>\psi(a+\Omega)</math>
|<math>\psi(\Omega_\omega+\Omega)</math>
|<math>\psi(\sigma^\omega a+\Omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\Omega)</math>
|(0)(1,1,1,1)(1,1)
|-
|<math>\psi(\Omega_3+\psi_1(\Omega_3))</math>
|<math>\psi(a+\psi_1(\Omega_3))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_3))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\Omega_3))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\Omega_3))</math>
|(0)(1,1,1,1)(1,1)(2,2,1)
|-
|<math>\psi(\Omega_3+\psi_1(\psi_3(\Omega_5)))</math>
|<math>\psi(a+\psi_1(\Omega_4))</math>
|<math>\psi(\Omega_\omega+\psi_1(\psi_3(\Omega_5)))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\Omega_4))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\Omega_4))</math>
|(0)(1,1,1,1)(1,1)(2,2,1)(3,3,1)
|-
|<math>\psi(\Omega_3+\psi_1(\psi_3(\Omega_6)))</math>
|<math>\psi(a+\psi_1(\psi_a(a_2)))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_4))</math>
|<math>\psi(\sigma^\omega a+\psi_1(a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(a))</math>
|(0)(1,1,1,1)(1,1)(2,2,1)(3,3,2)
|-
|<math>\psi(\Omega_3+\psi_1(\psi_3(\psi_6(\Omega_{10}))))</math>
|<math>\psi(a+\psi_1(\psi_a(\psi_{\sigma a}(\sigma a_2))))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_5))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\sigma a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\psi_S(\sigma S\times3)))</math>
|(0)(1,1,1,1)(1,1)(2,2,1)(3,3,2)(4,4,3)
|-
|<math>\psi(\Omega_3+\psi_1(\Omega_4))</math>
|<math>\psi(a+\psi_1(a))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(1,1)(2,2,1,1)
|-
|<math>\psi(\Omega_3+\psi_1(\Omega_4+\Omega_2))</math>
|<math>\psi(a+\psi_1(a+\Omega_2))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_\omega+\Omega_2))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\sigma^\omega a+\Omega_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\psi_S(\sigma S\times\omega)+\Omega_2))</math>
|(0)(1,1,1,1)(1,1)(2,2,1,1)(2,2)
|-
|<math>\psi(\Omega_3+\psi_1(\Omega_4+\psi_2(\Omega_5)))</math>
|<math>\psi(a+\psi_1(a+\psi_2(a)))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_\omega+\psi_2(\Omega_\omega)))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\sigma^\omega a+\psi_2(\sigma^\omega a)))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\psi_S(\sigma S\times\omega)+\psi_2(\psi_S(\sigma S\times\omega))))</math>
|(0)(1,1,1,1)(1,1)(2,2,1,1)(2,2)(3,3,1,1)
|-
|<math>\psi(\Omega_3+\Omega_2)</math>
|<math>\psi(a+\Omega_2)</math>
|<math>\psi(\Omega_\omega+\Omega_2)</math>
|<math>\psi(\sigma^\omega a+\Omega_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\Omega_2)</math>
|(0)(1,1,1,1)(1,1,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_4))</math>
|<math>\psi(a+\Omega_3)</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_4))</math>
|<math>\psi(\sigma^\omega a+\Omega_3)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\Omega_3)</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_4\omega))</math>
|<math>\psi(a+\Omega_\omega)</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_4\omega))</math>
|<math>\psi(\sigma^\omega a+\Omega_\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\Omega_\omega)</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)(3)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_4\Omega_3))</math>
|<math>\psi(a+\psi_a(\Omega_{a+1}a))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_4\Omega_3))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\Omega_{a+1}a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\Omega_{a+1}a))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)(3,2)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_4^2))</math>
|<math>\psi(a+\psi_a(\Omega_{a+1}^2))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_4^2))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\Omega_{a+1}^2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\Omega_{a+1}^2))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)(3,2,1)
|-
|<math>\psi(\Omega_3+\psi_2(\psi_4(\Omega_5)))</math>
|<math>\psi(a+\psi_a(\varepsilon_{\Omega_{a+1}+1}))</math>
|<math>\psi(\Omega_\omega+\psi_2(\psi_4(\Omega_5)))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\varepsilon_{\Omega_{a+1}+1}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\varepsilon_{\Omega_{a+1}+1}))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)(3,3)
|-
|<math>\psi(\Omega_3+\psi_2(\psi_4(\Omega_6)))</math>
|<math>\psi(a+\psi_a(\Omega_{a+2}))</math>
|<math>\psi(\Omega_\omega+\psi_2(\psi_4(\Omega_6)))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\Omega_{a+2}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\Omega_{a+2}))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)(3,3,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_5))</math>
|<math>\psi(a+\psi_a(a_2))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_5))</math>
|<math>\psi(\sigma^\omega a+\psi_a(a_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(a_2))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2)
|-
|<math>\psi(\Omega_3+\psi_2(\psi_5(\Omega_8)))</math>
|<math>\psi(a+\psi_a(a_3))</math>
|<math>\psi(\Omega_\omega+\psi_2(\psi_5(\Omega_8)))</math>
|<math>\psi(\sigma^\omega a+\psi_a(a_3))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(a_3))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2)(3,3,2)
|-
|<math>\psi(\Omega_3+\psi_2(\psi_5(\Omega_9)))</math>
|<math>\psi(a+\psi_a(\psi_{\sigma a}(\sigma a_2)))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_6))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\sigma a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\psi_S(\sigma S\times3)))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2)(3,3,3)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6))</math>
|<math>\psi(a+\psi_a(\sigma a))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\Omega_4))</math>
|<math>\psi(a+\psi_a(\sigma a+\Omega_{a+1}))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_\omega+\Omega_4))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\sigma^\omega a+\Omega_{a+1}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\psi_S(\sigma S\times\omega)+\Omega_{a+1}))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_4(\Omega_8)))</math>
|<math>\psi(a+\psi_a(\sigma a+\psi_{a_2}(\sigma a)))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_\omega+\psi_4(\Omega_\omega)))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\sigma^\omega a+\psi_{a_2}(\sigma^\omega a)))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\psi_S(\sigma S\times\omega)+\psi_{a_2}(\psi_S(\sigma S\times\omega))))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,1)(3,3,2,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\Omega_5))</math>
|<math>\psi(a+\psi_a(\sigma a+a_2))</math>
|<math>\psi(\Omega_\omega+\Omega_3)</math>
|<math>\psi(\sigma^\omega a+a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+a)</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_5(\Omega_8)))</math>
|<math>\psi(a+\psi_a(\sigma a+a_3))</math>
|<math>\psi(\Omega_\omega+\psi_3(\Omega_6))</math>
|<math>\psi(\sigma^\omega a+a_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+a_2)</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,2)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_5(\Omega_9)))</math>
|<math>\psi(a+\psi_a(\sigma a+\psi_{\sigma a}(\sigma a_2)))</math>
|<math>\psi(\Omega_\omega+\psi_3(\Omega_7))</math>
|<math>\psi(\sigma^\omega a+\psi_{\sigma a}(\sigma a_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_S(\sigma S\times2+S_2))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,3)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_5(\Omega_{10})))</math>
|<math>\psi(a+\psi_a(\sigma a+\psi_{\sigma a}(\sigma^2a)))</math>
|<math>\psi(\Omega_\omega+\psi_3(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a+\psi_{\sigma a}(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_{\psi_S(\sigma S\times3)}(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,3,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_5(\Omega_{10}+\Omega_9)))</math>
|<math>\psi(a+\psi_a(\sigma a+\psi_{\sigma a}(\sigma^2a+\sigma a_2)))</math>
|<math>\psi(\Omega_\omega+\Omega_4)</math>
|<math>\psi(\sigma^\omega a+\sigma a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_S(\sigma S\times3))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,3,1)(3,3,3)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_5(\Omega_{10}+\psi_9(\Omega_{15}))))</math>
|<math>\psi(a+\psi_a(\sigma a+\psi_{\sigma a}(\sigma^2a+\psi_{\sigma^2a}(\sigma^3a))))</math>
|<math>\psi(\Omega_\omega+\psi_4(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a+\psi_{\sigma^2a}(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_{\psi_S(\sigma S\times4)}(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,3,1)(3,3,3)(4,4,4,1)
|-
|<math>\psi(\Omega_32)</math>
|<math>\psi(a2)</math>
|<math>\psi(\Omega_\omega2)</math>
|<math>\psi(\sigma^\omega a2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times2)</math>
|(0)(1,1,1,1)(1,1,1,1)
|-
|<math>\psi(\Omega_32+\Omega_2)</math>
|<math>\psi(a2+\Omega_2)</math>
|<math>\psi(\Omega_\omega2+\Omega_2)</math>
|<math>\psi(\sigma^\omega a2+\Omega_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times2+\Omega_2)</math>
|(0)(1,1,1,1)(1,1,1,1)(1,1,1)
|-
|<math>\psi(\Omega_32+\psi_2(\Omega_6))</math>
|<math>\psi(a2+\psi_a(\sigma a))</math>
|<math>\psi(\Omega_\omega2+\psi_2(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a2+\psi_a(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times2+\psi_a(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(1,1,1,1)(1,1,1)(2,2,2,1)
|-
|<math>\psi(\Omega_32+\psi_2(\Omega_62))</math>
|<math>\psi(a2+\psi_a(\sigma a2))</math>
|<math>\psi(\Omega_\omega2+\psi_2(\Omega_\omega2))</math>
|<math>\psi(\sigma^\omega a2+\psi_a(\sigma^\omega a2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times2+\psi_a(\psi_S(\sigma S\times\omega)\times2))</math>
|(0)(1,1,1,1)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2,1)
|-
|<math>\psi(\Omega_32+\psi_2(\Omega_62+\Omega_5))</math>
|<math>\psi(a2+\psi_a(\sigma a2+a_2))</math>
|<math>\psi(\Omega_\omega2+\Omega_3)</math>
|<math>\psi(\sigma^\omega a2+a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times2+a)</math>
|(0)(1,1,1,1)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2,1)(2,2,2)
|-
|<math>\psi(\Omega_33)</math>
|<math>\psi(a3)</math>
|<math>\psi(\Omega_\omega3)</math>
|<math>\psi(\sigma^\omega a3)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times3)</math>
|(0)(1,1,1,1)(1,1,1,1)(1,1,1,1)
|-
|<math>\psi(\Omega_3\omega)</math>
|<math>\psi(a\omega)</math>
|<math>\psi(\Omega_\omega\omega)</math>
|<math>\psi(\sigma^\omega a\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\omega)</math>
|(0)(1,1,1,1)(2)
|-
|<math>\psi(\Omega_3\times(\omega+1))</math>
|<math>\psi(a\times(\omega+1))</math>
|<math>\psi(\Omega_\omega\times(\omega+1))</math>
|<math>\psi(\sigma^\omega a\times(\omega+1))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times(\omega+1))</math>
|(0)(1,1,1,1)(2)(1,1,1,1)
|-
|<math>\psi(\Omega_3\times\omega2)</math>
|<math>\psi(a\times\omega2)</math>
|<math>\psi(\Omega_\omega\times\omega2)</math>
|<math>\psi(\sigma^\omega a\times\omega2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\omega2)</math>
|(0)(1,1,1,1)(2)(1,1,1,1)(2)
|-
|<math>\psi(\Omega_3\times\omega^2)</math>
|<math>\psi(a\times\omega^2)</math>
|<math>\psi(\Omega_\omega\times\omega^2)</math>
|<math>\psi(\sigma^\omega a\times\omega^2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\omega^2)</math>
|(0)(1,1,1,1)(2)(2)
|-
|<math>\psi(\Omega_3\times\omega^\omega)</math>
|<math>\psi(a\times\omega^\omega)</math>
|<math>\psi(\Omega_\omega\times\omega^\omega)</math>
|<math>\psi(\sigma^\omega a\times\omega^\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\omega^\omega)</math>
|(0)(1,1,1,1)(2)(3)
|-
|<math>\psi(\Omega_3\times\varepsilon_0)</math>
|<math>\psi(a\times\varepsilon_0)</math>
|<math>\psi(\Omega_\omega\times\varepsilon_0)</math>
|<math>\psi(\sigma^\omega a\times\varepsilon_0)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\varepsilon_0)</math>
|(0)(1,1,1,1)(2)(3,1)
|-
|<math>\psi(\Omega_3\times\psi(\Omega_2))</math>
|<math>\psi(a\times\psi(\Omega_2))</math>
|<math>\psi(\Omega_\omega\times\psi(\Omega_2))</math>
|<math>\psi(\sigma^\omega a\times\psi(\Omega_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi(\Omega_2))</math>
|(0)(1,1,1,1)(2)(3,1,1)
|-
|<math>\psi(\Omega_3\times\psi(\Omega_3))</math>
|<math>\psi(a\times\psi(a))</math>
|<math>\psi(\Omega_\omega\times\psi(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a\times\psi(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2)(3,1,1,1)
|-
|<math>\psi(\Omega_3\Omega)</math>
|<math>\psi(a\Omega)</math>
|<math>\psi(\Omega_\omega\Omega)</math>
|<math>\psi(\sigma^\omega a\Omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega)</math>
|(0)(1,1,1,1)(2,1)
|}

== 分析2：(0)(1,1,1,1)(2,1)~(0)(1,1,1,1)(2,1)(1,1,1,1) ==
{| class="wikitable" style="white-space: nowrap;"
|+分析2：(0)(1,1,1,1)(2,1)~(0)(1,1,1,1)(2,1)(1,1,1,1)
!0Yψ
!强LPrSS投影
!拓展HPrSSψ
!弱LPrSS投影
!弱LPrSS向上投影
!BMS
|-
|<math>\psi(\Omega_3\Omega)</math>
|<math>\psi(a\Omega)</math>
|<math>\psi(\Omega_\omega\Omega)</math>
|<math>\psi(\sigma^\omega a\Omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega)</math>
|(0)(1,1,1,1)(2,1)
|-
|<math>\psi(\Omega_3\Omega+\Omega)</math>
|<math>\psi(a\Omega+\Omega)</math>
|<math>\psi(\Omega_\omega\Omega+\Omega)</math>
|<math>\psi(\sigma^\omega a\Omega+\Omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\Omega)</math>
|(0)(1,1,1,1)(2,1)(1,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_1(\Omega_4))</math>
|<math>\psi(a\Omega+\psi_1(a))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_1(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a\Omega+\psi_1(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_1(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(1,1)(2,2,1,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_1(\Omega_4\Omega))</math>
|<math>\psi(a\Omega+\psi_1(a\Omega))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_1(\Omega_\omega\Omega))</math>
|<math>\psi(\sigma^\omega a\Omega+\psi_1(\sigma^\omega a\Omega))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_1(\psi_S(\sigma S\times\omega)\times\Omega))</math>
|(0)(1,1,1,1)(2,1)(1,1)(2,2,1,1)(3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_1(\Omega_4\Omega_2))</math>
|<math>\psi(a\Omega+\psi_1(a\Omega_2))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_1(\Omega_\omega\Omega_2))</math>
|<math>\psi(\sigma^\omega a\Omega+\psi_1(\sigma^\omega a\Omega_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_1(\psi_S(\sigma S\times\omega)\times\Omega_2))</math>
|(0)(1,1,1,1)(2,1)(1,1)(2,2,1,1)(3,2)
|-
|<math>\psi(\Omega_3\Omega+\Omega_2)</math>
|<math>\psi(a\Omega+\Omega_2)</math>
|<math>\psi(\Omega_\omega\Omega+\Omega_2)</math>
|<math>\psi(\sigma^\omega a\Omega+\Omega_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\Omega_2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_4))</math>
|<math>\psi(a\Omega+\Omega_3)</math>
|<math>\psi(\Omega_\omega\Omega+\psi_2(\Omega_4))</math>
|<math>\psi(\sigma^\omega a\Omega+\Omega_3)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\Omega_3)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_5))</math>
|<math>\psi(a\Omega+\psi_a(a_2))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_2(\Omega_5))</math>
|<math>\psi(\sigma^\omega a\Omega+\psi_a(a_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_a(a_2))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\psi_5(\Omega_9)))</math>
|<math>\psi(a\Omega+\psi_a(\psi_{\sigma a}(\sigma a_2)))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_2(\Omega_6))</math>
|<math>\psi(\sigma^\omega a\Omega+\psi_a(\sigma a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_a(\psi_S(\sigma S\times3)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2)(3,3,3)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_2(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a\Omega+\psi_a(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_a(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\Omega))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_2(\Omega_\omega\Omega))</math>
|<math>\psi(\sigma^\omega a\Omega+\psi_a(\sigma^\omega a\Omega))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_a(\psi_S(\sigma S\times\omega)\times\Omega))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega+\Omega_5))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\Omega+a_2))</math>
|<math>\psi(\Omega_\omega\Omega+\Omega_3)</math>
|<math>\psi(\sigma^\omega a\Omega+a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+a)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(2,2,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega+\psi_5(\Omega_{10}\Omega)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\Omega+\psi_{\sigma a}(\sigma^2 a\Omega)))</math>
|<math>\psi(\Omega_\omega\Omega+\psi_3(\Omega_\omega\Omega))</math>
|<math>\psi(\sigma^\omega a\Omega+\psi_{\sigma a}(\sigma^\omega a\Omega))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_{\psi_S(\sigma S\times3)}(\psi_S(\sigma S\times\omega)\times\Omega))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(2,2,2)(3,3,3,1)(4,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega+\psi_5(\Omega_{10}\Omega+\Omega_9)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\Omega+\psi_{\sigma a}(\sigma^2 a\Omega+\sigma a_2)))</math>
|<math>\psi(\Omega_\omega\Omega+\Omega_4)</math>
|<math>\psi(\sigma^\omega a\Omega+\sigma a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega+\psi_S(\sigma S\times3))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(2,2,2)(3,3,3,1)(4,1)(3,3,3)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times(\Omega+1)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times(\Omega+1)))</math>
|<math>\psi(\Omega_\omega\times(\Omega+1))</math>
|<math>\psi(\sigma^\omega a\times(\Omega+1))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times(\Omega+1))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times(\Omega+2)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times(\Omega+2)))</math>
|<math>\psi(\Omega_\omega\times(\Omega+2))</math>
|<math>\psi(\sigma^\omega a\times(\Omega+2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times(\Omega+2))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(2,2,2,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\Omega2))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\Omega2))</math>
|<math>\psi(\Omega_\omega\times\Omega2)</math>
|<math>\psi(\sigma^\omega a\times\Omega2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(2,2,2,1)(3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\Omega^2))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\Omega^2))</math>
|<math>\psi(\Omega_\omega\times\Omega^2)</math>
|<math>\psi(\sigma^\omega a\times\Omega^2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega^2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_1(\Omega_2)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_1(\Omega_2)))</math>
|<math>\psi(\Omega_\omega\times\psi_1(\Omega_2))</math>
|<math>\psi(\sigma^\omega a\times\psi_1(\Omega_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_1(\Omega_2))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(4,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_1(\Omega_3)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_1(\Omega_3)))</math>
|<math>\psi(\Omega_\omega\times\psi_1(\Omega_3))</math>
|<math>\psi(\sigma^\omega a\times\psi_1(\Omega_3))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_1(\Omega_3))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(4,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_1(\psi_3(\Omega_5))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_1(\Omega_4)))</math>
|<math>\psi(\Omega_\omega\times\psi_1(\psi_3(\Omega_5)))</math>
|<math>\psi(\sigma^\omega a\times\psi_1(\Omega_4))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_1(\Omega_4))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(4,2,1)(5,3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_1(\psi_3(\Omega_6))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_1(\psi_a(a_2))))</math>
|<math>\psi(\Omega_\omega\times\psi_1(\Omega_4))</math>
|<math>\psi(\sigma^\omega a\times\psi_1(a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_1(a))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(4,2,1)(5,3,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_1(\Omega_4)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_1(a)))</math>
|<math>\psi(\Omega_\omega\times\psi_1(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a\times\psi_1(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_1(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1)(4,2,1,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_2))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\Omega_2))</math>
|<math>\psi(\Omega_\omega\Omega_2)</math>
|<math>\psi(\sigma^\omega a\Omega_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega_2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times(\Omega_2+1)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times(\Omega_2+1)))</math>
|<math>\psi(\Omega_\omega\times(\Omega_2+1))</math>
|<math>\psi(\sigma^\omega a\times(\Omega_2+1))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times(\Omega_2+1))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\Omega_3)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_2(\Omega_3)))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_3))</math>
|<math>\psi(\sigma^\omega a\times\psi_2(\Omega_3))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_2(\Omega_3))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\Omega_4)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\Omega_3))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_4))</math>
|<math>\psi(\sigma^\omega a\Omega_3)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega_3)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\Omega_4\omega)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\Omega_\omega))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_4\omega))</math>
|<math>\psi(\sigma^\omega a\Omega_\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega_\omega)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,1)(5)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\Omega_4\Omega_3)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_a(\Omega_{a+1}a)))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_4\Omega_3))</math>
|<math>\psi(\sigma^\omega a\times\psi_a(\Omega_{a+1}a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_a(\Omega_{a+1}a))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,1)(5,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\Omega_4^2)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_a(\Omega_{a+1}^2)))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_4^2))</math>
|<math>\psi(\sigma^\omega a\times\psi_a(\Omega_{a+1}^2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_a(\Omega_{a+1}^2))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,1)(5,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\psi_4(\Omega_5))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_a(\varepsilon_{\Omega_{a+1}+1})))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\psi_4(\Omega_5)))</math>
|<math>\psi(\sigma^\omega a\times\psi_a(\varepsilon_{\Omega_{a+1}+1}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_a(\varepsilon_{\Omega_{a+1}+1}))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,1)(5,3)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\psi_4(\Omega_6))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_a(\Omega_{a+2})))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\psi_4(\Omega_6)))</math>
|<math>\psi(\sigma^\omega a\times\psi_a(\Omega_{a+2}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_a(\Omega_{a+2}))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,1)(5,3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\Omega_5)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_a(a_2)))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_5))</math>
|<math>\psi(\sigma^\omega a\times\psi_a(a_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_a(a_2))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\psi_5(\Omega_9))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_a(\psi_{\sigma a}(\sigma a_2))))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_6))</math>
|<math>\psi(\sigma^\omega a\times\psi_a(\sigma a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_a(\psi_S(\sigma S\times3)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,2)(5,3,3)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\times\psi_2(\Omega_6)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma a\times\psi_a(\sigma a)))</math>
|<math>\psi(\Omega_\omega\times\psi_2(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a\times\psi_a(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_a(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,1,1)(4,2,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa))</math>
|<math>\psi(\Omega_\omega\Omega_3)</math>
|<math>\psi(\sigma^\omega aa)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times a)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\Omega_5))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+a_2))</math>
|<math>\psi(\Omega_\omega\Omega_3+\Omega_3)</math>
|<math>\psi(\sigma^\omega aa+a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times a+a)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10})))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2a)))</math>
|<math>\psi(\Omega_\omega\Omega_3+\psi_3(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega aa+\psi_{\sigma a}(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times a+\psi_{\psi_S(\sigma S\times3)}(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\Omega_3)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2aa)))</math>
|<math>\psi(\Omega_\omega\Omega_3+\psi_3(\Omega_\omega\Omega_3))</math>
|<math>\psi(\sigma^\omega aa+\psi_{\sigma a}(\sigma^\omega aa))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times a+\psi_{\psi_S(\sigma S\times3)}(\psi_S(\sigma S\times\omega)\times a))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\Omega_3+\Omega_9)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2aa+\sigma a)))</math>
|<math>\psi(\Omega_\omega\Omega_3+\Omega_4)</math>
|<math>\psi(\sigma^\omega aa+\sigma a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times a+\psi_S(\sigma S\times3))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,2)(3,3,3)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\times(\Omega_3+1))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2a\times(a+1))))</math>
|<math>\psi(\Omega_\omega\times(\Omega_3+1))</math>
|<math>\psi(\sigma^\omega a\times(a+1))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times(a+1))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,2)(3,3,3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\times\psi_3(\Omega_4))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2a\times\varepsilon_{a+1})))</math>
|<math>\psi(\Omega_\omega\times\psi_3(\Omega_4))</math>
|<math>\psi(\sigma^\omega a\times\varepsilon_{a+1})</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\varepsilon_{a+1})</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,2)(5,3)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\Omega_4)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2a\times\Omega_{a+1})))</math>
|<math>\psi(\Omega_\omega\times\psi_3(\Omega_5))</math>
|<math>\psi(\sigma^\omega a\times\Omega_{a+1})</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega_{a+1})</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,2,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\Omega_5)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2a\times a_2)))</math>
|<math>\psi(\Omega_\omega\times\psi_3(\Omega_6))</math>
|<math>\psi(\sigma^\omega a\times a_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times a_2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,2,2)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\times\psi_5(\Omega_{10}))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2a\times\psi_{\sigma a}(\sigma^2a))))</math>
|<math>\psi(\Omega_\omega\times\psi_3(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a\times\psi_{\sigma a}(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi_{\psi_S(\sigma S\times3)}(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,2,2)(5,3,3,1)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\Omega_6)))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2a\sigma a)))</math>
|<math>\psi(\Omega_\omega\Omega_4)</math>
|<math>\psi(\sigma^\omega a\sigma a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times \psi_S(\sigma S\times3))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,3)
|-
|<math>\psi(\Omega_3\Omega+\psi_2(\Omega_6\Omega_3+\psi_5(\Omega_{10}\Omega_6+\psi_9(\Omega_{15}\Omega_{10}))))</math>
|<math>\psi(a\Omega+\psi_a(\sigma aa+\psi_{\sigma a}(\sigma^2 a\sigma a+\psi_{\sigma^2a}(\sigma^3a\sigma^2a))))</math>
|<math>\psi(\Omega_\omega\Omega_5)</math>
|<math>\psi(\sigma^\omega a\sigma^2a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times \psi_S(\sigma S\times4))</math>
|(0)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2)(3,3,3,1)(4,3)(3,3,3)(4,4,4,1)(5,4)
|-
|<math>\psi(\Omega_3\times(\Omega+1))</math>
|<math>\psi(a\times(\Omega+1))</math>
|<math>\psi(\Omega_\omega^2)</math>
|<math>\psi(\sigma^\omega a^2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)
|}

== 分析3：(0)(1,1,1,1)(2,1)(1,1,1,1)~(0)(1,1,1,1)(2,1)(3,2) ==
{| class="wikitable" style="white-space: nowrap;"
|+分析3：(0)(1,1,1,1)(2,1)(1,1,1,1)~(0)(1,1,1,1)(2,1)(3,2)
!0Yψ
!强LPrSS投影
!拓展HPrSSψ
!弱LPrSS投影
!弱LPrSS向上投影
!BMS
|-
|<math>\psi(\Omega_3\times(\Omega+1))</math>
|<math>\psi(a\times(\Omega+1))</math>
|<math>\psi(\Omega_\omega^2)</math>
|<math>\psi(\sigma^\omega a^2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)
|-
|<math>\psi(\Omega_3\times(\Omega+2))</math>
|<math>\psi(a\times(\Omega+2))</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega)</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega))</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(1,1,1,1)
|-
|<math>\psi(\Omega_3\times(\Omega+\omega))</math>
|<math>\psi(a\times(\Omega+\omega))</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\omega)</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times\omega)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2)
|-
|<math>\psi(\Omega_3\times\Omega2)</math>
|<math>\psi(a\times\Omega2)</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega)</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a\Omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times\Omega)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)
|-
|<math>\psi(\Omega_3\times\Omega2+\Omega_2)</math>
|<math>\psi(a\times\Omega2+\Omega_2)</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega+\Omega_2)</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a\Omega+\Omega_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times\Omega+\Omega_2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)(1,1,1)
|-
|<math>\psi(\Omega_3\times\Omega2+\psi_2(\Omega_6))</math>
|<math>\psi(a\times\Omega2+\psi_a(\sigma a))</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega+\psi_2(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a\Omega+\psi_a(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times\Omega+\psi_a(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3\times\Omega2+\psi_2(\Omega_6\times(\Omega_3+\Omega)))</math>
|<math>\psi(a\times\Omega2+\psi_a(\sigma a\times(a+\Omega)))</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega+\psi_2(\Omega_\omega^2+\Omega_\omega\Omega))</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a\Omega+\psi_a(\sigma^\omega a^2+\sigma^\omega a\Omega))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times\Omega+\psi_a(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2,1)(3,1)
|-
|<math>\psi(\Omega_3\times\Omega2+\psi_2(\Omega_6\times(\Omega_3+\Omega)+\Omega_5))</math>
|<math>\psi(a\times\Omega2+\psi_a(\sigma a\times(a+\Omega)+a_2))</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega+\Omega_3)</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a\Omega+a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times\Omega+a)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2,1)(3,1)(2,2,2)
|-
|<math>\psi(\Omega_3\times\Omega2+\psi_2(\Omega_6\times(\Omega_3+\Omega+1)))</math>
|<math>\psi(a\times\Omega2+\psi_a(\sigma a\times(a+\Omega+1)))</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\times(\Omega+1))</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a\times(\Omega+1))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times(\Omega+1))</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2,1)(3,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3\times\Omega2+\psi_2(\Omega_6\times(\Omega_3+\Omega_2)))</math>
|<math>\psi(a\times\Omega2+\psi_a(\sigma a\times(a+\Omega_2)))</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega_2)</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega a\Omega_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times\Omega_2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2,1)(3,1,1)
|-
|<math>\psi(\Omega_3\times\Omega2+\psi_2(\Omega_6\times\Omega_32))</math>
|<math>\psi(a\times\Omega2+\psi_a(\sigma a\times a2))</math>
|<math>\psi(\Omega_\omega^2+\Omega_\omega\Omega_3)</math>
|<math>\psi(\sigma^\omega a^2+\sigma^\omega aa)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2+\psi_S(\sigma S\times\omega)\times a)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)(1,1,1)(2,2,2,1)(3,2)(2,2,2,1)(3,2)
|-
|<math>\psi(\Omega_3\times(\Omega2+1))</math>
|<math>\psi(a\times(\Omega2+1))</math>
|<math>\psi(\Omega_\omega^22)</math>
|<math>\psi(\sigma^\omega a^22)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2\times2)</math>
|(0)(1,1,1,1)(2,1)(1,1,1,1)(2,1)(1,1,1,1)
|-
|<math>\psi(\Omega_3\times\Omega\omega)</math>
|<math>\psi(a\times\Omega\omega)</math>
|<math>\psi(\Omega_\omega^2\omega)</math>
|<math>\psi(\sigma^\omega a^2\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2\times\omega)</math>
|(0)(1,1,1,1)(2,1)(2)
|-
|<math>\psi(\Omega_3\times\Omega^2)</math>
|<math>\psi(a\times\Omega^2)</math>
|<math>\psi(\Omega_\omega^2\Omega)</math>
|<math>\psi(\sigma^\omega a^2\Omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^2\times\Omega)</math>
|(0)(1,1,1,1)(2,1)(2,1)
|-
|<math>\psi(\Omega_3\times(\Omega^2+1))</math>
|<math>\psi(a\times(\Omega^2+1))</math>
|<math>\psi(\Omega_\omega^3)</math>
|<math>\psi(\sigma^\omega a^3)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^3)</math>
|(0)(1,1,1,1)(2,1)(2,1)(1,1,1,1)
|-
|<math>\psi(\Omega_3\times\Omega^\omega)</math>
|<math>\psi(a\times\Omega^\omega)</math>
|<math>\psi(\Omega_\omega^\omega)</math>
|<math>\psi(\sigma^\omega a^\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^\omega)</math>
|(0)(1,1,1,1)(2,1)(3)
|-
|<math>\psi(\Omega_3\times\Omega^\Omega)</math>
|<math>\psi(a\times\Omega^\Omega)</math>
|<math>\psi(\Omega_\omega^\Omega)</math>
|<math>\psi(\sigma^\omega a^\Omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^\Omega)</math>
|(0)(1,1,1,1)(2,1)(3,1)
|-
|<math>\psi(\Omega_3\times(\Omega^\Omega+1))</math>
|<math>\psi(a\times(\Omega^\Omega+1))</math>
|<math>\psi(\Omega_\omega^{\Omega_\omega})</math>
|<math>\psi(\sigma^\omega a^{\sigma^\omega a})</math>
|<math>\psi(\psi_S(\sigma S\times\omega)^{\psi_S(\sigma S\times\omega)})</math>
|(0)(1,1,1,1)(2,1)(3,1)(1,1,1,1)
|-
|<math>\psi(\Omega_3\times\psi_1(\Omega_2))</math>
|<math>\psi(a\times\psi_1(\Omega_2))</math>
|<math>\psi(\psi_\omega(\Omega_{\omega+1}))=\psi(\varepsilon_{\Omega_\omega+1})</math>
|<math>\psi(\psi_{\sigma^\omega a+1}(\Omega_{\sigma^\omega a+1}))=\psi(\varepsilon_{\sigma^\omega a+1})</math>
|<math>\psi(\psi_S(\sigma S\times\omega+S))</math>
|(0)(1,1,1,1)(2,1)(3,2)
|}

未完待续
[[分类:分析]]

0Yψ vs 拓展HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影分析

2026-08-01T06:27:02Z

量子杰克：分类

0Yψ vs 拓展HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影分析

2026-08-01T06:26:12Z

量子杰克：到0,1111,21,1111

SHO

2026-07-31T20:36:50Z

量子杰克：

SHO（Small Hydra Ordinal），又称BMO（Bashicu Matrix Ordinal），由 FataliS1024 命名，该名字原本指 <math>\varepsilon_0</math>（[[SCO]]），后来因为不明原因变成了 [[BMS]] 极限。该序数在 [[Googology]] 中有着极其重要的地位。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[稳定序数]]
|<math>\le\psi(\rm{psd.}\Sigma_\omega-\rm{stb})</math>
|-
|[[投影序数#向上投影|向上投影]]
|<math>\psi(\psi_H(\varepsilon_{H+1}))</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,3</math>
|-
|[[Mountain Notation]]
|<math>(0)(,,1)</math>
|-
|[[MMS]]
|<math>(0)(1,1)</math>
|-
|[[DBMS]]
|<math>(0)(1,,1)</math>
|-
|[[Fake Fake Fake Zeta]]
|<math>\psi_Z[\varepsilon_\omega](\varepsilon_\omega)</math>
|-
|FOS
|<math>0,1,\omega,\varepsilon_0</math>
|}

=== 性质 ===
证明论序数：SHO 的证明论强度在 ggg 界还没有定论，主流的观点认为 <math>\rm{SHO}=\rm{PTO}(Z_2)=\rm{PTO}(\mathrm{KP}\omega+\Pi_N-\rm{Collection})</math>，通常将这个PTO称为βO。

极限在此处的记号：几乎所有[[Kirby-Paris Hydra|多行 Hydra]] 记号极限都是 SHO，包括但不限 [[BMS]]，[[0-Y]]，[[Ex-hydra]] 等等。[[BHM]]、[[BSM]] 的极限也很可能为 SHO。

如果 <math>\rm{SHO}=\rm{PTO}(Z_2)</math> 的假设成立，则 [[Σ1稳定序数#Non-Gandy 现象|adm 稳定和 pfec 稳定]]的 [[Catching]] 点有可能位于 SHO。
[[分类:序数]]

TSSO

2026-07-31T20:35:59Z

量子杰克：

TSSO（Trio Sequence System Ordinal），是一个重要的序数，指代三行[[BMS]]的极限，同时也是简单投影序数折叠记号等序数记号的极限。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[投影序数]]
|<math>\psi(\alpha(\omega;0))</math>
|-
|[[向上投影]]
|<math>\psi(\psi_S(\sigma S\times\omega))</math>
|-
|[[BMS]]
|<math>(0)(1,1,1,1)</math>
|-
|[[0-Y]]
|<math>1,5</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,16</math>
|-
|[[Fake Fake Fake Zeta]]
|<math>\psi_\Zeta(\varepsilon_1)</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^{\omega^\omega}</math>
|}

=== 性质 ===
极限在此处的记号：三行[[BMS]]、简单投影、HPrSSψ等记号
[[分类:序数]]

LRO

2026-07-31T20:35:06Z

量子杰克：

LRO（Large Rathjen Ordinal），是一个重要的序数，指代 <math>\rm{psd.}\omega.\rm{ply}-\rm{stb}</math> 折叠后的结果，其真实大小目前尚没有明确结论，主流的观点是 LRO=[[TSSO]]。另一个更常用的版本叫做 pfec.LRO（简称 pLRO），忽略 [[Σ1稳定序数#Non-Gandy 现象|Non-Gandy 现象]]，其大小等于 BMS(0)(1,1,1)(2,2,2)，这个序数又称 SBO（Small Bashicu Ordinal）或 OBO（Omega Back Ordinal）。<ref>BashicuHyudora (2015). バシク行列の解析 [Analysis of the Bashicu matrix]. ''(EB/OL), Googology Wiki''. Available at: https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:BashicuHyudora/%E3%83%90%E3%82%B7%E3%82%AF%E8%A1%8C%E5%88%97%E3%81%AE%E8%A7%A3%E6%9E%90</ref>
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[稳定序数]]
|<math>\psi(\omega.\rm{ply}-\Pi_0)</math>
|-
|[[投影序数]]
|<math>\psi(\psi_\alpha(\alpha_\omega))</math>
|-
|[[UNOCF|Aarex's exUNOCF]]
|<math>\psi(C(1\{:\omega\}0))</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,2,2)</math>
|-
|[[0-Y]]
|<math>1,4,10</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,15</math>
|-
|[[Ex-hydra]]
|<math>p1(p3(p6))</math>
|-
|[[Fake Fake Fake Zeta]]
|<math>\psi_\Zeta[\varepsilon_1](\rm{BO})</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^{\omega^2}</math>
|}

=== 性质 ===
[[证明论序数]]：<math>\Pi_2^1-\rm{CA}_0</math>，<math>\rm{KPnp}</math>（可能是 <math>\mathrm{KP}+\exist N \ \mathrm{admissibles-stable},N\in\omega</math> 的证明论序数<ref>HypCos (n.d.). TON vs. stability (remastered). ''(EB/OL), Googology Wiki''. Available at: https://googology.fandom.com/wiki/User:Hyp_cos/TON_vs._stability_(remastered)#Up_to_%CF%89_admissibles-stable</ref>）

极限在此处的记号：[[LMN]]，[[LON]]，non-recursive FGH，weak DLON，Lumi's LPSS，WDmEN，IUN，CCN，Sudden Hydra，[[Catching 函数|Catching Function]]，2-Proj，A Notation，1-Waiting Hydra

== 参考资料 ==
<references />
[[分类:序数]]

TSO

2026-07-31T20:34:18Z

量子杰克：

TSO（Triply Stability Ordinal），指第一个涉及三段[[稳定序数|稳定]]链的序数。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[稳定序数]]
|<math>\psi(\lambda\alpha.(\lambda\beta.(\lambda\gamma.\gamma+1-\Pi_0[\beta+1])-\Pi_0[\alpha+1])-\Pi_0)</math>
|-
|[[投影序数]]
|<math>\psi(\psi_\alpha(\varepsilon_{\Omega_{\alpha_3+1}+1}))</math>
|-
|[[UNOCF|Aarex's exUNOCF]]
|<math>\psi(\Omega_{C(1::;;0)+1})</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,2,1)(3,3,1)(4,4)</math>
|-
|[[0-Y]]
|<math>1,4,9,16,24</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,14,22,31</math>
|-
|[[Ex-hydra]]
|<math>p1(p3(p5(p7(p8))))</math>
|-
|[[Fake Fake Fake Zeta]]
|<math>\psi_\Zeta[\varepsilon_1](\psi_\Zeta[\varepsilon_0](\varepsilon_1))</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^{\omega2},\omega^{\omega3},\omega^{\omega3+1}</math>
|}

=== 性质 ===
是第一个涉及三段[[稳定序数|稳定]]链的序数。
[[分类:序数]]

DSO

2026-07-31T20:33:23Z

量子杰克：

DSO（Doubly Stability Ordinal），指第一个涉及二段[[稳定序数|稳定]]链的序数。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[稳定序数]]
|<math>\psi(\lambda\alpha.(\lambda\beta.\beta+1-\Pi_0[\alpha+1])-\Pi_0)</math>
|-
|[[投影序数]]
|<math>\psi(\psi_\alpha(\varepsilon_{\Omega_{\alpha_2+1}+1}))</math>
|-
|[[UNOCF|Aarex's exUNOCF]]
|<math>\psi(\Omega_{C(1:;;0)+1})</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,2,1)(3,3)</math>
|-
|[[0-Y]]
|<math>1,4,9,15</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,14,21</math>
|-
|[[Ex-hydra]]
|<math>p1(p3(p5(p6)))</math>
|-
|[[Fake Fake Fake Zeta]]
|<math>\psi_\Zeta[\varepsilon_1](\psi_\Zeta[\varepsilon_0](\psi_\Zeta[\varepsilon_0](\varepsilon_1)))</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^{\omega2},\omega^{\omega2+1}</math>
|}

=== 性质 ===
极限在此处的记号：E Notation

是第一个涉及二段[[稳定序数|稳定]]链的序数。
[[分类:序数]]

LDO

2026-07-31T20:32:21Z

量子杰克：

LDO（Large Dropping Ordinal），由 Username5243 命名，指代拓展 [[UNOCF]] 极限。该名字曾经也用于指代 <math>(0)(1,1,1)(2,2,1)(3,1)(2)</math>（<math>\psi(\psi_\alpha(\Omega_{\alpha_2+1}\times\alpha))</math>）。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[稳定序数]]
|<math>\psi(\lambda\alpha.\Phi(1,\alpha+1)-\Pi_0)</math>
|-
|[[投影序数]]
|<math>\psi(\psi_\alpha(\Omega_{\alpha_2+1}\times\alpha_2))</math>
|-
|[[投影序数#向上投影|向上投影]]
|<math>\psi(\psi_S(\sigma S+\psi_{S_3}(\sigma S+S_2)))</math>
|-
|[[UNOCF|Aarex's exUNOCF]]
|<math>\psi(C(1\{1:0\}0)))</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,2,1)(3,2)</math>
|-
|[[0-Y]]
|<math>1,4,9,13</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,14,19</math>
|-
|[[Ex-hydra]]
|<math>p1(p3(p5(p4)))</math>
|-
|[[Fake Fake Fake Zeta]]
|<math>\psi_\Zeta[\varepsilon_1](\psi_\Zeta[\varepsilon_0](\varepsilon_0\times\omega))</math>
|-
|[[Catching 函数]]
|<math>C(\Phi(1,0))</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^{\omega2},\omega^{\omega2}+\omega^{\omega+1}</math>
|}

=== 性质 ===
极限在此处的记号：[[SAN|NDAN]]，[[UNOCF|拓展 UNOCF]] ，LXN，MCS，CIAN v1
[[分类:序数]]

SDO

2026-07-31T20:30:19Z

量子杰克：

SDO（Small Dropping Ordinal），由 Username5243 命名<ref>https://googology.fandom.com/wiki/User:Username5243/Username%27s_OCF</ref>，指代原版 [[UNOCF]] 极限，同时也是 [[Dropping Hydra|N-dropping]] 和 [[N-shifting]] 模式的极限。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[稳定序数]]
|<math>\psi(\lambda\alpha.\Omega_{\alpha+\omega}-\Pi_0)</math>
|-
|[[投影序数]]
|<math>\psi(\psi_\alpha(\Omega_{\alpha+\omega}))</math>
|-
|[[投影序数#向上投影|向上投影]]
|<math>\psi(\psi_S(\sigma S*2+\psi_{S_3}(\sigma S+1)))</math>
|-
|[[UNOCF]]
|<math>\psi(C(1\{\omega\}0)))</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,2,1)(3)</math>
|-
|[[0-Y]]
|<math>1,4,9,10</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,14,15</math>
|-
|[[Ex-hydra]]
|<math>p1(p3(p5(p1))))</math>
|-
|[[Fake Fake Fake Zeta]]
|<math>\psi_\Zeta[\varepsilon_1,\psi_\Zeta[\varepsilon_0,\varepsilon_0\times\omega](\varepsilon_0\times\omega)](\psi_\Zeta[\varepsilon_0,\varepsilon_0\times\omega](\varepsilon_0\times\omega))</math>
|-
|[[Catching 函数]]
|<math>C(\Omega_\omega)</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^{\omega2},\omega^{\omega2}+1</math>
|}

=== 性质 ===
极限在此处的记号：[[SAN]]，R函数，[[Dropping Hydra]] 等 [[Dropping Hydra|N-dropping]]记号，[[TON]] 主记号等 [[N-shifting]] 记号，[[UNOCF]] 等多逗号模式记号，LPrSS Hydra
<references />
[[分类:序数]]

BGO

2026-07-31T20:29:35Z

量子杰克：

BGO（1st TSS Back Gear Ordinal），由Bashicu命名，原来指代 BMS(0)(1,1,1)(2,2)<ref>BashicuHyudora (2015). バシク行列の解析 [Analysis of the Bashicu matrix]. ''(EB/OL), Googology Wiki''. Available at: https://googology.fandom.com/ja/wiki/%E3%83%A6%E3%83%BC%E3%82%B6%E3%83%BC%E3%83%96%E3%83%AD%E3%82%B0:BashicuHyudora/%E3%83%90%E3%82%B7%E3%82%AF%E8%A1%8C%E5%88%97%E3%81%AE%E8%A7%A3%E6%9E%90</ref>，后来因不明原因变成了 BMS(0)(1,1,1)(2,2,1)。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[稳定序数]]
|<math>\psi(\Pi_1(\lambda\alpha.\Omega_{\alpha+2}-\Pi_1))</math>
|-
|[[投影序数]]
|<math>\psi(\psi_\alpha(\Omega_{\alpha+2}\times\omega))</math>
|-
|[[UNOCF]]
|<math>\psi(T_\omega)</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,2,1)</math>
|-
|[[0-Y]]
|<math>1,4,9</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,14</math>
|-
|[[Ex-hydra]]
|<math>p1(p3(p5))</math>
|-
|[[Fake Fake Fake Zeta]]
|<math>\psi_\Zeta[\varepsilon_1](\rm{BHO})</math>
|-
|[[Catching 函数]]
|<math>C(\Omega_2)</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^{\omega2}</math>
|}

=== 性质 ===
是 [[BMS]] 的第一个三行传递所在处，可以形象化的表述为：如果称 <math>\Pi_\omega</math>-[[反射序数|反射]]具有 <math>\varepsilon_0</math> 的反射结构，则 BGO 是第一个满足“α 具有 α 的反射结构”的序数。

== 参考资料 ==

APO

2026-07-31T20:28:48Z

量子杰克：

APO（Admissible-Parameter free effective cardinal Ordinal），是 [[Σ1稳定序数#Non-Gandy 现象|pfec 稳定和 adm 稳定]]的分歧点。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[稳定序数]]
|<math>\psi(\Pi_1(\lambda\alpha.\Omega_{\alpha+1}-\Pi_1))</math>
|-
|[[投影序数]]
|<math>\psi(\psi_\alpha(\varphi(\Omega_{\alpha+1},1)\times\omega))</math>
|-
|[[UNOCF]]
|<math>\psi(\Omega_{T+1}^T+\psi_{\Omega_{T+1}}(\Omega_{T+1}^T+1))</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,2)(3,2)(4,1,1)</math>
|-
|[[0-Y]]
|<math>1,4,8,12,15</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,13,18,22</math>
|-
|[[Ex-hydra]]
|<math>p1(p3(p4(p4(p3))))</math>
|-
|[[Fake Fake Fake Zeta]]
|<math>\psi_\Zeta[\varepsilon_1](\varphi(\varepsilon_0,0))</math>
|-
|[[Catching 函数]]
|<math>C(\varphi(\Omega,1))</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^{\omega+1},\omega^{\omega+1}2,\omega^{\omega+1}2+\omega^\omega</math>
|}

=== 性质 ===
极限在此处的记号：adm PrSS

是 [[Σ1稳定序数#Non-Gandy 现象|pfec 稳定和 adm 稳定]]的分歧点，在 <math>\lambda\alpha.\Omega_{\alpha+1}-\Pi_1</math> 之后，[[稳定序数]] 将会因为出现 [[Σ1稳定序数#Non-Gandy 现象|Non-Gandy 效应]]而大幅增强。同时也是永进稳定和非永进稳定的分歧点。

<math>\lambda\alpha.\Omega_{\alpha+1}-\Pi_1</math> 曾经被误认为是 [[Dropping Hydra|2-Dropping]] 序数，然而后来的扽西表明这实际上是 <math>\lambda\alpha.\Omega_{\alpha+2}-\Pi_1</math>。
[[分类:序数]]

LSO

2026-07-31T20:27:48Z

量子杰克：

LSO（Large Stegert Ordinal），是 Stability 的证明论序数，该结论由 Stegert 给出，因此得名。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[稳定序数]]
|<math>\psi(\lambda\alpha.\alpha2-\Pi_0)</math>
|-
|[[投影序数]]
|<math>\psi(\psi_\alpha(\varphi(\alpha,\Omega_{\alpha+1})))</math>
|-
|[[UNOCF]]
|<math>\psi(\Omega_{T+1}^T)</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,2)(3,2)(4,1)(2)</math>
|-
|[[0-Y]]
|<math>1,4,8,12,14,5</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,13,18,21,9</math>
|-
|[[Ex-hydra]]
|<math>p1(p3(p4(p4(p2))+p1))</math>
|-
|[[Fake Fake Fake Zeta]]
|<math>\psi_\Zeta[\varepsilon_1,\varphi(\omega,0)\times\omega](\varphi(\omega,0)\times\omega)</math>
|-
|[[Catching 函数]]
|<math>C(\varphi(\omega,\Omega+1)\times\omega)</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^{\omega+1},\omega^{\omega+1}2,\omega^{\omega+1}2+\omega^2,\omega^\omega+1</math>
|}

=== 性质 ===
[[证明论序数]]：<math>\rm{Stability}</math>

极限在此处的记号：Stegert's OCF，EUAN，62XXY's OCF
[[分类:序数]]

SSO

2026-07-31T20:25:07Z

量子杰克：

SSO（Small Stegert Ordinal），是 <math>\rm{KP+\Pi_N-ref},N\in\omega</math> 的证明论序数，该结论由 Stegert 给出，因此得名。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[反射序数]]
|<math>\psi(\rm{psd.}\Pi_\omega)</math>
|-
|[[稳定序数]]
|<math>\psi(\lambda\alpha.\alpha+1-\Pi_0)</math>
|-
|[[投影序数]]
|<math>\psi(\psi_\alpha(\varepsilon_{\Omega_{\alpha+1}+1}))=\psi(\psi_\alpha(\alpha_2))</math>
|-
|[[UNOCF]]
|<math>\psi(\varepsilon_{T+1})</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,2)</math>
|-
|[[0-Y]]
|<math>1,4,8</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,13</math>
|-
|[[Ex-hydra]]
|<math>p1(p3(p4))</math>
|-
|[[Fake Fake Fake Zeta]]
|<math>\psi_\Zeta[\varepsilon_1](\varepsilon_1)</math>
|-
|[[Catching 函数]]
|<math>C(\varepsilon_{\Omega+1})</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^{\omega+1}</math>
|}

=== 性质 ===
[[证明论序数]]：<math>\rm{KP+\Pi_N-ref},N\in\omega</math>

极限在此处的记号：[[SAN|pDAN]]、[[Dropping#M 记号|M 记号]]等 [[Dropping Hydra|2-dropping]] 记号，[[反射序数]]
[[分类:序数]]

DO

2026-07-31T20:24:11Z

量子杰克：

DO（Duchhart's Ordinal），是一个重要的[[序数]]。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega_{\kappa+1})</math>
|-
|[[反射序数]]
|<math>\psi(2 \ \text{aft} \ 4)</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)(5,1)(6,2)</math>
|-
|[[0-Y]]
|<math>1,4,7,10,13,15,19</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,12,16,20,23,27</math>
|-
|[[ex-hydra]]
|<math>p1(p3(p3(p3(p3(p2(p3))))))</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>p(p(M^{M^{M^M}}+M))</math>
|-
|[[投影序数|投影]]
|<math>\psi(\psi_\alpha(\Omega_{\alpha+1}^{\Omega_{\alpha+1}^{\Omega_{\alpha+1}^{\varepsilon_{\alpha+1}}}}))</math>
|-
|[[Catching 函数]]
|<math>C(\Omega^{\Omega^{\Omega^{\varepsilon_0}}})</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^\omega2,\omega^\omega3,\omega^\omega4,\omega^\omega4+\omega^2,\omega^\omega4+\omega^3</math>
|}

=== 性质 ===
[[证明论序数]]：<math>\rm KP+\Pi_4-Reflection</math>

极限在此处的记号：Duchhart's OCF
[[分类:序数]]

SKO

2026-07-31T20:23:13Z

量子杰克：

SKO（Small Weakly-Compact Ordinal），是一个重要的[[序数]]。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(K_\omega)</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,1,1)(3,1,1)(4,1,1)</math>
|-
|[[反射序数]]
|<math>\psi(1-3)</math>
|-
|[[0-Y]]
|<math>1,4,7,10,13</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,12,16,20</math>
|-
|[[ex-hydra]]
|<math>p1(p3(p3(p3(p3))))</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>p(p(M^{M^M}\times\omega))</math>
|-
|[[投影序数|投影]]
|<math>\psi(\psi_\alpha(\Omega_{\alpha+1}^{\Omega_{\alpha+1}^{\Omega_{\alpha+1}}}\times\omega))</math>
|-
|[[Catching 函数]]
|<math>C(\Omega^{\Omega^\Omega})</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^\omega2,\omega^\omega3,\omega^\omega4</math>
|}
[[分类:序数]]

RO

2026-07-31T20:22:23Z

量子杰克：

RO（Rathjen's Ordinal），是一个重要的[[序数]]。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega_{K+1})</math>
|-
|[[反射序数]]
|<math>\psi(2\ \text{aft}\ 3)</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,1,1)(3,1,1)(4,1)(5,2)</math>
|-
|[[0-Y]]
|<math>1,4,7,10,12,15</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,12,16,19,23</math>
|-
|[[ex-hydra]]
|<math>p1(p3(p3(p3(p2(p3)))))</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>p(p(M^{M^M}+M))</math>
|-
|[[投影序数|投影]]
|<math>\psi(\psi_\alpha(\Omega_{\alpha+1}^{\Omega_{\alpha+1}^{\varepsilon_{\alpha+1}}}))</math>
|-
|[[Catching 函数]]
|<math>C(\Omega^{\Omega^{\varepsilon_0}})</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^\omega2,\omega^\omega3,\omega^\omega3+\omega^2,\omega^\omega3+\omega^3</math>
|}

=== 性质 ===
[[证明论序数]]：<math>\rm{KP+\Pi_3-reflection}</math>

极限在此处的记号：[[Rathjen's Ξ]]
[[分类:序数]]

SNO

2026-07-31T20:21:25Z

量子杰克：

SNO（Small Nonconvertible Ordinal），是一个重要的[[序数]]。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(N_\omega)</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)(3,1,1)</math>
|-
|[[反射序数]]
|<math>\psi(1-2-2-2)</math>
|-
|[[0-Y]]
|<math>1,4,7,10,10,10</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,12,16,16,16</math>
|-
|[[ex-hydra]]
|<math>p1(p3(p3(p3+p3+p3)))</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>p(p(M^{M^2}\times\omega))</math>
|-
|[[投影序数|投影]]
|<math>\psi(\psi_\alpha(\Omega_{\alpha+1}^{\Omega_{\alpha+1}^2}\times\omega))</math>
|-
|[[Catching 函数]]
|<math>C(\Omega^{\Omega^2})</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^\omega2,\omega^\omega3,\omega^\omega3,\omega^\omega3</math>
|}
[[分类:序数]]

SMO

2026-07-31T20:20:30Z

量子杰克：

SMO（Small Mahlo Ordinal），是一个重要的[[序数]]。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(M_\omega)</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)</math>
|-
|[[反射序数]]
|<math>\psi(1-2-2)</math>
|-
|[[0-Y]]
|<math>1,4,7,10,10</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,12,16,16</math>
|-
|[[ex-hydra]]
|<math>p1(p3(p3(p3+p3)))</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>p(p(M^M\times\omega))</math>
|-
|[[投影序数|投影]]
|<math>\psi(\psi_\alpha(\Omega_{\alpha+1}^{\Omega_{\alpha+1}}\times\omega))</math>
|-
|[[Catching 函数]]
|<math>C(\Omega^\Omega)</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^\omega2,\omega^\omega3,\omega^\omega3</math>
|}

=== 性质 ===
极限在此处的记号：[[Rathjen's χ]]，Byte Notation，NAON，KumaKuma ψ function
[[分类:序数]]

SRO

2026-07-31T20:19:43Z

量子杰克：

SRO（Small Rathjen's Ordinal），是一个重要的[[序数]]。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega_{M+1})</math>
|-
|[[反射序数]]
|<math>\psi(2 \ \text{aft}\ 2-2)</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(4,2)</math>
|-
|[[0-Y]]
|<math>1,4,7,10,9,12</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,12,16,15,19</math>
|-
|[[ex-hydra]]
|<math>p1(p3(p3(p3+p2(p3))))</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>p(p(M^M+M))</math>
|-
|[[投影序数|投影]]
|<math>\psi(\psi_\alpha(\Omega_{\alpha+1}^{\varepsilon_{\alpha+1}}))</math>
|-
|[[Catching 函数]]
|<math>C(\Omega^{\varepsilon_0})</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^\omega2,\omega^\omega3,\omega^\omega2+\omega^2,\omega^\omega2+\omega^3</math>
|}

=== 性质 ===
[[证明论序数]]：<math>\rm KPM</math>

极限在此处的记号：62XXY's Milk φ
[[分类:序数]]

TBO

2026-07-31T20:18:42Z

量子杰克：

TBO（Transfinity Buchholz Ordinal），是一个重要的[[序数]]，因为它是[[多元 Buchholz 函数|序数元 Buchholz 函数]]的极限而得名。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(I(1,0,0))</math>
|-
|[[反射序数]]
|<math>\psi((2\ 1-)^{(1,0)}))</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2)</math>
|-
|[[0-Y]]
|<math>1,4,7,10,9,5</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,12,16,15,9</math>
|-
|[[ex-hydra]]
|<math>p1(p3(p3(p3(p2))+p1))</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>p(p(M^M))</math>
|-
|[[投影序数|投影]]
|<math>\psi(\psi_\alpha(\Omega_{\alpha+1}^\alpha))</math>
|-
|[[Catching 函数]]
|<math>C(\Omega^\omega\omega)</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^\omega2,\omega^\omega3,\omega^\omega2+\omega^2,\omega^\omega+1</math>
|}

=== 性质 ===
极限在此处的记号：[[多元 Buchholz 函数|序数元 Buchholz 函数]]等<math>\Omega_{\alpha+1}</math>进制数阵
[[分类:序数]]

MBO

2026-07-31T20:17:26Z

量子杰克：

MBO（Multiple Buchholz Ordinal），是一个重要的[[序数]]，因为它是[[多元 Buchholz 函数]]的极限而得名。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(I(\omega,0))</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,1,1)(3,1,1)(3)</math>
|-
|[[0-Y]]
|<math>1,4,7,10,8</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,12,16,13</math>
|-
|[[ex-hydra]]
|<math>p1(p3(p3(p3+p1)))</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>p(p(M^\omega))</math>
|-
|[[投影序数|投影]]
|<math>\psi(\psi_\alpha(\Omega_{\alpha+1}^\omega))</math>
|-
|[[Catching 函数]]
|<math>C(\Omega^\omega)</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^\omega2,\omega^\omega3,\omega^\omega2+1</math>
|}

=== 性质 ===
极限在此处的记号：[[PDAN|pDAN 第一部分]]、[[多元 Buchholz 函数]]等 <math>\Omega_{\alpha+1}</math> 进制数阵，SSUN，SCN-3，EFAN，UIAN，SIAN，Linear R function，FAN
[[分类:序数]]

SIO

2026-07-31T20:16:07Z

量子杰克：

SIO（Small Inaccessible Ordinal），是一个重要的[[序数]]。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(I_\omega)</math>
|-
|[[BMS]]
|<math>(0)(1,1,1)(2,1,1)(3,1,1)</math>
|-
|[[0-Y]]
|<math>1,4,7,10</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,12,16</math>
|-
|[[ex-hydra]]
|<math>p1(p3(p3(p3)))</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>p(p(M^2\times\omega))</math>
|-
|[[投影序数|投影]]
|<math>\psi(\psi_\alpha(\Omega_{\alpha+1}^2\times\omega))</math>
|-
|[[Catching 函数]]
|<math>C(\Omega)</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^\omega2,\omega^\omega3</math>
|}

=== 性质 ===
是 α→([[增长层级#快速增长层级|FGH]] 和 [[增长层级#慢速增长层级|SGH]] 的第 α 个 [[Catching]] 点) 的第一个不动点；是 [[序数坍缩函数#BOCF|BOCF]] 和 [[NOCF]] 的第一个 [[Catching]] 点。
[[分类:序数]]

JO

2026-07-31T20:14:35Z

量子杰克：

JO（Jäger's Ordinal），是一个重要的[[序数]]。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega_{I+1})</math>
|-
|[[BMS]]
|<math>\begin{pmatrix} 0 & 1 & 2 & 3 & 4\\
0 & 1 & 1 & 1 & 2\\
0 & 1 & 1 & 0 & 0\end{pmatrix}
=(0)(1,1,1)(2,1,1)(3,1)(4,2)</math>
|-
|[[0-Y]]
|<math>1,4,7,9,12</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,12,15,19</math>
|-
|[[ex-hydra]]
|<math>p1(p3(p3(p2(p3))))</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>p(p(M^2+M))</math>
|-
|[[投影序数|投影]]
|<math>\psi(\psi_\alpha(\Omega_{\alpha+1}\times\varepsilon_{\alpha+1}))</math>
|-
|[[Catching 函数]]
|<math>C(\varepsilon_0)</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^\omega2,\omega^\omega2+\omega^2,\omega^\omega2+\omega^3</math>
|}

=== 性质 ===
[[证明论序数]]：<math>\rm \Delta_2^1-CA+BI</math>，<math>\rm \Sigma_2^1-AC+BI</math>，<math>\rm KPi</math>，<math>{\rm KP}\beta</math>，<math>\rm CZF+REA</math>，<math>\rm T_0</math>

极限在此处的记号：[[Jäger-Buchholz 函数]]，[[Rathjen's Φ|多维 Rathjen's Φ]]

[[分类:序数]]

EBO

2026-07-31T20:13:17Z

量子杰克：

'''EBO（Extended Buchholz Ordinal）'''，是扩展 BOCF 的极限。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[序数坍缩函数#BOCF|BOCF]]
|<math>\psi(\Omega_{\Omega_\ddots})=\psi(I)</math>
|-
|[[序数坍缩函数#MOCF|MOCF]]
|<math>\psi(\Omega_{\Omega_\ddots})=\psi(\psi_I(0))</math>
|-
|[[BMS]]
|<math>\begin{pmatrix}
0&1&2&3&2\\
0&1&1&1&0\\
0&1&1&0&0
\end{pmatrix}
=(0)(1,1,1)(2,1,1)(3,1)(2)</math>
|-
|[[0-Y]]
|<math>1,4,7,9,5</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,12,15,9</math>
|-
|[[BHM]]
|<math>\begin{pmatrix}
0&1&1&2&1\\
0&1&0&0&1
\end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix}
0&1\\
0&1
\end{pmatrix}</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M^2))</math>
|-
|[[Catching 函数]]
|<math>C(\omega)</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^\omega2,\omega^\omega2+\omega^2,\omega^\omega+1</math>
|}

=== 性质 ===
[[证明论序数]]：<math>\rm \Pi_1^1-TR_0</math>，<math>\rm \Pi_1^1-TR_0+\Delta_2^1-CA_0</math>，<math>\rm \Delta_2^1-CA+BI(impl\ \Sigma_2^1)</math>，<math>\rm \Delta_2^1-CA+BR(impl\ \Sigma_2^1)</math>，<math>\rm RCA_0+\Delta_2^0-det.</math>，<math>\rm RCA_0+\Delta_1^1-RT</math>，<math>{\rm Aut-KPl}^r</math>，<math>{\rm Aut-KPl}^r+{\rm KPi}^r</math>，<math>\rm KPi^\omega+FOUNDR(impl-\Sigma)</math>，<math>\rm KPi^\omega+FOUND(impl-\Sigma)</math>，<math>{\rm Aut-ID}_0^{pos}</math>，<math>{\rm Aut-ID}_0^{mon}</math>

极限在此处的记号：SSS（一行 [[BSM]]），扩展 [[序数坍缩函数#BOCF|BOCF]]，EBPF，ISSS，PrDS

EBO 是 [[增长层级#快速增长层级|FGH]] 和 [[增长层级#慢速增长层级|SGH]] 的第 <math>\omega</math> 个[[Catching|追平]]点。

是 [[BMS]] 的第一处循环提升，(0)(1,1,1)(2,1,1)(3,1) 的 (3,1) 依次被 (1,1,1)、(1,1,1)(2,1,1)、(1,1,1)(2,1,1)(3,1) 等提升，直到提升到 <math>\Omega</math> [[不动点]]。

[[分类:序数]]

BIO

2026-07-31T20:11:25Z

量子杰克：

BIO（Bird's Ordinal），是 [[Googology]] 中一个重要的[[序数]]。它是[[BAN|鸟之记号]]（Bird's Array Notation）的极限。
{| class="wikitable"
![[序数记号]]
!表达式
|-
![[序数坍缩函数#BOCF|BOCF]] / [[序数坍缩函数#MOCF|MOCF]]
!<math>\psi(\Omega_\Omega)</math>
|-
|[[BMS]]
|<math>\begin{pmatrix} 0 & 1 & 2 & 3\\
0 & 1 & 1 & 1\\
0 & 1 & 1 & 0\end{pmatrix}
=(0)(1,1,1)(2,1,1)(3,1)</math>
|-
|[[0-Y]]
|<math>1,4,7,9</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,12,14</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>p(p(M*p(M)))</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^\omega2,\omega^\omega2+\omega</math>
|}

=== 性质 ===
极限在此处的记号：[[BAN]]
[[分类:序数]]

TFBO

2026-07-31T20:10:03Z

量子杰克：

'''TFBO（Takeuti-Feferman-Buchholz ordinal）'''，是 [[Buchholz Hydra]] 的极限的[[序数]]。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[序数坍缩函数#BOCF|BOCF]]
|<math>\psi(\Omega_{\omega+1})</math>
|-
|[[序数坍缩函数#MOCF|MOCF]]
|<math>\psi(\psi_\omega(0))</math>
|-
|[[BMS]]
|<math>\begin{pmatrix}
0&1&2&3\\
0&1&1&2\\
0&1&0&0
\end{pmatrix}
=(0)(1,1,1)(2,1)(3,2)</math>
|-
|[[0-Y]]
|<math>1,4,6,9</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8,11,15</math>
|-
|[[BHM]]
|<math>\begin{pmatrix}
0&1&1&2&1&1&2&2&3&1&2&3\\
0&1&0&0&0&0&1&0&0&0&0&0
\end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix}
0&1&2&2&3&0&1&1&2&1&1&2
\end{pmatrix}</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M\times\omega+M))</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega,\omega^\omega+\omega^2,\omega^\omega+\omega^3</math>
|}

=== 性质 ===
[[证明论序数]]：<math>\rm\Pi^1_1-CA+BI</math>，<math>\rm KPl</math>，<math>\rm ID_\omega</math>，<math>\rm BID_\omega^2</math>

极限在此处的记号：BPF，[[Buchholz Hydra]]，MPF，Feferman's θ

[[分类:序数]]

BO

2026-07-31T20:04:22Z

量子杰克：

BO（Buchholz's Ordinal），是 [[Googology]] 中一个非常重要的序数。它被认为是具有“里程碑”意义的大序数，是 [[PSS Hydra]]、[[HPrSS]]、双行 [[BMS]] 及诸多[[序数记号]]的极限。学会一个 BO 级别的序数记号被认为是 googology 新人入门的标志。
{| class="wikitable"
![[序数记号]]
!表达式
|-
![[序数坍缩函数#BOCF|BOCF]] / [[序数坍缩函数#MOCF|MOCF]]
!<math>\psi(\Omega_{\omega})</math>
|-
|[[BMS]]
|<math>\begin{pmatrix} 0 & 1 \\ 0 & 1\\0&1 \end{pmatrix}=(0)(1,1,1)</math>
|-
|[[0-Y]]
|<math>1,4</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,8</math>
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1&1&2 \\ 0 & 1&0&0 \end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0&1&2&2&3 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_{\Omega_{\omega}})/\psi(\Omega_{\Omega_{\psi(\Omega)}})</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M\times\omega))</math>
|-
|[[Catching 函数]]
|<math>C(0)</math>
|-
|FOS
|<math>0,1,\omega,\omega^\omega</math>
|}

=== 性质 ===
[[证明论序数]]：<math>\rm \Pi_1^1-CA_0</math>，<math>\rm \Delta_2^1-CA_0</math>，<math>\rm RCA_0+\Sigma_1^0\land\Pi_1^0-det.</math>，<math>\rm RCA_0+\Delta_2^0-RT</math>，<math>{\rm KPl}^r</math>，<math>{\rm KPi}^r</math>，<math>{\rm KP}\beta^r</math>，<math>{\rm ID}_{<\omega}</math>，<math>({\rm ID}_{<\omega}^2)_0</math>

极限在此处的记号： [[PSS Hydra]]，[[HPrSS]]，双行 [[BMS]]（PSS），SIUN，PrGS，b-THIAN，[[BEAF|带 & 的 BEAF]]，ABN I，三就跳函数，FPrSS，mEAN

BO 是 [[增长层级#快速增长层级|FGH]] 和 [[增长层级#慢速增长层级|SGH]] 的第一个[[Catching|追平点]]。

[[分类:序数]]

BHO

2026-07-31T20:03:07Z

量子杰克：

BHO（Bachmann-Howard Ordinal），是一个重要的[[序数]]。它被认为是具有“里程碑”意义的一个序数。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[Veblen 函数]]
|\(\varphi(1@(1@(\cdots)))=\varphi(\min\;\alpha\mapsto1@(\alpha)\;\text{Fixed Point})\)
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega_2)=\psi(\psi_1(\psi_1(\psi_1(\cdots))))</math>
|-
|[[OCF#MOCF|MOCF]]
|<math>\psi(\psi_1(0)) = \psi(\varepsilon_{\Omega+1}) = \psi(\Omega^{\Omega^{\Omega^{\cdots}}})</math>
|-
|[[BMS]]
|<math>\left(\begin{smallmatrix}0&1&2\\0&1&2\end{smallmatrix}\right)=(0)(1,1)(2,2)</math>
|-
|[[HPrSS]]
|<math>1,4</math>
|-
|[[0-Y]]
|<math>1,3,6</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,7</math>
|-
|[[PSS Hydra]]
|<math>\psi^{\text{H}}_1(\psi^{\text{H}}_2(\psi^{\text{H}}_3(0))))</math>
|-
|[[weak Veblen 函数]]
|\(\varphi(1@(1@(\cdots)))=\varphi(\min\;\alpha\mapsto1@(\alpha)\;\text{Fixed Point})\)
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1&1&1&2&1&2&3 \\ 0&1&0&0&1&0&0&0 \end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0&1&2&0&1&1&2 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_{\Omega}+\Omega_{\omega})/\psi(\Omega_{\Omega}+\Omega_{\psi(\Omega)})</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M\times2))</math>
|-
| FOS
|<math>0,1,\omega,\omega^2</math>
|}

=== 性质 ===
BHO 是 [[weak Veblen 函数]]与 [[Veblen 函数]]的[[Catching|追平点]]。

[[证明论序数]]：<math>\rm ACA+BI</math>，<math>\rm ACA_{0}+\Pi_{1}^{1}-CA^{-}</math>，<math>\text{ID}_1</math>，<math>\rm KP</math>，<math>{\rm RCA_0}+\forall X\exists M(X\in M\land M\vDash_\omega{\rm ACA+BI})</math>

极限在此处的记号：[[OCF#MOCF|MPF]]，[[BAN|带 / 的 BAN]]，[[BAN|Bird's H]]，Ω 记号，[[Veblen 函数]]，[[weak Veblen 函数]]

[[分类:序数]]

LVO

2026-07-31T20:01:57Z

量子杰克：

LVO（Large Veblen Ordinal，大维布伦[[序数]]），是[[Veblen 函数#序数元_Veblen_函数|序元 Veblen 函数]]的极限。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[Veblen 函数]]
|\(\varphi(1@(1,0))=\min \alpha\mapsto\varphi(1@\alpha)\;\text{Fixed Point}\)
|-
|[[序数坍缩函数#BOCF|BOCF]]/[[序数坍缩函数#MOCF|MOCF]]
|<math>\psi(\Omega^{\Omega^\Omega})</math>
|-
|[[BMS]]
|<math>\begin{pmatrix}
0&1&2&3&4\\
0&1&1&1&1
\end{pmatrix}
=(0)(1,1)(2,1)(3,1)(4,1)</math>
|-
|[[HPrSS]] / [[0-Y]]
|<math>1,3,5,7,9</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,6,8,10</math>
|-
|[[PSS Hydra]]
|<math>\psi^H_1(\psi^H_2(\psi^H_2(\psi^H_2(\psi^H_2(0)))))</math>
|-
|[[weak Veblen 函数]]
| \(\varphi(1\text{@}(1\text{@}(1,0)))\)
|-
|[[BSM]]
|<math>\begin{pmatrix}
0&1&2&0&1&1&1&1&0&1&2
\end{pmatrix}</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M+\psi(M+\psi(M+\psi(M)))))</math>
|-
| FOS
|<math>0,1,\omega,\omega2,\omega3,\omega4</math>
|}

=== 性质 ===
[[证明论序数]]：|<math>\rm ACA+BI</math>，<math>\rm ACA_0+\Pi_1^1-CA^-</math>，<math>\rm \Pi_1^0-FXP_0</math>，<math>\rm KP</math>，<math>\rm KP+\Pi_2^{set}-Reflection</math>，<math>\rm KP+(BI^*)</math>，<math>\rm KP+(ATR_0^*)</math>，<math>\rm CZF</math>，<math>{\rm KP}\omega_2\upharpoonright+\Delta_1-{\rm CA}+s\Pi_1^1-{\rm ref}</math>，<math>\rm ID_1</math>，<math>\rm ID_1^2</math>，<math>\rm ML_1\ V</math>

极限在此处的记号：[[Veblen 函数#序数元_Veblen_函数|序元 Veblen 函数]]，[[BEAF|带 & 的 BEAF]]
[[分类:序数]]

CO

2026-07-31T20:01:38Z

量子杰克：

'''CO（Cantor Ordinal）'''是一个[[序数]]。
[[文件:Ζ.jpg|缩略图|图片仅供参考]]
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[康托范式]]
|<math>\zeta_0</math>
|-
|[[Veblen 函数]]
|<math>\varphi(2,0)</math>
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega^2)/\psi(\psi_1(\psi_1(0)))</math>
|-
|[[OCF#MOCF|MOCF]]
|<math>\psi(\Omega)</math>
|-
|[[BMS]]
|<math>\begin{pmatrix} 0 & 1 & 2\\ 0 & 1 & 1 \end{pmatrix}=(0)(1,1)(2,1)</math>
|-
|[[长初等序列|LPrSS]]
|<math>1,4</math>
|-
|[[HPrSS]] / [[0-Y]]
|<math>1,3,5</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,6</math>
|-
|[[PSS Hydra]]
|<math>\psi^H_1(\psi^H_2(\psi^H_2(0)))</math>
|-
|[[weak Veblen 函数]]
|<math>\varphi(1,0,0,0)</math>
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1 & 2 & 1 & 2 \end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0 & 1 & 1 & 2 & 1 & 2 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_{\omega^2})/\psi(\Omega_{\psi(\psi_1(\psi_1(0)))})</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M+\psi(M)))</math>
|-
|FOS
|<math>0,1,\omega,\omega2</math>
|}

=== 性质 ===
[[证明论序数]]：<math>{\rm ACA_0}+\forall X\exists Y({\rm TJ}(\omega,X,Y))</math>，<math>\rm ACA_0+(BR)</math>，<math>\rm p_1(ACA_0)</math>

极限在此处的记号：ε 函数，扩展多维数阵

[[分类:序数]]

LCO

2026-07-31T20:01:21Z

量子杰克：

[[文件:Image 1752201913143.jpg|缩略图|图片仅供参考]]
'''LCO（Large Cantor's Ordinal）'''是一个[[序数]]。
{| class="wikitable"
!记号
!表达式
|-
|[[康托范式]]
|<math>\eta_0</math>
|-
|[[Veblen 函数]]
|<math>\varphi(3,0)</math>
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega^3)/\psi(\psi_1(\psi_1(0)\times2))</math>
|-
|[[OCF#MOCF|MOCF]]
|<math>\psi(\Omega^2)</math>
|-
|[[BMS]]
|<math>\begin{pmatrix} 0 & 1 & 2 & 2 \\ 0 & 1 & 1 & 1 \end{pmatrix}=(0)(1,1)(2,1)(2,1)</math>
|-
|[[长初等序列|LPrSS]]
|<math>1,5</math>
|-
|[[HPrSS]] / [[0-Y]]
|<math>1,3,5,5</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,6,6</math>
|-
|[[PSS Hydra]]
|<math>\psi^H_1(\psi^H_2(\psi^H_2(0)+\psi^H_2(0)))</math>
|-
|[[weak Veblen 函数]]
|<math>\varphi(1,0,0,0,0)</math>
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1 & 2 & 1 & 2 & 1 & 2 \end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0 & 1 & 1 & 2 & 1 & 2 & 1 & 2 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_{\omega^3})/\psi(\Omega_{\psi(\psi_1(\psi_1(\psi_1(0))))})</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M+\psi(M)\times2))</math>
|-
|FOS
|<math>0,1,\omega,\omega2,\omega2</math>
|}

=== 性质 ===
[[证明论序数]]：<math>{\rm ACA_0}+\forall X\exists Y({\rm TJ}(\varepsilon_0,X,Y))</math>

极限在此处的记号：ζ 函数
[[分类:序数]]

SVO

2026-07-31T20:00:56Z

量子杰克：

SVO（Small Veblen's Ordinal），是[[Veblen 函数#有限元_Veblen_函数|有限元 Veblen 函数]]的极限的[[序数]]。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[Veblen 函数]]
| \(\varphi(1\text{@}\omega)\)
|-
|[[序数坍缩函数#BOCF|BOCF]]/[[序数坍缩函数#MOCF|MOCF]]
|<math>\psi(\Omega^{\Omega^\omega})=\psi(\psi_1(\psi_1(\psi_1(1))))</math>
|-
|[[BMS]]
|<math>\left(\begin{smallmatrix}0&1&2&3&4\\0&1&1&1&0\end{smallmatrix} \right)=(0)(1,1)(2,1)(3,1)(4)</math>
|-
|[[超初等序列|HPrSS]] / [[0-Y]]
|<math>1,3,5,7,8</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,6,8,9</math>
|-
|[[PSS Hydra]]
|<math>\psi^{\text{H}}_1(\psi^{\text{H}}_2(\psi^{\text{H}}_2(\psi^{\text{H}}_2(1))))</math>
|-
|[[weak Veblen 函数]]
| \(\varphi(1\text{@}(1\text{@}\omega))\)
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1&1&1&2&1&2&2&2 \\ 0&1&0&0&1&0&0&0&0 \end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0&1&2&0&1&1&1&1 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_{\Omega}+\Omega_4)</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M+\psi(M+\psi(M+1))))</math>
|-
| FOS
|<math>0,1,\omega,\omega2,\omega3,\omega3+1</math>
|}

=== 性质 ===
[[证明论序数]]： <math>\rm ACA_{0}+\Pi_{2}^{1}-BI</math>，<math>\rm \Pi_{1}^{1}-RFN</math>，<math>\rm KP\omega^{-}+\Pi_{2}^{set}-Foundation</math>，<math>\rm RCA_0^*+\Pi_1^1-CA^-</math>，<math>\rm p_3(ACA_0)</math>，<math>\rm FIT</math>，<math>\rm TID</math>

极限在此处的记号：[[Veblen 函数#有限元_Veblen_函数|有限元 Veblen 函数]]，[[TREE函数|tree 函数]]，Kruskal 树定理，Bird’s θ
[[分类:序数]]

FSO

2026-07-31T20:00:36Z

量子杰克：

'''FSO（Feferman-Schütte Ordinal，费弗曼-舒特序数）'''，是[[Veblen 函数#二元 Veblen 函数|二元 Veblen 函数]]的极限。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|常用表示
|<math>\Gamma_0</math>
|-
|[[Veblen 函数]]
|<math>\varphi(1,0,0)</math>
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega^\Omega)=\psi(\psi_1(\psi_1(\psi_1(0))))</math>
|-
|[[OCF#MOCF|MOCF]]
|<math>\psi(\Omega^\Omega)</math>
|-
|[[BMS]]
|<math>\begin{pmatrix} 0 & 1 & 2&3 \\ 0 & 1 & 1&1 \end{pmatrix}=(0)(1,1)(2,1)(3,1)</math>
|-
|[[HPrSS]] / [[0-Y]]
|<math>1,3,5,7</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,6,8</math>
|-
|[[PSS Hydra]]
|<math>\psi^\text{H}_1(\psi^\text{H}_2(\psi^\text{H}_2(\psi^\text{H}_2(0))))</math>
|-
|[[weak Veblen 函数]]
| \(\varphi(1@(1,0))\)
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1 \\ 0 & 1 \end{pmatrix}=(0)(1,1)</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0 & 1 & 2 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_\Omega)</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M+\psi(M+\psi(M))))</math>
|-
| FOS
|<math>0,1,\omega,\omega2,\omega3</math>
|}

=== 性质 ===
FSO 是第一个不可直谓[[序数]]。

[[证明论序数]]：<math>\rm ATR_0</math>，<math>\rm \Delta_1^1-CA+BR</math>，<math>\rm RCA_0+\Sigma_1^0-RT</math>，<math>\rm RCA_0+\Delta_1^0-RT</math>，<math>\rm RCA_0+\Sigma_1^0-det.</math>，<math>\rm RCA_0+\Delta_1^0-det.</math>，<math>\rm FP_0</math>，<math>\rm KPi^-</math>，<math>\rm CZF^-+INAC</math>，<math>\widehat{\rm ID}_{<\omega}</math>，<math>\widehat{\rm ID}^*</math>，<math>{\rm ML}_{<\omega}</math>，<math>\rm MLU</math>，<math>\rm U(PA)</math>

极限在此处的记号：UnAN，[[Veblen 函数#二元 Veblen 函数|二元 Veblen 函数]]

[[分类:序数]]

SVO

2026-07-31T19:59:30Z

量子杰克：

SVO（Small Veblen's Ordinal），是[[Veblen 函数#有限元_Veblen_函数|有限元 Veblen 函数]]的极限的[[序数]]。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[Veblen 函数]]
| \(\varphi(1\text{@}\omega)\)
|-
|[[序数坍缩函数#BOCF|BOCF]]/[[序数坍缩函数#MOCF|MOCF]]
|<math>\psi(\Omega^{\Omega^\omega})=\psi(\psi_1(\psi_1(\psi_1(1))))</math>
|-
|[[BMS]]
|<math>\left(\begin{smallmatrix}0&1&2&3&4\\0&1&1&1&0\end{smallmatrix} \right)=(0,0)(1,1)(2,1)(3,1)(4)</math>
|-
|[[超初等序列|HPrSS]] / [[0-Y]]
|<math>1,3,5,7,8</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,6,8,9</math>
|-
|[[PSS Hydra]]
|<math>\psi^{\text{H}}_1(\psi^{\text{H}}_2(\psi^{\text{H}}_2(\psi^{\text{H}}_2(1))))</math>
|-
|[[weak Veblen 函数]]
| \(\varphi(1\text{@}(1\text{@}\omega))\)
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1&1&1&2&1&2&2&2 \\ 0&1&0&0&1&0&0&0&0 \end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0&1&2&0&1&1&1&1 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_{\Omega}+\Omega_4)</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M+\psi(M+\psi(M+1))))</math>
|-
| FOS
|<math>0,1,\omega,\omega2,\omega3,\omega3+1</math>
|}

=== 性质 ===
[[证明论序数]]： <math>\rm ACA_{0}+\Pi_{2}^{1}-BI</math>，<math>\rm \Pi_{1}^{1}-RFN</math>，<math>\rm KP\omega^{-}+\Pi_{2}^{set}-Foundation</math>，<math>\rm RCA_0^*+\Pi_1^1-CA^-</math>，<math>\rm p_3(ACA_0)</math>，<math>\rm FIT</math>，<math>\rm TID</math>

极限在此处的记号：[[Veblen 函数#有限元_Veblen_函数|有限元 Veblen 函数]]，[[TREE函数|tree 函数]]，Kruskal 树定理，Bird’s θ
[[分类:序数]]

ACO

2026-07-31T19:58:04Z

量子杰克：

ACO（Ackerman's Ordinal，阿克曼序数），是[[Veblen 函数#有限元 Veblen 函数|三元 Veblen 函数]]的极限。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[Veblen 函数]]
|<math>\varphi(1,0,0,0)</math>
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega^{\Omega^2})</math>
|-
|[[OCF#MOCF|MOCF]]
|<math>\psi(\Omega^{\Omega^2})</math>
|-
|[[BMS]]
|<math>(0)(1,1)(2,1)(3,1)(3,1)</math>
|-
|[[HPrSS]] / [[0-Y]]
|<math>1,3,5,7,7</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,6,8,8</math>
|-
|[[PSS Hydra]]
|<math>p1(p2(p2(p2+p2)))</math>
|-
|[[weak Veblen 函数]]
|\(\varphi(1@(1,0,0))\)
|-
|[[Dropping#M 记号|M 记号]]
|<math>p(p(M+p(M+p(M)+p(M))))</math>
|-
| FOS
|<math>0,1,\omega,\omega2,\omega3,\omega3</math>
|}

=== 性质 ===
证明论序数：<math>\rm p_1(\Sigma_1^1-TDC_0)</math>

极限在此处的记号：[[Veblen 函数#有限元 Veblen 函数|三元 Veblen 函数]]

巧合的是，如果使用攀爬法将[[阿克曼函数]]引入序数运算，得到的极限正好是 ACO。
[[分类:序数]]

FSO

2026-07-31T19:56:48Z

量子杰克：

'''FSO（Feferman-Schütte Ordinal，费弗曼-舒特序数）'''，是[[Veblen 函数#二元 Veblen 函数|二元 Veblen 函数]]的极限。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|常用表示
|<math>\Gamma_0</math>
|-
|[[Veblen 函数]]
|<math>\varphi(1,0,0)</math>
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega^\Omega)=\psi(\psi_1(\psi_1(\psi_1(0))))</math>
|-
|[[OCF#MOCF|MOCF]]
|<math>\psi(\Omega^\Omega)</math>
|-
|[[BMS]]
|<math>\begin{pmatrix} 0 & 1 & 2&3 \\ 0 & 1 & 1&1 \end{pmatrix}=(0,0)(1,1)(2,1)(3,1)</math>
|-
|[[HPrSS]] / [[0-Y]]
|<math>1,3,5,7</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,6,8</math>
|-
|[[PSS Hydra]]
|<math>\psi^\text{H}_1(\psi^\text{H}_2(\psi^\text{H}_2(\psi^\text{H}_2(0))))</math>
|-
|[[weak Veblen 函数]]
| \(\varphi(1@(1,0))\)
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1 \\ 0 & 1 \end{pmatrix}=(0)(1,1)</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0 & 1 & 2 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_\Omega)</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M+\psi(M+\psi(M))))</math>
|-
| FOS
|<math>0,1,\omega,\omega2,\omega3</math>
|}

=== 性质 ===
FSO 是第一个不可直谓[[序数]]。

[[证明论序数]]：<math>\rm ATR_0</math>，<math>\rm \Delta_1^1-CA+BR</math>，<math>\rm RCA_0+\Sigma_1^0-RT</math>，<math>\rm RCA_0+\Delta_1^0-RT</math>，<math>\rm RCA_0+\Sigma_1^0-det.</math>，<math>\rm RCA_0+\Delta_1^0-det.</math>，<math>\rm FP_0</math>，<math>\rm KPi^-</math>，<math>\rm CZF^-+INAC</math>，<math>\widehat{\rm ID}_{<\omega}</math>，<math>\widehat{\rm ID}^*</math>，<math>{\rm ML}_{<\omega}</math>，<math>\rm MLU</math>，<math>\rm U(PA)</math>

极限在此处的记号：UnAN，[[Veblen 函数#二元 Veblen 函数|二元 Veblen 函数]]

[[分类:序数]]

HCO

2026-07-31T19:54:14Z

量子杰克：

'''HCO（Hyper Cantor's Ordinal）'''，是一个重要的[[序数]]。它也是 [[OCF#BOCF|BOCF]] 和 [[OCF#MOCF|MOCF]] 的第一个[[Catching|追平点]]。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[Veblen 函数|Veblen 函数]]
|<math>\varphi(\omega,0)</math>
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega^\omega)/\psi(\psi_1(\psi_1(1)))</math>
|-
|[[OCF#MOCF|MOCF]]
|<math>\psi(\Omega^\omega)</math>
|-
|[[BMS]]
|<math>\begin{pmatrix} 0 & 1 & 2&3 \\ 0 & 1 & 1&0 \end{pmatrix}=(0)(1,1)(2,1)(3)</math>
|-
|[[HPrSS]] / [[0-Y]]
|<math>1,3,5,6</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,6,7</math>
|-
|[[PSS Hydra]]
|<math>\psi^H_1(\psi^H_2(\psi^H_2(\psi^H_1(0))))</math>
|-
|[[weak Veblen 函数]]
| \(\varphi(1\text{@}\omega)\)
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1 & 2 & 2 \end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0 & 1 & 1 & 2 & 2 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_{\omega^\omega})/\psi(\Omega_{\psi(\Omega_2)})</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M+\psi(M+1)))</math>
|-
|FOS
|<math>0,1,\omega,\omega2,\omega2+1</math>
|}

=== 性质 ===
[[证明论序数]]：<math>\rm \Delta_1^1-CR</math>，<math>\rm RCA_0^*+\Pi_1^1-CA^-</math>，<math>\rm \Sigma_1^1-DC_0</math>，<math>\rm ID_1^\#</math>，<math>\rm EM_0+JR</math>，<math>\rm PID</math>，<math>\rm Acc-ID(Acc)</math>，<math>\rm (\Pi_0^0(P),P\cup N)-ID</math>，<math>\rm (\Pi_0^0(P),P\land N)-ID(Acc)</math>

极限在此处的记号：[[长初等序列|LPrSS]]，[[序数超运算]]，0-IUN，NAN
[[分类:序数]]

LCO

2026-07-31T19:52:04Z

量子杰克：

[[文件:Image 1752201913143.jpg|缩略图|图片仅供参考]]
'''LCO（Large Cantor's Ordinal）'''是一个[[序数]]。
{| class="wikitable"
!记号
!表达式
|-
|[[康托范式]]
|<math>\eta_0</math>
|-
|[[Veblen 函数]]
|<math>\varphi(3,0)</math>
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega^3)/\psi(\psi_1(\psi_1(0)\times2))</math>
|-
|[[OCF#MOCF|MOCF]]
|<math>\psi(\Omega^2)</math>
|-
|[[BMS]]
|<math>\begin{pmatrix} 0 & 1 & 2 & 2 \\ 0 & 1 & 1 & 1 \end{pmatrix}=(0,0)(1,1)(2,1)(2,1)</math>
|-
|[[长初等序列|LPrSS]]
|<math>1,5</math>
|-
|[[HPrSS]] / [[0-Y]]
|<math>1,3,5,5</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,6,6</math>
|-
|[[PSS Hydra]]
|<math>\psi^H_1(\psi^H_2(\psi^H_2(0)+\psi^H_2(0)))</math>
|-
|[[weak Veblen 函数]]
|<math>\varphi(1,0,0,0,0)</math>
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1 & 2 & 1 & 2 & 1 & 2 \end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0 & 1 & 1 & 2 & 1 & 2 & 1 & 2 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_{\omega^3})/\psi(\Omega_{\psi(\psi_1(\psi_1(\psi_1(0))))})</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M+\psi(M)\times2))</math>
|-
|FOS
|<math>0,1,\omega,\omega2,\omega2</math>
|}

=== 性质 ===
[[证明论序数]]：<math>{\rm ACA_0}+\forall X\exists Y({\rm TJ}(\varepsilon_0,X,Y))</math>

极限在此处的记号：ζ 函数
[[分类:序数]]

CO

2026-07-31T19:51:19Z

量子杰克：

'''CO（Cantor Ordinal）'''是一个[[序数]]。
[[文件:Ζ.jpg|缩略图|图片仅供参考]]
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[康托范式]]
|<math>\zeta_0</math>
|-
|[[Veblen 函数]]
|<math>\varphi(2,0)</math>
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega^2)/\psi(\psi_1(\psi_1(0)))</math>
|-
|[[OCF#MOCF|MOCF]]
|<math>\psi(\Omega)</math>
|-
|[[BMS]]
|<math>\begin{pmatrix} 0 & 1 & 2\\ 0 & 1 & 1 \end{pmatrix}=(0,0)(1,1)(2,1)</math>
|-
|[[长初等序列|LPrSS]]
|<math>1,4</math>
|-
|[[HPrSS]] / [[0-Y]]
|<math>1,3,5</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,6</math>
|-
|[[PSS Hydra]]
|<math>\psi^H_1(\psi^H_2(\psi^H_2(0)))</math>
|-
|[[weak Veblen 函数]]
|<math>\varphi(1,0,0,0)</math>
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1 & 2 & 1 & 2 \end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0 & 1 & 1 & 2 & 1 & 2 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_{\omega^2})/\psi(\Omega_{\psi(\psi_1(\psi_1(0)))})</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M+\psi(M)))</math>
|-
|FOS
|<math>0,1,\omega,\omega2</math>
|}

=== 性质 ===
[[证明论序数]]：<math>{\rm ACA_0}+\forall X\exists Y({\rm TJ}(\omega,X,Y))</math>，<math>\rm ACA_0+(BR)</math>，<math>\rm p_1(ACA_0)</math>

极限在此处的记号：ε 函数，扩展多维数阵

[[分类:序数]]

CO

2026-07-31T19:49:47Z

量子杰克：

'''CO（Cantor Ordinal）'''是一个[[序数]]。
[[文件:Ζ.jpg|缩略图|图片仅供参考]]
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[康托范式]]
|<math>\zeta_0</math>
|-
|[[Veblen 函数]]
|<math>\varphi(2,0)</math>
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega^2)/\psi(\psi_1(\psi_1(0)))</math>
|-
|[[OCF#MOCF|MOCF]]
|<math>\psi(\Omega)</math>
|-
|[[BMS]]
|<math>\begin{pmatrix} 0 & 1 & 2\\ 0 & 1 & 1 \end{pmatrix}=(0,0)(1,1)(2,1)</math>
|-
|[[长初等序列|LPrSS]]
|<math>1,4</math>
|-
|[[HPrSS]] / [[0-Y]]
|<math>1,3,5</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,4</math>
|-
|[[PSS Hydra]]
|<math>\psi^H_1(\psi^H_2(\psi^H_2(0)))</math>
|-
|[[weak Veblen 函数]]
|<math>\varphi(1,0,0,0)</math>
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1 & 2 & 1 & 2 \end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0 & 1 & 1 & 2 & 1 & 2 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_{\omega^2})/\psi(\Omega_{\psi(\psi_1(\psi_1(0)))})</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M+\psi(M)))</math>
|-
|FOS
|<math>0,1,\omega,\omega2</math>
|}

=== 性质 ===
[[证明论序数]]：<math>{\rm ACA_0}+\forall X\exists Y({\rm TJ}(\omega,X,Y))</math>，<math>\rm ACA_0+(BR)</math>，<math>\rm p_1(ACA_0)</math>

极限在此处的记号：ε 函数，扩展多维数阵

[[分类:序数]]

CO

2026-07-31T19:48:47Z

量子杰克：

'''CO（Cantor Ordinal）'''是一个[[序数]]。
[[文件:Ζ.jpg|缩略图|图片仅供参考]]
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[康托范式]]
|<math>\zeta_0</math>
|-
|[[Veblen 函数]]
|<math>\varphi(2,0)</math>
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega^2)/\psi(\psi_1(\psi_1(0)))</math>
|-
|[[OCF#MOCF|MOCF]]
|<math>\psi(\Omega)</math>
|-
|[[BMS]]
|<math>\begin{pmatrix} 0 & 1 & 2\\ 0 & 1 & 1 \end{pmatrix}=(0,0)(1,1)(2,1)</math>
|-
|[[长初等序列|LPrSS]]
|<math>1,4</math>
|-
|[[HPrSS]] / [[0-Y]]
|<math>1,3,5</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4,4</math>
|-
|[[PSS Hydra]]
|<math>\psi^H_1(\psi^H_2(\psi^H_2(0)))</math>
|-
|[[weak Veblen 函数]]
|<math>\varphi(1,0,0,0)</math>
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1 & 2 & 1 & 2 \end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0 & 1 & 1 & 2 & 1 & 2 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_{\omega^2})/\psi(\Omega_{\psi(\psi_1(\psi_1(0)))})</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M+\psi(M)))</math>
|}

=== 性质 ===
[[证明论序数]]：<math>{\rm ACA_0}+\forall X\exists Y({\rm TJ}(\omega,X,Y))</math>，<math>\rm ACA_0+(BR)</math>，<math>\rm p_1(ACA_0)</math>

极限在此处的记号：ε 函数，扩展多维数阵

[[分类:序数]]

SCO

2026-07-31T19:47:39Z

量子杰克：

'''SCO（Small Cantor's Ordinal）'''，是一个重要的序数。它被认为是具有“里程碑”意义的一个序数。它也是 [[增长层级#快速增长层级|FGH]] 和 [[增长层级#哈代层级|HH]] 的第一个[[Catching|追平点]]。

[[文件:D9d74070393528d7b74a28c888717d2d2354dbd6.jpg|缩略图|（图片仅供参考）]]

{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[康托范式]]
|<math>\varepsilon_0</math>
|-
|[[Veblen 函数]]
|<math>\varphi(1,0)</math>
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega)/\psi(\psi_1(0))</math>
|-
|[[OCF#MOCF|MOCF]]
|<math>\psi(0)</math>
|-
|[[BMS]]
|<math>\begin{pmatrix} 0 & 1 \\ 0 & 1 \end{pmatrix}=(0)(1,1)</math>
|-
|[[长初等序列|LPrSS]] / [[HPrSS]] / [[0-Y]]
|<math>1,3</math>
|-
|[[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,4</math>
|-
|[[PSS Hydra]]
|<math>\psi^H_1(\psi^H_2(0))</math>
|-
|[[weak Veblen 函数]]
|<math>\varphi(1,0,0)</math>
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1&2 \end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0&1&1&2 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_{\omega})/\psi(\Omega_{\psi(\Omega)})</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M))</math>
|-
|FOS
|<math>0,1,\omega</math>
|}

=== 性质 ===
证明论序数：<math>\rm ACA_{0}</math>，<math>\rm KP^{-\infin}</math>，<math>\rm \Delta_{1}^{1}-CA_{0}</math>，<math>\rm \Sigma_{1}^{1}-AC_{0}</math>，<math>\rm \Pi_{0}^{1}-CA_{0}</math>，<math>\rm EM_{0}</math>，[[皮亚诺公理体系|PA]]

极限在此处的记号：[[PrSS]]，[[Kirby-Paris Hydra#Hydra_函数|Hydra 函数]]，[[Beklemishev's Worm|Worm 序列]]，[[燃烧数]]，[[-1-Y]]，[[Goodstein序列|Goodstein 序列]]，Brace 数阵，多维数阵，Friedman 序列，级联 E 记号

[[分类:序数]]

LAO

2026-07-31T19:45:05Z

量子杰克：

'''LAO（Linar Array Ordinal，线性数阵序数）'''，因在 [[Googology|googology]] 一度经典的线性数阵的极限是该[[序数]]而得名。
{| class="wikitable"
|+LAO
![[序数记号]]
!表达式
|-
|[[康托范式]]
|<math>\omega^\omega</math>
|-
|[[Veblen 函数]]
|<math>\varphi(\varphi(1))</math>
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\psi(0))</math>
|-
|[[初等序列系统|PrSS]]
|<math>0,1,2</math>
|-
|[[BMS]]
|<math>\begin{pmatrix} 0 & 1 & 2 \end{pmatrix}</math>
|-
|[[长初等序列|LPrSS]] / [[HPrSS]] / [[0-Y]] / [[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2,3</math>
|-
|[[PSS Hydra]]
|<math>\psi^H_1(\psi^H_1(1))</math>
|-
|[[weak Veblen 函数]]
|<math>\varphi(\omega,0)</math>
|-
|[[BHM]] / [[BSM]]
|<math>\begin{pmatrix} 0 & 1&1 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_2)</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(1))</math>
|}

=== 性质 ===
LAO 是 [[增长层级#快速增长层级|FGH]] 和 [[增长层级#中速增长层级|MGH]] 的第一个 [[Catching]] 点。

证明论序数：<math>\rm RCA_0</math>，<math>\rm WKL_0</math>，<math>\rm PRA</math>，<math>\rm RCA_0^2</math>，<math>\rm CPRC</math>，<math>\rm KP^-+\Pi_1^{set}-Foundation+IND</math>

极限在此处的记号：[[线性数阵]]，(-2)-Y，TmAF
[[分类:序数]]

FTO

2026-07-31T19:44:10Z

量子杰克：

'''FTO（First Transfinite Ordinal，第一个超限序数，即'''<math>\omega</math>'''）'''，是一个重要的[[序数]]。它被认为是具有“里程碑”意义的一个序数。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[康托范式]]
|<math>\omega</math>
|-
|[[Veblen 函数]]
|<math>\varphi(1)</math>
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(0)</math>
|-
|[[初等序列系统|PrSS]]
|<math>0,1</math>
|-
|[[BMS]] / [[BHM]] / [[BSM]]
|<math>\begin{pmatrix} 0 & 1 \end{pmatrix}</math>
|-
|[[长初等序列|LPrSS]] / [[HPrSS]] / [[0-Y]] / [[Y序列|1-Y]] / [[ω-Y]]
|<math>1,2</math>
|-
|[[PSS Hydra]]
|<math>\psi^H_1(1)</math>
|-
|[[weak Veblen 函数]]
|<math>\varphi(1,0)</math>
|-
|[[NOCF]]
|<math>\psi(\Omega)</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(1)</math>
|}

=== 性质 ===
ω 是最小的[[序数#超限序数|超限序数]]，最小的非零[[序数#极限序数|极限序数]]，最小的不满足 <math>1+\alpha=\alpha+1</math> 的序数<math>\alpha</math>。

<math>\omega = |\omega| = \aleph_{0} </math>，详见[[基数]]。

[[证明论序数]]：<math>\rm Q</math>，<math>\rm KP^-</math>

极限在此处的记号：[[高德纳箭头]]，[[阿克曼函数]]，[[斯坦豪斯-莫泽表示法]]，[[下箭号表示法]]，[[Sudan 函数|苏丹函数]]，超运算

[[分类:序数]]

BHO

2026-07-20T01:41:05Z

量子杰克：

BHO（Bachmann-Howard Ordinal），是一个重要的[[序数]]。它被认为是具有“里程碑”意义的一个序数。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[Veblen 函数]]
|\(\varphi(1@(1@(\cdots)))=\varphi(\min\;\alpha\mapsto1@(\alpha)\;\text{Fixed Point})\)
|-
|[[OCF#BOCF|BOCF]]
|<math>\psi(\Omega_2)=\psi(\psi_1(\psi_1(\psi_1(\cdots))))</math>
|-
|[[OCF#MOCF|MOCF]]
|<math>\psi(\psi_1(0)) = \psi(\varepsilon_{\Omega+1}) = \psi(\Omega^{\Omega^{\Omega^{\cdots}}})</math>
|-
|[[BMS]]
|<math>\left(\begin{smallmatrix}0&1&2\\0&1&2\end{smallmatrix}\right)=(0,0)(1,1)(2,2)</math>
|-
|[[HPrSS]]
|<math>1,4</math>
|-
|[[0-Y]]
|<math>1,3,6</math>
|-
|[[Y序列|1-Y]]
|<math>1,2,4,7</math>
|-
|[[PSS Hydra]]
|<math>\psi^{\text{H}}_1(\psi^{\text{H}}_2(\psi^{\text{H}}_3(0))))</math>
|-
|[[weak Veblen 函数]]
|\(\varphi(1@(1@(\cdots)))=\varphi(\min\;\alpha\mapsto1@(\alpha)\;\text{Fixed Point})\)
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1&1&1&2&1&2&3 \\ 0&1&0&0&1&0&0&0 \end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0&1&2&0&1&1&2 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_{\Omega}+\Omega_{\omega})/\psi(\Omega_{\Omega}+\Omega_{\psi(\Omega)})</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M\times2))</math>
|-
| +ω法[[序数超运算]]
|<math>\omega\{\Omega\uparrow\uparrow\omega\}\omega</math>
|}

=== 性质 ===
BHO 是 [[weak Veblen 函数]]与 [[Veblen 函数]]的[[Catching|追平点]]。

[[证明论序数]]：<math>\rm ACA+BI</math>，<math>\rm ACA_{0}+\Pi_{1}^{1}-CA^{-}</math>，<math>\text{ID}_1</math>，<math>\rm KP</math>，<math>{\rm RCA_0}+\forall X\exists M(X\in M\land M\vDash_\omega{\rm ACA+BI})</math>

极限在此处的记号：[[OCF#MOCF|MPF]]，[[BAN|带 / 的 BAN]]，[[BAN|Bird's H]]，Ω 记号，[[Veblen 函数]]，[[weak Veblen 函数]]

[[分类:序数]]

LVO

2026-07-20T01:40:34Z

量子杰克：

LVO（Large Veblen Ordinal，大维布伦[[序数]]），是[[Veblen 函数#序数元_Veblen_函数|序元 Veblen 函数]]的极限。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[Veblen 函数]]
|\(\varphi(1@(1,0))=\min \alpha\mapsto\varphi(1@\alpha)\;\text{Fixed Point}\)
|-
|[[序数坍缩函数#BOCF|BOCF]]/[[序数坍缩函数#MOCF|MOCF]]
|<math>\psi(\Omega^{\Omega^\Omega})</math>
|-
|[[BMS]]
|<math>\begin{pmatrix}
0&1&2&3&4\\
0&1&1&1&1
\end{pmatrix}
=(0,0)(1,1)(2,1)(3,1)(4,1)</math>
|-
|[[超初等序列|HPrSS]]
|<math>1,3,5,7,9</math>
|-
|[[0-Y]]
|<math>1,3,5,7,9</math>
|-
|[[Y序列|1-Y]]
|<math>1,2,4,6,8,10</math>
|-
|[[PSS Hydra]]
|<math>\psi^H_1(\psi^H_2(\psi^H_2(\psi^H_2(\psi^H_2(0)))))</math>
|-
|[[weak Veblen 函数]]
| \(\varphi(1\text{@}(1\text{@}(1,0)))\)
|-
|[[BSM]]
|<math>\begin{pmatrix}
0&1&2&0&1&1&1&1&0&1&2
\end{pmatrix}</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M+\psi(M+\psi(M+\psi(M)))))</math>
|-
| +ω法[[序数超运算]]
|<math>\omega\{\Omega^\Omega\}\omega</math>
|}

=== 性质 ===
[[证明论序数]]：|<math>\rm ACA+BI</math>，<math>\rm ACA_0+\Pi_1^1-CA^-</math>，<math>\rm \Pi_1^0-FXP_0</math>，<math>\rm KP</math>，<math>\rm KP+\Pi_2^{set}-Reflection</math>，<math>\rm KP+(BI^*)</math>，<math>\rm KP+(ATR_0^*)</math>，<math>\rm CZF</math>，<math>{\rm KP}\omega_2\upharpoonright+\Delta_1-{\rm CA}+s\Pi_1^1-{\rm ref}</math>，<math>\rm ID_1</math>，<math>\rm ID_1^2</math>，<math>\rm ML_1\ V</math>

极限在此处的记号：[[Veblen 函数#序数元_Veblen_函数|序元 Veblen 函数]]，[[BEAF|带 & 的 BEAF]]
[[分类:序数]]

SVO

2026-07-20T01:39:41Z

量子杰克：

SVO（Small Veblen's Ordinal），是[[Veblen 函数#有限元_Veblen_函数|有限元 Veblen 函数]]的极限的[[序数]]。
{| class="wikitable"
![[序数记号]]
!表达式
|-
|[[Veblen 函数]]
| \(\varphi(1\text{@}\omega)\)
|-
|[[序数坍缩函数#BOCF|BOCF]]/[[序数坍缩函数#MOCF|MOCF]]
|<math>\psi(\Omega^{\Omega^\omega})=\psi(\psi_1(\psi_1(\psi_1(1))))</math>
|-
|[[BMS]]
|<math>\left(\begin{smallmatrix}0&1&2&3&4\\0&1&1&1&0\end{smallmatrix} \right)=(0,0)(1,1)(2,1)(3,1)(4,0)</math>
|-
|[[超初等序列|HPrSS]]/[[0-Y]]
|<math>1,3,5,7,8</math>
|-
|[[Y序列|1-Y]]
|<math>1,2,4,6,8,9</math>
|-
|[[PSS Hydra]]
|<math>\psi^{\text{H}}_1(\psi^{\text{H}}_2(\psi^{\text{H}}_2(\psi^{\text{H}}_2(1))))</math>
|-
|[[weak Veblen 函数]]
| \(\varphi(1\text{@}(1\text{@}\omega))\)
|-
|[[BHM]]
|<math>\begin{pmatrix} 0 & 1&1&1&2&1&2&2&2 \\ 0&1&0&0&1&0&0&0&0 \end{pmatrix}</math>
|-
|[[BSM]]
|<math>\begin{pmatrix} 0&1&2&0&1&1&1&1 \end{pmatrix}</math>
|-
|[[NOCF]]
|<math>\psi(\Omega_{\Omega}+\Omega_4)</math>
|-
|[[Dropping#M 记号|M 记号]]
|<math>\psi(\psi(M+\psi(M+\psi(M+1))))</math>
|-
| +ω法[[序数超运算]]
|<math>\omega\{\Omega^\omega\}\omega</math>
|}

=== 性质 ===
[[证明论序数]]： <math>\rm ACA_{0}+\Pi_{2}^{1}-BI</math>，<math>\rm \Pi_{1}^{1}-RFN</math>，<math>\rm KP\omega^{-}+\Pi_{2}^{set}-Foundation</math>，<math>\rm RCA_0^*+\Pi_1^1-CA^-</math>，<math>\rm p_3(ACA_0)</math>，<math>\rm FIT</math>，<math>\rm TID</math>

极限在此处的记号：[[Veblen 函数#有限元_Veblen_函数|有限元 Veblen 函数]]，[[TREE函数|tree 函数]]，Kruskal 树定理，Bird’s θ
[[分类:序数]]

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0Yψ vs 拓展HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影 分析

HPrSSψ vs LPrSS投影 vs LPrSS反射 分析

0Yψ vs 拓展HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影 分析

0Yψ vs 拓展HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影 分析

0Yψ vs 拓展HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影 分析

SHO

TSSO

LRO

TSO

DSO

LDO

SDO

BGO

APO

LSO

SSO

DO

SKO

RO

SNO

SMO

SRO

TBO

MBO

SIO

JO

EBO

BIO

TFBO

BO

BHO

LVO

CO

LCO

SVO

FSO

SVO

ACO

FSO

HCO

LCO

CO

CO

CO

SCO

LAO

FTO

BHO

LVO

SVO

0Yψ vs 拓展HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影分析

HPrSSψ vs LPrSS投影 vs LPrSS反射分析

0Yψ vs 拓展HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影分析

0Yψ vs 拓展HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影分析

0Yψ vs 拓展HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影分析