LPrSSψ分析

以下为长初等序列序数折叠函数（LPrSSψ）的分析。LPrSSψ与BOCF在BHO前完全一致，但强度大得多，可达(0)(1,1,1)(2,2,1)(3)以上。

分析1：BHO~BO

此阶段分析很简单，仅需将每一层从对应的ψ拆出来即可。

分析1：BHO~BO

LPrSSψ	BOCF	BMS
$\psi ({\psi }_1({\mathrm{\Omega }}_2))=\psi ({\epsilon }_{\mathrm{\Omega }+1})$	$\psi ({\mathrm{\Omega }}_2)$	(0)(1,1)(2,2)
$\psi ({\psi }_1({\mathrm{\Omega }}_2)+1)$	$\psi ({\mathrm{\Omega }}_2+1)$	(0)(1,1)(2,2)(1)
$\psi ({\psi }_1({\mathrm{\Omega }}_2)+\mathrm{\Omega })$	$\psi ({\mathrm{\Omega }}_2+\mathrm{\Omega })$	(0)(1,1)(2,2)(1,1)
$\psi ({\psi }_1({\mathrm{\Omega }}_2)\times 2)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2))$	(0)(1,1)(2,2)(1,1)(2,2)
$\psi ({\psi }_1({\mathrm{\Omega }}_2)\times 3)$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2)\times 2)$	(0)(1,1)(2,2)(1,1)(2,2)(1,1)(2,2)
$\psi ({\psi }_1({\mathrm{\Omega }}_2+1))$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+1))$	(0)(1,1)(2,2)(2)
$\psi ({\psi }_1({\mathrm{\Omega }}_2+\omega ))$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+\omega ))$	(0)(1,1)(2,2)(2)(3)
$\psi ({\psi }_1({\mathrm{\Omega }}_2+\mathrm{\Omega }))$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+\mathrm{\Omega }))$	(0)(1,1)(2,2)(2,1)
$\psi ({\psi }_1({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2)))$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2)))$	(0)(1,1)(2,2)(2,1)(3,2)
$\psi ({\psi }_1({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2))))$	$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2))))$	(0)(1,1)(2,2)(2,1)(3,2)(3,1)(4,2)
$\psi ({\psi }_1({\mathrm{\Omega }}_{2}2))=\psi ({\epsilon }_{\mathrm{\Omega }+2})$	$\psi ({\mathrm{\Omega }}_{2}2)$	(0)(1,1)(2,2)(2,2)
$\psi ({\psi }_1({\mathrm{\Omega }}_{2}2)\times 2)$	$\psi ({\mathrm{\Omega }}_{2}2+{\psi }_1({\mathrm{\Omega }}_{2}2))$	(0)(1,1)(2,2)(2,2)(1,1)(2,2)(2,2)
$\psi ({\psi }_1({\mathrm{\Omega }}_{2}2+1))$	$\psi ({\mathrm{\Omega }}_{2}2+{\psi }_1({\mathrm{\Omega }}_{2}2+1))$	(0)(1,1)(2,2)(2,2)(2)
$\psi ({\psi }_1({\mathrm{\Omega }}_{2}3))$	$\psi ({\mathrm{\Omega }}_{2}3)$	(0)(1,1)(2,2)(2,2)(2,2)
$\psi ({\psi }_1({\mathrm{\Omega }}_2\omega ))=\psi ({\epsilon }_{\mathrm{\Omega }+\omega })$	$\psi ({\mathrm{\Omega }}_2\omega )$	(0)(1,1)(2,2)(3)
$\psi ({\psi }_1({\mathrm{\Omega }}_2\mathrm{\Omega }))=\psi ({\epsilon }_{\mathrm{\Omega }2})$	$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega })$	(0)(1,1)(2,2)(3,1)
$\psi ({\psi }_1({\mathrm{\Omega }}_2\times {\psi }_1({\mathrm{\Omega }}_2)))=\psi ({\epsilon }_{{\epsilon }_{\mathrm{\Omega }+1}})$	$\psi ({\mathrm{\Omega }}_2\times {\psi }_1({\mathrm{\Omega }}_2))$	(0)(1,1)(2,2)(3,1)(4,2)
$\psi ({\psi }_1({\mathrm{\Omega }}_2^2))=\psi ({\zeta }_{\mathrm{\Omega }+1})$	$\psi ({\mathrm{\Omega }}_2^2)$	(0)(1,1)(2,2)(3,2)
$\psi ({\psi }_1({\mathrm{\Omega }}_2^2)\times 2)$	$\psi ({\mathrm{\Omega }}_2^2+{\psi }_1({\mathrm{\Omega }}_2^2))$	(0)(1,1)(2,2)(3,2)(1,1)(2,2)(3,2)
$\psi ({\psi }_1({\mathrm{\Omega }}_2^2+{\mathrm{\Omega }}_2))$	$\psi ({\mathrm{\Omega }}_2^2+{\mathrm{\Omega }}_2)$	(0)(1,1)(2,2)(3,2)(2,2)
$\psi ({\psi }_1({\mathrm{\Omega }}_2^{2}2))$	$\psi ({\mathrm{\Omega }}_2^{2}2)$	(0)(1,1)(2,2)(3,2)(2,2)(3,2)
$\psi ({\psi }_1({\mathrm{\Omega }}_2^3))$	$\psi ({\mathrm{\Omega }}_2^3)$	(0)(1,1)(2,2)(3,2)(3,2)
$\psi ({\psi }_1({\mathrm{\Omega }}_2^{\omega }))=\psi (\phi (\omega ,\mathrm{\Omega }+1))$	$\psi ({\mathrm{\Omega }}_2^{\omega })$	(0)(1,1)(2,2)(3,2)(4)
$\psi ({\psi }_1({\mathrm{\Omega }}_2^{\mathrm{\Omega }}))=\psi (\phi (\mathrm{\Omega },1))$	$\psi ({\mathrm{\Omega }}_2^{\mathrm{\Omega }})$	(0)(1,1)(2,2)(3,2)(4,1)
$\psi ({\psi }_1({\mathrm{\Omega }}_2^{{\psi }_1({\mathrm{\Omega }}_2)}))$	$\psi ({\mathrm{\Omega }}_2^{{\psi }_1({\mathrm{\Omega }}_2)})$	(0)(1,1)(2,2)(3,2)(4,1)(5,2)
$\psi ({\psi }_1({\mathrm{\Omega }}_2^{{\mathrm{\Omega }}_2}))=\psi ({\mathrm{\Gamma }}_{\mathrm{\Omega }+1})$	$\psi ({\mathrm{\Omega }}_2^{{\mathrm{\Omega }}_2})$	(0)(1,1)(2,2)(3,2)(4,2)
$\psi ({\psi }_1({\mathrm{\Omega }}_2\uparrow \uparrow 3))$	$\psi ({\mathrm{\Omega }}_2\uparrow \uparrow 3)$	(0)(1,1)(2,2)(3,2)(4,2)(5,2)
$\psi ({\psi }_1({\psi }_2({\mathrm{\Omega }}_3)))=\psi ({\psi }_1({\epsilon }_{{\mathrm{\Omega }}_2+1}))$	$\psi ({\mathrm{\Omega }}_3)$	(0)(1,1)(2,2)(3,3)
$\psi ({\psi }_1({\psi }_2({\mathrm{\Omega }}_3))\times 2)$	$\psi ({\mathrm{\Omega }}_3+{\psi }_1({\mathrm{\Omega }}_3))$	(0)(1,1)(2,2)(3,3)(1,1)(2,2)(3,3)
$\psi ({\psi }_1({\psi }_2({\mathrm{\Omega }}_3)+1))$	$\psi ({\mathrm{\Omega }}_3+{\psi }_1({\mathrm{\Omega }}_3+1))$	(0)(1,1)(2,2)(3,3)(2)
$\psi ({\psi }_1({\psi }_2({\mathrm{\Omega }}_3)+{\mathrm{\Omega }}_2))$	$\psi ({\mathrm{\Omega }}_3+{\mathrm{\Omega }}_2)$	(0)(1,1)(2,2)(3,3)(2,2)
$\psi ({\psi }_1({\psi }_2({\mathrm{\Omega }}_3)\times 2))$	$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_3))$	(0)(1,1)(2,2)(3,3)(2,2)(3,3)
$\psi ({\psi }_1({\psi }_2({\mathrm{\Omega }}_3+1)))$	$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_3+1))$	(0)(1,1)(2,2)(3,3)(3)
$\psi ({\psi }_1({\psi }_2({\mathrm{\Omega }}_3+{\mathrm{\Omega }}_2)))$	$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_3+{\mathrm{\Omega }}_2))$	(0)(1,1)(2,2)(3,3)(3,2)
$\psi ({\psi }_1({\psi }_2({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_3))))$	$\psi ({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_3)))$	(0)(1,1)(2,2)(3,3)(3,2)(4,3)
$\psi ({\psi }_1({\psi }_2({\mathrm{\Omega }}_{3}2)))$	$\psi ({\mathrm{\Omega }}_{3}2)$	(0)(1,1)(2,2)(3,3)(3,3)
$\psi ({\psi }_1({\psi }_2({\mathrm{\Omega }}_3\omega )))$	$\psi ({\mathrm{\Omega }}_3\omega )$	(0)(1,1)(2,2)(3,3)(4)
$\psi ({\psi }_1({\psi }_2({\mathrm{\Omega }}_3^2)))$	$\psi ({\mathrm{\Omega }}_3^2)$	(0)(1,1)(2,2)(3,3)(4,3)
$\psi ({\psi }_1({\psi }_2({\mathrm{\Omega }}_3^{{\mathrm{\Omega }}_3})))$	$\psi ({\mathrm{\Omega }}_3^{{\mathrm{\Omega }}_3})$	(0)(1,1)(2,2)(3,3)(4,3)(5,3)
$\psi ({\psi }_1({\psi }_2({\psi }_3({\mathrm{\Omega }}_4))))$	$\psi ({\mathrm{\Omega }}_4)$	(0)(1,1)(2,2)(3,3)(4,4)
$\psi ({\psi }_1({\psi }_2({\psi }_3({\psi }_4({\mathrm{\Omega }}_5)))))$	$\psi ({\mathrm{\Omega }}_5)$	(0)(1,1)(2,2)(3,3)(4,4)(5,5)
$\psi ({\mathrm{\Omega }}_2)=\psi ({\psi }_1({\psi }_2({\psi }_3({\psi }_4(...)))))$	$\psi ({\mathrm{\Omega }}_{\omega })$	(0)(1,1,1)

分析2：BO~(0)(1,1,1)(2,1)

到(0)(1,1,1)(2,1)的分析仍较简单，仅需找层即可，但此后，LPrSSψ的行为更类似BMS，而不是BOCF，因为具有(0)(1,1,1)(2,1)(1,1,1)提升。

分析2：BO~FBLO

LPrSSψ	BOCF	BMS
$\psi ({\mathrm{\Omega }}_2)$	$\psi ({\mathrm{\Omega }}_{\omega })$	(0)(1,1,1)
$\psi ({\mathrm{\Omega }}_2+1)$	$\psi ({\mathrm{\Omega }}_{\omega }+1)$	(0)(1,1,1)(1)
$\psi ({\mathrm{\Omega }}_2+\mathrm{\Omega })$	$\psi ({\mathrm{\Omega }}_{\omega }+\mathrm{\Omega })$	(0)(1,1,1)(1,1)
$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_2))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_2))$	(0)(1,1,1)(1,1)(2,2)
$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\psi }_2({\mathrm{\Omega }}_3)))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_3))$	(0)(1,1,1)(1,1)(2,2)(3,3)
$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_3))=\psi ({\mathrm{\Omega }}_2+{\psi }_1({\psi }_2({\psi }_3(...))))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }))$	(0)(1,1,1)(1,1)(2,2,1)
$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_3)\times 2)$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega })\times 2)$	(0)(1,1,1)(1,1)(2,2,1)(1,1)(2,2,1)
$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_3+1))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }+1))$	(0)(1,1,1)(1,1)(2,2,1)(2)
$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_3+\mathrm{\Omega }))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }+\mathrm{\Omega }))$	(0)(1,1,1)(1,1)(2,2,1)(2,1)
$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_3+{\psi }_1({\mathrm{\Omega }}_2)))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_2)))$	(0)(1,1,1)(1,1)(2,2,1)(2,1)(3,2)
$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_3+{\psi }_1({\mathrm{\Omega }}_3)))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }+{\psi }_1({\mathrm{\Omega }}_{\omega })))$	(0)(1,1,1)(1,1)(2,2,1)(2,1)(3,2,1)
$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_3+{\mathrm{\Omega }}_2))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\mathrm{\Omega }}_2)$	(0)(1,1,1)(1,1)(2,2,1)(2,2)
$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_3+{\mathrm{\Omega }}_{2}2))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\mathrm{\Omega }}_{2}2)$	(0)(1,1,1)(1,1)(2,2,1)(2,2)(2,2)
$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_3+{\mathrm{\Omega }}_2^2))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\mathrm{\Omega }}_2^2)$	(0)(1,1,1)(1,1)(2,2,1)(2,2)(3,2)
$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_3)))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_2({\mathrm{\Omega }}_3))$	(0)(1,1,1)(1,1)(2,2,1)(2,2)(3,3)
$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_4)))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_2({\mathrm{\Omega }}_{\omega }))$	(0)(1,1,1)(1,1)(2,2,1)(2,2)(3,3,1)
$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_4+{\mathrm{\Omega }}_3)))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\mathrm{\Omega }}_3)$	(0)(1,1,1)(1,1)(2,2,1)(2,2)(3,3,1)(3,3)
$\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_4+{\psi }_3({\mathrm{\Omega }}_5))))$	$\psi ({\mathrm{\Omega }}_{\omega }+{\psi }_3({\mathrm{\Omega }}_{\omega }))$	(0)(1,1,1)(1,1)(2,2,1)(2,2)(3,3,1)(3,3)(4,4,1)
$\psi ({\mathrm{\Omega }}_{2}2)=\psi ({\mathrm{\Omega }}_2+{\psi }_1({\mathrm{\Omega }}_3+{\psi }_2({\mathrm{\Omega }}_4+{\psi }_3({\mathrm{\Omega }}_5+...))))$	$\psi ({\mathrm{\Omega }}_{\omega }2)$	(0)(1,1,1)(1,1,1)
$\psi ({\mathrm{\Omega }}_{2}2+{\psi }_1({\mathrm{\Omega }}_3))$	$\psi ({\mathrm{\Omega }}_{\omega }2+{\psi }_1({\mathrm{\Omega }}_{\omega }))$	(0)(1,1,1)(1,1,1)(1,1)(2,2,1)
$\psi ({\mathrm{\Omega }}_{2}2+{\psi }_1({\mathrm{\Omega }}_{3}2))$	$\psi ({\mathrm{\Omega }}_{\omega }2+{\psi }_1({\mathrm{\Omega }}_{\omega }2))$	(0)(1,1,1)(1,1,1)(1,1)(2,2,1)(2,2,1)
$\psi ({\mathrm{\Omega }}_{2}2+{\psi }_1({\mathrm{\Omega }}_{3}2+{\mathrm{\Omega }}_2))$	$\psi ({\mathrm{\Omega }}_{\omega }2+{\mathrm{\Omega }}_2)$	(0)(1,1,1)(1,1,1)(1,1)(2,2,1)(2,2,1)(2,2)
$\psi ({\mathrm{\Omega }}_{2}3)$	$\psi ({\mathrm{\Omega }}_{\omega }3)$	(0)(1,1,1)(1,1,1)(1,1,1)
$\psi ({\mathrm{\Omega }}_2\omega )$	$\psi ({\mathrm{\Omega }}_{\omega }\omega )$	(0)(1,1,1)(2)
$\psi ({\mathrm{\Omega }}_2\times (\omega +1))$	$\psi ({\mathrm{\Omega }}_{\omega }\times (\omega +1))$	(0)(1,1,1)(2)(1,1,1)
$\psi ({\mathrm{\Omega }}_2\times \psi (\mathrm{\Omega }))$	$\psi ({\mathrm{\Omega }}_{\omega }\times \psi (\mathrm{\Omega }))$	(0)(1,1,1)(2)(3,1)
$\psi ({\mathrm{\Omega }}_2\times \psi ({\mathrm{\Omega }}_2))$	$\psi ({\mathrm{\Omega }}_{\omega }\times \psi ({\mathrm{\Omega }}_{\omega }))$	(0)(1,1,1)(2)(3,1,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega })$	$\psi ({\mathrm{\Omega }}_{\omega }\mathrm{\Omega })$	(0)(1,1,1)(2,1)

分析3：(0)(1,1,1)(2,1)~(0)(1,1,1)(2,1)(1,1,1)

分析进入提升阶段。可见LPrSSψ中的一个Ω_2对应的不是BOCF中的一个Ω_ω，而是BMS中的一个(1,1,1)。这里注意LPrSSψ一般不单独定义Ω_0，展开方式，Ω_2展开出ψ_1时，把外面的Ω变成了里面的Ω_2，以此类推，但ω不提升。因为阶差为d时，Ω_(n+1)变出的ψ_n只把外面的x>=n的Ω_x提升为Ω_(x+d)。不然，若定义Ω_0=ω，并在这种位置将其提升为Ω，会与没有【特别地，如果坏根中元素不是坏部中某项的祖先项，则该项在复制过程中将保持不变。】规则的BMS一样，发生无穷降链。此外，若无此种提升，可能可以得到类似IBMS的ILPrSSψ。

分析3：(0)(1,1,1)(2,1)~(0)(1,1,1)(2,1)(1,1,1)

LPrSSψ	BOCF	BMS
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega })$	$\psi ({\mathrm{\Omega }}_{\omega }\mathrm{\Omega })$	(0)(1,1,1)(2,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3))$	$\psi ({\mathrm{\Omega }}_{\omega }\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\mathrm{\Omega }))$	$\psi ({\mathrm{\Omega }}_{\omega }\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }\mathrm{\Omega }))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\mathrm{\Omega }+1))$	$\psi ({\mathrm{\Omega }}_{\omega }\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }\mathrm{\Omega }+1))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\mathrm{\Omega }+\mathrm{\Omega }))$	$\psi ({\mathrm{\Omega }}_{\omega }\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }\mathrm{\Omega }+\mathrm{\Omega }))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\mathrm{\Omega })))$	$\psi ({\mathrm{\Omega }}_{\omega }\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_{\omega }\mathrm{\Omega })))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,1)(3,2,1)(4,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\mathrm{\Omega }+{\mathrm{\Omega }}_2))$	$\psi ({\mathrm{\Omega }}_{\omega }\mathrm{\Omega }+{\mathrm{\Omega }}_2)$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\mathrm{\Omega }+{\psi }_2({\mathrm{\Omega }}_4)))$	$\psi ({\mathrm{\Omega }}_{\omega }\mathrm{\Omega }+{\psi }_2({\mathrm{\Omega }}_{\omega }))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,3,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\mathrm{\Omega }+{\psi }_2({\mathrm{\Omega }}_4\mathrm{\Omega })))$	$\psi ({\mathrm{\Omega }}_{\omega }\mathrm{\Omega }+{\psi }_2({\mathrm{\Omega }}_{\omega }\mathrm{\Omega }))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,3,1)(4,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\mathrm{\Omega }+{\psi }_2({\mathrm{\Omega }}_4\mathrm{\Omega }+{\mathrm{\Omega }}_3)))$	$\psi ({\mathrm{\Omega }}_{\omega }\mathrm{\Omega }+{\mathrm{\Omega }}_3)$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,3,1)(4,1)(3,3)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\times (\mathrm{\Omega }+1)))=\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\mathrm{\Omega }+{\psi }_2({\mathrm{\Omega }}_4\mathrm{\Omega }+...)))$	$\psi ({\mathrm{\Omega }}_{\omega }\times (\mathrm{\Omega }+1))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\times (\mathrm{\Omega }+2)))$	$\psi ({\mathrm{\Omega }}_{\omega }\times (\mathrm{\Omega }+2))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(2,2,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\times (\mathrm{\Omega }+\omega )))$	$\psi ({\mathrm{\Omega }}_{\omega }\times (\mathrm{\Omega }+\omega ))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(3)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\times \mathrm{\Omega }2))$	$\psi ({\mathrm{\Omega }}_{\omega }\times \mathrm{\Omega }2)$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2,1)(3,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\times \mathrm{\Omega }\omega ))$	$\psi ({\mathrm{\Omega }}_{\omega }\times \mathrm{\Omega }\omega )$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(3)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\times {\mathrm{\Omega }}^2))$	$\psi ({\mathrm{\Omega }}_{\omega }\times {\mathrm{\Omega }}^2)$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(3,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\times {\mathrm{\Omega }}^{\omega }))$	$\psi ({\mathrm{\Omega }}_{\omega }\times {\mathrm{\Omega }}^{\omega })$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\times {\mathrm{\Omega }}^{\mathrm{\Omega }}))$	$\psi ({\mathrm{\Omega }}_{\omega }\times {\mathrm{\Omega }}^{\mathrm{\Omega }})$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\times {\psi }_1({\mathrm{\Omega }}_2)))$	$\psi ({\mathrm{\Omega }}_{\omega }\times {\psi }_1({\mathrm{\Omega }}_2))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4,2)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\times {\psi }_1({\mathrm{\Omega }}_3)))$	$\psi ({\mathrm{\Omega }}_{\omega }\times {\psi }_1({\mathrm{\Omega }}_{\omega }))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4,2,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3\times {\psi }_1({\mathrm{\Omega }}_3\times {\psi }_1({\mathrm{\Omega }}_3))))$	$\psi ({\mathrm{\Omega }}_{\omega }\times {\psi }_1({\mathrm{\Omega }}_{\omega }\times {\psi }_1({\mathrm{\Omega }}_{\omega })))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(4,2,1)(5,1)(6,2,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3{\mathrm{\Omega }}_2))$	$\psi ({\mathrm{\Omega }}_{\omega }{\mathrm{\Omega }}_2)$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3{\mathrm{\Omega }}_2+{\mathrm{\Omega }}_2))$	$\psi ({\mathrm{\Omega }}_{\omega }{\mathrm{\Omega }}_2+{\mathrm{\Omega }}_2)$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3{\mathrm{\Omega }}_2+{\psi }_2({\mathrm{\Omega }}_3)))$	$\psi ({\mathrm{\Omega }}_{\omega }{\mathrm{\Omega }}_2+{\psi }_2({\mathrm{\Omega }}_3))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3{\mathrm{\Omega }}_2+{\psi }_2({\mathrm{\Omega }}_4)))$	$\psi ({\mathrm{\Omega }}_{\omega }{\mathrm{\Omega }}_2+{\psi }_2({\mathrm{\Omega }}_{\omega }))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3{\mathrm{\Omega }}_2+{\psi }_2({\mathrm{\Omega }}_4\mathrm{\Omega })))$	$\psi ({\mathrm{\Omega }}_{\omega }{\mathrm{\Omega }}_2+{\psi }_2({\mathrm{\Omega }}_{\omega }\mathrm{\Omega }))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3{\mathrm{\Omega }}_2+{\psi }_2({\mathrm{\Omega }}_4{\mathrm{\Omega }}_2)))$	$\psi ({\mathrm{\Omega }}_{\omega }{\mathrm{\Omega }}_2+{\psi }_2({\mathrm{\Omega }}_{\omega }{\mathrm{\Omega }}_2))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3{\mathrm{\Omega }}_2+{\psi }_2({\mathrm{\Omega }}_4{\mathrm{\Omega }}_2+{\mathrm{\Omega }}_3)))$	$\psi ({\mathrm{\Omega }}_{\omega }{\mathrm{\Omega }}_2+{\mathrm{\Omega }}_3)$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)(3,3)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3{\mathrm{\Omega }}_2+{\psi }_2({\mathrm{\Omega }}_4\times ({\mathrm{\Omega }}_2+1))))$	$\psi ({\mathrm{\Omega }}_{\omega }\times ({\mathrm{\Omega }}_2+1))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)(3,3,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3{\mathrm{\Omega }}_2+{\psi }_2({\mathrm{\Omega }}_4\times {\mathrm{\Omega }}_{2}2)))$	$\psi ({\mathrm{\Omega }}_{\omega }\times {\mathrm{\Omega }}_{2}2)$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)(3,3,1)(4,2)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3{\mathrm{\Omega }}_2+{\psi }_2({\mathrm{\Omega }}_4\times {\psi }_2({\mathrm{\Omega }}_4))))$	$\psi ({\mathrm{\Omega }}_{\omega }\times {\psi }_2({\mathrm{\Omega }}_{\omega }))$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,2)(5,3,1)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3{\mathrm{\Omega }}_2+{\psi }_2({\mathrm{\Omega }}_4{\mathrm{\Omega }}_3)))$	$\psi ({\mathrm{\Omega }}_{\omega }{\mathrm{\Omega }}_3)$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,3)
$\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3{\mathrm{\Omega }}_2+{\psi }_2({\mathrm{\Omega }}_4{\mathrm{\Omega }}_3+{\psi }_3({\mathrm{\Omega }}_5{\mathrm{\Omega }}_4))))$	$\psi ({\mathrm{\Omega }}_{\omega }{\mathrm{\Omega }}_4)$	(0)(1,1,1)(2,1)(1,1)(2,2,1)(3,2)(2,2)(3,3,1)(4,3)(3,3)(4,4,1)(5,4)
$\psi ({\mathrm{\Omega }}_2\times (\mathrm{\Omega }+1))=\psi ({\mathrm{\Omega }}_2\mathrm{\Omega }+{\psi }_1({\mathrm{\Omega }}_3{\mathrm{\Omega }}_2+{\psi }_2({\mathrm{\Omega }}_4{\mathrm{\Omega }}_3+...)))$	$\psi ({\mathrm{\Omega }}_{\omega }^2)$	(0)(1,1,1)(2,1)(1,1,1)

未完待续