非递归BMS分析：修订间差异

2025年7月19日 (六) 22:36的版本

本条目展示非递归BMS和其他非递归记号的列表分析

1


非递归BMS	其他记号
$\emptyset$	$0$
$(1)$	$1$
$(1) (1)$	$2$
$(1) (2)$	$ω$
$(1) (2) (1)$	$ω + 1$
$(1) (2) (2)$	$ω^{2}$
$(1) (2) (3)$	$ω^{ω}$
$(1) (2, 1)$	$ε_{0}$
$(1) (2, 1, 1)$	$ψ (Ω_{ω})$
$(1, 1)$	$Ω$

2


非递归BMS	其他记号
$(1, 1)$	$Ω$
$(1, 1) (1)$	$Ω + 1$
$(1, 1) (1) (2)$	$Ω + ω$
$(1, 1) (1) (2, 1)$	$Ω + ε_{0}$
$(1, 1) (1) (2, 1, 1)$	$Ω + ψ (Ω_{ω})$
$(1, 1) (1, 1)$	$Ω \times 2$
$(1, 1) (1, 1) (1, 1)$	$Ω \times 3$
$(1, 1) (2)$	$Ω \times ω$
$(1, 1) (2) (1, 1)$	$Ω \times ω + Ω$
$(1, 1) (2) (2)$	$Ω \times ω^{2}$
$(1, 1) (2) (3, 1, 1)$	$Ω \times ψ (Ω_{ω})$
$(1, 1) (2, 1)$	$Ω^{2}$
$(1, 1) (2, 1) (1, 1) (2, 1)$	$Ω^{2} \times 2$
$(1, 1) (2, 1) (2)$	$Ω^{2} \times ω$
$(1, 1) (2, 1) (2) (3, 1, 1)$	$Ω^{2} \times ψ (Ω_{ω})$
$(1, 1) (2, 1) (2, 1)$	$Ω^{3}$
$(1, 1) (2, 1) (2, 1) (2, 1)$	$Ω^{4}$
$(1, 1) (2, 1) (3)$	$Ω^{ω}$
$(1, 1) (2, 1) (3) (4, 1, 1)$	$Ω^{ψ (Ω_{ω})}$
$(1, 1) (2, 1) (3, 1)$	$Ω^{Ω}$
$(1, 1) (2, 1) (3, 1) (4, 1)$	$Ω^{Ω^{Ω}}$
$(1, 1) (2, 2)$	$ψ_{1} (Ω_{2})$
$(1, 1) (2, 2) (2, 1)$	$ψ_{1} (Ω_{2} + Ω)$
$(1, 1) (2, 2) (2, 1) (2, 1)$	$ψ_{1} (Ω_{2} + Ω \times 2)$
$(1, 1) (2, 2) (2, 1) (3)$	$ψ_{1} (Ω_{2} + Ω \times ω)$
$(1, 1) (2, 2) (2, 1) (3, 1)$	$ψ_{1} (Ω_{2} + Ω^{2})$
$(1, 1) (2, 2) (2, 1) (3, 2)$	$ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2}))$
$(1, 1) (2, 2) (2, 1) (3, 2) (2, 1) (3, 2)$	$ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2}) \times 2)$
$(1, 1) (2, 2) (2, 1) (3, 2) (3)$	$ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2} + 1))$
$(1, 1) (2, 2) (2, 1) (3, 2) (3, 1) (4, 2)$	$ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2} + ψ_{1} (Ω_{2})))$
$(1, 1) (2, 2) (2, 2)$	$ψ_{1} (Ω_{2} \times 2)$
$(1, 1) (2, 2) (3)$	$ψ_{1} (Ω_{2} \times ω)$
$(1, 1) (2, 2) (3, 1) (4, 2)$	$ψ_{1} (Ω_{2} \times ψ_{1} (Ω_{2}))$
$(1, 1) (2, 2) (3, 2)$	$ψ_{1} (Ω_{2}^{2})$
$(1, 1) (2, 2) (3, 2) (4, 2)$	$ψ_{1} (Ω_{2}^{Ω_{2}})$
$(1, 1) (2, 2) (3, 3)$	$ψ_{1} (Ω_{3})$
$(1, 1) (2, 2, 1)$	$ψ_{1} (Ω_{ω})$
$(1, 1) (2, 2, 1, 1)$	$ψ_{1} (ω - p r o j .)$
$(1, 1, 1)$	$Ω_{2}$

3


非递归BMS	其他记号
$(1, 1, 1)$	$Ω_{2}$
$(1, 1, 1) (1, 1)$	$Ω_{2} + Ω$
$(1, 1, 1) (1, 1) (2, 2, 1, 1)$	$Ω_{2} + ψ_{1} (ω - p r o j .)$
$(1, 1, 1) (1, 1, 1)$	$Ω_{2} \times 2$
$(1, 1, 1) (2)$	$Ω_{2} \times ω$
$(1, 1, 1) (2, 1)$	$Ω_{2} \times Ω$
$(1, 1, 1) (2, 1) (2, 1)$	$Ω_{2} \times Ω^{2}$
$(1, 1, 1) (2, 1) (3, 2)$	$Ω_{2} \times ψ_{1} (Ω_{2})$
$(1, 1, 1) (2, 1) (3, 2, 1, 1)$	$Ω_{2} \times ψ_{1} (ω - p r o j .)$
$(1, 1, 1) (2, 1, 1)$	$Ω_{2}^{2}$
$(1, 1, 1) (2, 1, 1) (2, 1, 1)$	$Ω_{2}^{3}$
$(1, 1, 1) (2, 1, 1) (3, 1, 1)$	$Ω_{2}^{Ω_{2}}$
$(1, 1, 1) (2, 2)$	$ψ_{2} (Ω_{3})$
$(1, 1, 1) (2, 2) (2, 1, 1) (3, 2)$	$ψ_{2} (Ω_{3} + ψ_{2} (Ω_{3}))$
$(1, 1, 1) (2, 2) (2, 2)$	$ψ_{2} (Ω_{3} \times 2)$
$(1, 1, 1) (2, 2) (3, 1, 1) (4, 2)$	$ψ_{2} (Ω_{3} \times ψ_{2} (Ω_{3}))$
$(1, 1, 1) (2, 2) (3, 2)$	$ψ_{2} (Ω_{3}^{2})$
$(1, 1, 1) (2, 2) (3, 3)$	$ψ_{2} (Ω_{4})$
$(1, 1, 1) (2, 2) (3, 3, 1)$	$ψ_{2} (Ω_{ω})$
$(1, 1, 1) (2, 2) (3, 3, 1, 1)$	$ψ_{2} (ω - p r o j .)$
$(1, 1, 1) (2, 2, 1)$	$Ω_{3}$
$(1, 1, 1) (2, 2, 1) (2, 1)$	$Ω_{3} \times Ω$
$(1, 1, 1) (2, 2, 1) (2, 1, 1)$	$Ω_{3} \times Ω_{2}$
$(1, 1, 1) (2, 2, 1) (2, 1, 1) (2, 1, 1)$	$Ω_{3} \times Ω_{2}^{2}$
$(1, 1, 1) (2, 2, 1) (2, 1, 1) (3, 2)$	$Ω_{3} \times ψ_{2} (Ω_{3})$
$(1, 1, 1) (2, 2, 1) (2, 1, 1) (3, 2) (3, 2)$	$Ω_{3} \times ψ_{2} (Ω_{3} \times 2)$
$(1, 1, 1) (2, 2, 1) (2, 1, 1) (3, 2) (4, 3)$	$Ω_{3} \times ψ_{2} (Ω_{4})$
$(1, 1, 1) (2, 2, 1) (2, 1, 1) (3, 2) (4, 3, 1, 1)$	$Ω_{3} \times ψ_{2} (ω - p r o j .)$
$(1, 1, 1) (2, 2, 1) (2, 1, 1) (3, 2, 1)$	$Ω_{3}^{2}$
$(1, 1, 1) (2, 2, 1) (2, 1, 1) (3, 2, 1) (2, 1, 1) (3, 2, 1)$	$Ω_{3}^{3}$
$(1, 1, 1) (2, 2, 1) (2, 1, 1) (3, 2, 1) (3)$	$Ω_{3}^{ω}$
$(1, 1, 1) (2, 2, 1) (2, 1, 1) (3, 2, 1) (3, 1, 1) (4, 2, 1)$	$Ω_{3}^{Ω_{3}}$
$(1, 1, 1) (2, 2, 1) (2, 2)$	$ψ_{3} (Ω_{4})$
$(1, 1, 1) (2, 2, 1) (2, 2) (2, 2)$	$ψ_{3} (Ω_{4} \times 2)$
$(1, 1, 1) (2, 2, 1) (2, 2) (3, 3, 1)$	$ψ_{3} (Ω_{ω})$
$(1, 1, 1) (2, 2, 1) (2, 2) (3, 3, 1, 1)$	$ψ_{3} (ω - p r o j .)$
$(1, 1, 1) (2, 2, 1) (2, 2, 1)$	$Ω_{4}$
$(1, 1, 1) (2, 2, 1) (2, 2, 1) (2, 2, 1)$	$Ω_{5}$
$(1, 1, 1) (2, 2, 1) (3)$	$Ω_{ω}$

4


非递归BMS	其他记号
$(1, 1, 1) (2, 2, 1) (3)$	$Ω_{ω}$
$(1, 1, 1) (2, 2, 1) (3, 1)$	$Ω_{Ω}$
$(1, 1, 1) (2, 2, 1) (3, 1) (2, 2, 1) (3, 1)$	$Ω_{Ω \times 2}$
$(1, 1, 1) (2, 2, 1) (3, 1) (3, 1)$	$Ω_{Ω^{2}}$
$(1, 1, 1) (2, 2, 1) (3, 1) (4, 2)$	$Ω_{ψ_{1} (Ω_{2})}$
$(1, 1, 1) (2, 2, 1) (3, 1) (4, 2, 1, 1)$	$Ω_{ψ_{1} (ω - p r o j .)}$
$(1, 1, 1) (2, 2, 1) (3, 1, 1)$	$Ω_{Ω_{2}}$
$(1, 1, 1) (2, 2, 1) (3, 1, 1) (4, 2)$	$Ω_{ψ_{2} (Ω_{3})}$
$(1, 1, 1) (2, 2, 1) (3, 1, 1) (4, 2) (5, 3, 1, 1)$	$Ω_{ψ_{2} (ω - p r o j .)}$
$(1, 1, 1) (2, 2, 1) (3, 1, 1) (4, 2, 1)$	$Ω_{Ω_{3}}$
$(1, 1, 1) (2, 2, 1) (3, 1, 1) (4, 2, 1) (4, 2, 1)$	$Ω_{Ω_{4}}$
$(1, 1, 1) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5)$	$Ω_{Ω_{ω}}$
$(1, 1, 1) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5, 1, 1)$	$Ω_{Ω_{Ω_{2}}}$
$(1, 1, 1) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5, 1, 1) (6, 2, 1)$	$Ω_{Ω_{Ω_{3}}}$
$(1, 1, 1) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5, 1, 1) (6, 2, 1) (7)$	$Ω_{Ω_{Ω_{ω}}}$
$(1, 1, 1) (2, 2, 1) (3, 2)$	$ψ_{I} (I)$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1)$	$ψ_{I} (I + 1)$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1) (3, 1, 1)$	$ψ_{I} (I + Ω_{2})$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5, 2)$	$ψ_{I} (I + ψ_{I} (I))$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5, 2) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5, 2)$	$ψ_{I} (I + ψ_{I} (I) \times 2)$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5, 2) (3, 1, 1)$	$ψ_{I} (I + ψ_{I} (I) \times Ω_{2})$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5, 2) (3, 1, 1) (4, 2, 1) (5, 2)$	$ψ_{I} (I + ψ_{I} (I)^{2})$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5, 2) (4, 1, 1) (5, 2, 1) (6, 2)$	$ψ_{I} (I + ψ_{I} (I)^{ψ_{I} (I)})$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5, 2) (4, 2)$	$ψ_{I} (I + ψ_{ψ_{I} (I + 1)} (ψ_{I} (I + 1)))$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5, 2) (4, 2) (5, 3, 1, 1)$	$ψ_{I} (I + ψ_{ψ_{I} (I + 1)} (ω - p r o j .))$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5, 2) (4, 2, 1)$	$ψ_{I} (I + ψ_{I} (I + 1))$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5, 2) (4, 2, 1) (4, 2, 1)$	$ψ_{I} (I + ψ_{I} (I + 2)$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5, 2) (4, 2, 1) (5)$	$ψ_{I} (I + ψ_{I} (I + ω))$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5, 2) (4, 2, 1) (5, 1, 1) (6, 2, 1) (7, 2)$	$ψ_{I} (I + ψ_{I} (I + ψ_{I} (I)))$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1) (3, 2)$	$ψ_{I} (I \times 2)$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1) (3, 2) (2, 2, 1)$	$ψ_{I} (I \times 2 + 1)$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1) (3, 2) (2, 2, 1) (3, 1, 1) (4, 2, 1) (5, 2) (4, 2, 1) (5, 2)$	$ψ_{I} (I \times 2 + ψ_{I} (I \times 2))$
$(1, 1, 1) (2, 2, 1) (3, 2) (2, 2, 1) (3, 2) (2, 2, 1) (3, 2)$	$ψ_{I} (I \times 3)$
$(1, 1, 1) (2, 2, 1) (3, 2) (3)$	$ψ_{I} (I \times ω)$
$(1, 1, 1) (2, 2, 1) (3, 2) (3, 1, 1) (4, 2, 1) (5, 2)$	$ψ_{I} (I \times ψ_{I} (I))$
$(1, 1, 1) (2, 2, 1) (3, 2) (3, 2)$	$ψ_{I} (I^{2})$
$(1, 1, 1) (2, 2, 1) (3, 2) (3, 2) (3, 2)$	$ψ_{I} (I^{3})$
$(1, 1, 1) (2, 2, 1) (3, 2) (4)$	$ψ_{I} (I^{ω})$
$(1, 1, 1) (2, 2, 1) (3, 2) (4, 2)$	$ψ_{I} (I^{I})$
$(1, 1, 1) (2, 2, 1) (3, 2) (4, 3)$	$ψ_{I} (Ω_{I + 1})$
$(1, 1, 1) (2, 2, 1) (3, 2) (4, 3, 1, 1)$	$ψ_{I} (ω - p r o j .)$
$(1, 1, 1) (2, 2, 1) (3, 2, 1)$	$I$

@@ 第338行： / 第338行： @@
 |-
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-|<math>\rm \psi_I(I)</math>
+|<math>\psi_\mathrm{I}(\mathrm{I})</math>
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-|<math>\rm \psi_I(I+1)</math>
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-|<math>\rm \psi_I(I+\psi_{\psi_I(I+1)}(\omega-proj.))</math>
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-|<math>\rm \psi_I(I+\psi_I(I+1))</math>
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-|<math>\rm \psi_I(I+\psi_I(I+\psi_I(I)))</math>
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-|<math>\rm \psi_I(I\times2+1)</math>
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-|<math>\rm \psi_I(I\times2+\psi_I(I\times2))</math>
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-|<math>\rm \psi_I(I\times3)</math>
+|<math>\psi_\mathrm{I}(\mathrm{I}\times3)</math>
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-|<math>\rm \psi_I(I\times\psi_I(I))</math>
+|<math>\psi_\mathrm{I}(\mathrm{I}\times\psi_\mathrm{I}(\mathrm{I}))</math>
 |-
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-|<math>\rm \psi_I(I^2)</math>
+|<math>\psi_\mathrm{I}(\mathrm{I}^2)</math>
 |-
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-|<math>\rm \psi_I(I^3)</math>
+|<math>\psi_\mathrm{I}(\mathrm{I}^3)</math>
 |-
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-|<math>\rm \psi_I(I^\omega)</math>
+|<math>\psi_\mathrm{I}(\mathrm{I}^\omega)</math>
 |-
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-|<math>\rm \psi_I(I^I)</math>
+|<math>\psi_\mathrm{I}(\mathrm{I}^\mathrm{I})</math>
 |-
 |<math>(1,1,1)(2,2,1)(3,2)(4,3)</math>
-|<math>\rm \psi_I(\Omega_{I+1})</math>
+|<math>\psi_\mathrm{I}(\Omega_{\mathrm{I}+1})</math>
 |-
 |<math>(1,1,1)(2,2,1)(3,2)(4,3,1,1)</math>
-|<math>\rm \psi_I(\omega-proj.)</math>
+|<math>\psi_\mathrm{I}(\omega-proj.)</math>
 |-
 |<math>(1,1,1)(2,2,1)(3,2,1)</math>
-|<math>\rm I</math>
+|<math>\mathrm{I}</math>
 |}
 [[分类:分析]]