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非递归BMS分析

来自Googology Wiki
Tabelog留言 | 贡献2025年7月30日 (三) 15:35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。

Part 1

非递归 BMS 其他记号
0
(1) 1
(1)(1) 2
(1)(2) ω
(1)(2)(1) ω+1
(1)(2)(2) ω2
(1)(2)(3) ωω
(1)(2,1) ε0
(1)(2,1,1) ψ(Ωω)
(1,1) Ω

Part 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+ε0
(1,1)(1)(2,1,1) Ω+ψ(Ωω)
(1,1)(1,1) Ω×2
(1,1)(1,1)(1,1) Ω×3
(1,1)(2) Ω×ω
(1,1)(2)(1,1) Ω×ω+Ω
(1,1)(2)(2) Ω×ω2
(1,1)(2)(3,1,1) Ω×ψ(Ωω)
(1,1)(2,1) Ω2
(1,1)(2,1)(1,1)(2,1) Ω2×2
(1,1)(2,1)(2) Ω2×ω
(1,1)(2,1)(2)(3,1,1) Ω2×ψ(Ωω)
(1,1)(2,1)(2,1) Ω3
(1,1)(2,1)(2,1)(2,1) Ω4
(1,1)(2,1)(3) Ωω
(1,1)(2,1)(3)(4,1,1) Ωψ(Ωω)
(1,1)(2,1)(3,1) ΩΩ
(1,1)(2,1)(3,1)(4,1) ΩΩΩ
(1,1)(2,2) ψ1(Ω2)
(1,1)(2,2)(2,1) ψ1(Ω2+Ω)
(1,1)(2,2)(2,1)(2,1) ψ1(Ω2+Ω×2)
(1,1)(2,2)(2,1)(3) ψ1(Ω2+Ω×ω)
(1,1)(2,2)(2,1)(3,1) ψ1(Ω2+Ω2)
(1,1)(2,2)(2,1)(3,2) ψ1(Ω2+ψ1(Ω2))
(1,1)(2,2)(2,1)(3,2)(2,1)(3,2) ψ1(Ω2+ψ1(Ω2)×2)
(1,1)(2,2)(2,1)(3,2)(3) ψ1(Ω2+ψ1(Ω2+1))
(1,1)(2,2)(2,1)(3,2)(3,1)(4,2) ψ1(Ω2+ψ1(Ω2+ψ1(Ω2)))
(1,1)(2,2)(2,2) ψ1(Ω2×2)
(1,1)(2,2)(3) ψ1(Ω2×ω)
(1,1)(2,2)(3,1)(4,2) ψ1(Ω2×ψ1(Ω2))
(1,1)(2,2)(3,2) ψ1(Ω22)
(1,1)(2,2)(3,2)(4,2) ψ1(Ω2Ω2)
(1,1)(2,2)(3,3) ψ1(Ω3)
(1,1)(2,2,1) ψ1(Ωω)
(1,1)(2,2,1)(3,2,1) ψ1(Ωω2)
(1,1)(2,2,1)(3,2,1)(4,1) ψ1(ΩΩ)
(1,1)(2,2,1,1) ψ1(ωproj.)
(1,1,1) Ω2

Part 3

非递归 BMS 其他记号
(1,1,1) Ω2
(1,1,1)(1,1) Ω2+Ω
(1,1,1)(1,1)(2,2,1,1) Ω2+ψ1(ωproj.)
(1,1,1)(1,1,1) Ω2×2
(1,1,1)(2) Ω2×ω
(1,1,1)(2,1) Ω2×Ω
(1,1,1)(2,1)(2,1) Ω2×Ω2
(1,1,1)(2,1)(3,2) Ω2×ψ1(Ω2)
(1,1,1)(2,1)(3,2,1,1) Ω2×ψ1(ωproj.)
(1,1,1)(2,1,1) Ω22
(1,1,1)(2,1,1)(2,1,1) Ω23
(1,1,1)(2,1,1)(3,1,1) Ω2Ω2
(1,1,1)(2,2) ψ2(Ω3)
(1,1,1)(2,2)(2,1,1)(3,2) ψ2(Ω3+ψ2(Ω3))
(1,1,1)(2,2)(2,2) ψ2(Ω3×2)
(1,1,1)(2,2)(3,1,1)(4,2) ψ2(Ω3×ψ2(Ω3))
(1,1,1)(2,2)(3,2) ψ2(Ω32)
(1,1,1)(2,2)(3,3) ψ2(Ω4)
(1,1,1)(2,2)(3,3,1) ψ2(Ωω)
(1,1,1)(2,2)(3,3,1)(4,3,1)(5,1) ψ2(ΩΩ)
(1,1,1)(2,2)(3,3,1)(4,3,1)(5,1,1) ψ2(ΩΩ2)
(1,1,1)(2,2)(3,3,1,1) ψ2(ωproj.)
(1,1,1)(2,2,1) Ω3
(1,1,1)(2,2,1)(2,1) Ω3×Ω
(1,1,1)(2,2,1)(2,1,1) Ω3×Ω2
(1,1,1)(2,2,1)(2,1,1)(2,1,1) Ω3×Ω22
(1,1,1)(2,2,1)(2,1,1)(3,2) Ω3×ψ2(Ω3)
(1,1,1)(2,2,1)(2,1,1)(3,2)(3,2) Ω3×ψ2(Ω3×2)
(1,1,1)(2,2,1)(2,1,1)(3,2)(4,3) Ω3×ψ2(Ω4)
(1,1,1)(2,2,1)(2,1,1)(3,2)(4,3,1,1) Ω3×ψ2(ωproj.)
(1,1,1)(2,2,1)(2,1,1)(3,2,1) Ω32
(1,1,1)(2,2,1)(2,1,1)(3,2,1)(2,1,1)(3,2,1) Ω33
(1,1,1)(2,2,1)(2,1,1)(3,2,1)(3) Ω3ω
(1,1,1)(2,2,1)(2,1,1)(3,2,1)(3,1,1)(4,2,1) Ω3Ω3
(1,1,1)(2,2,1)(2,2) ψ3(Ω4)
(1,1,1)(2,2,1)(2,2)(2,2) ψ3(Ω4×2)
(1,1,1)(2,2,1)(2,2)(3,3,1) ψ3(Ωω)
(1,1,1)(2,2,1)(2,2)(3,3,1,1) ψ3(ωproj.)
(1,1,1)(2,2,1)(2,2,1) Ω4
(1,1,1)(2,2,1)(2,2,1)(2,2,1) Ω5
(1,1,1)(2,2,1)(3) Ωω

Part 4

非递归 BMS 其他记号
(1,1,1)(2,2,1)(3) Ωω
(1,1,1)(2,2,1)(3,1) ΩΩ
(1,1,1)(2,2,1)(3,1)(2,2,1)(3,1) ΩΩ×2
(1,1,1)(2,2,1)(3,1)(3,1) ΩΩ2
(1,1,1)(2,2,1)(3,1)(4,2) Ωψ1(Ω2)
(1,1,1)(2,2,1)(3,1)(4,2,1,1) Ωψ1(ωproj.)
(1,1,1)(2,2,1)(3,1,1) ΩΩ2
(1,1,1)(2,2,1)(3,1,1)(4,2) Ωψ2(Ω3)
(1,1,1)(2,2,1)(3,1,1)(4,2)(5,3,1,1) Ωψ2(ωproj.)
(1,1,1)(2,2,1)(3,1,1)(4,2,1) ΩΩ3
(1,1,1)(2,2,1)(3,1,1)(4,2,1)(4,2,1) ΩΩ4
(1,1,1)(2,2,1)(3,1,1)(4,2,1)(5) ΩΩω
(1,1,1)(2,2,1)(3,1,1)(4,2,1)(5,1,1) ΩΩΩ2
(1,1,1)(2,2,1)(3,1,1)(4,2,1)(5,1,1)(6,2,1) ΩΩΩ3
(1,1,1)(2,2,1)(3,1,1)(4,2,1)(5,1,1)(6,2,1)(7) ΩΩΩω
(1,1,1)(2,2,1)(3,2) ψI(I)
(1,1,1)(2,2,1)(3,2)(2,2,1) ψI(I+1)
(1,1,1)(2,2,1)(3,2)(2,2,1)(3,1,1) ψI(I+Ω2)
(1,1,1)(2,2,1)(3,2)(2,2,1)(3,1,1)(4,2,1)(5,2) ψI(I+ψI(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) ψI(I+ψI(I)×2)
(1,1,1)(2,2,1)(3,2)(2,2,1)(3,1,1)(4,2,1)(5,2)(3,1,1) ψI(I+ψI(I)×Ω2)
(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) ψI(I+ψI(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) ψI(I+ψI(I)ψI(I))
(1,1,1)(2,2,1)(3,2)(2,2,1)(3,1,1)(4,2,1)(5,2)(4,2) ψI(I+ψψI(I+1)(ψI(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) ψI(I+ψψI(I+1)(ωproj.))
(1,1,1)(2,2,1)(3,2)(2,2,1)(3,1,1)(4,2,1)(5,2)(4,2,1) ψI(I+ψI(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) ψI(I+ψI(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) ψI(I+ψI(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) ψI(I+ψI(I+ψI(I)))
(1,1,1)(2,2,1)(3,2)(2,2,1)(3,2) ψI(I×2)
(1,1,1)(2,2,1)(3,2)(2,2,1)(3,2)(2,2,1) ψI(I×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) ψI(I×2+ψI(I×2))
(1,1,1)(2,2,1)(3,2)(2,2,1)(3,2)(2,2,1)(3,2) ψI(I×3)
(1,1,1)(2,2,1)(3,2)(3) ψI(I×ω)
(1,1,1)(2,2,1)(3,2)(3,1,1)(4,2,1)(5,2) ψI(I×ψI(I))
(1,1,1)(2,2,1)(3,2)(3,2) ψI(I2)
(1,1,1)(2,2,1)(3,2)(3,2)(3,2) ψI(I3)
(1,1,1)(2,2,1)(3,2)(4) ψI(Iω)
(1,1,1)(2,2,1)(3,2)(4,2) ψI(II)
(1,1,1)(2,2,1)(3,2)(4,3) ψI(ΩI+1)
(1,1,1)(2,2,1)(3,2)(4,3,1,1) ψI(ωproj.)
(1,1,1)(2,2,1)(3,2,1) I=ψM(M2)

Part 5

非递归 BMS 其他记号
(1,1,1)(2,2,1)(3,2,1) I
(1,1,1)(2,2,1)(3,2,1)(2,2,1) ΩI+1
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,1,1) ΩI+Ω2
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,1,1)(4,2,1)(5,2,1) ΩI×2
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,1,1)(4,2,1)(5,2,1)(2,2,1)(3,1,1)(4,2,1)(5,2,1) ΩI×3
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,1,1)(4,2,1)(5,2,1)(3,1,1)(4,2,1)(5,2,1) ΩI2
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,1,1)(4,2,1)(5,2,1)(4,1,1)(5,2,1)(6,2,1) ΩII
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,1,1)(4,2,1)(5,2,1)(4,2) ΩψΩI+1(ΩI+1)
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,1,1)(4,2,1)(5,2,1)(4,2)(5,3,1,1) ΩψΩI+1(ωproj.)
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,1,1)(4,2,1)(5,2,1)(4,2,1) ΩΩI+1
(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) ΩΩI×2
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2) ψI2(I2)
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2)(2,2,1)(3,1,1)(4,2,1)(5,2,1)(4,2,1)(5,2) ψI2(I2+ψI2(I2))
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2)(2,2,1)(3,2) ψI2(I2×2)
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2)(3,2) ψI2(I22)
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2)(4,3) ψI2(ΩI2+1)
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2)(4,3,1,1) ψI2(ωproj.)
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2,1) I2
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2,1)(2,2,1) ΩI2+1
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2,1)(2,2,1)(3,1,1)(4,2,1)(5,2,1)(4,2,1)(5,2,1) ΩI2×2
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2,1)(2,2,1)(3,2) ψI3(I3)
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2,1)(2,2,1)(3,2)(4,3,1,1) ψI2(ωproj.)
(1,1,1)(2,2,1)(3,2,1)(2,2,1)(3,2,1)(2,2,1)(3,2,1) I3
(1,1,1)(2,2,1)(3,2,1)(3) Iω
(1,1,1)(2,2,1)(3,2,1)(3)(2,2,1) ΩIω+1
(1,1,1)(2,2,1)(3,2,1)(3)(2,2,1)(3,1,1)(4,2,1)(5,2,1)(5) ΩIω×2
(1,1,1)(2,2,1)(3,2,1)(3)(2,2,1)(3,2) ψIω+1(Iω+1)
(1,1,1)(2,2,1)(3,2,1)(3)(2,2,1)(3,2,1) Iω+1
(1,1,1)(2,2,1)(3,2,1)(3)(4,1,1,1) Iψ(ωproj.)
(1,1,1)(2,2,1)(3,2,1)(3,1) IΩ
(1,1,1)(2,2,1)(3,2,1)(3,1,1)(4,2,1)(5,2,1) II
(1,1,1)(2,2,1)(3,2,1)(3,1,1)(4,2,1)(5,2,1)(4,2,1)(5,2,1) II2
(1,1,1)(2,2,1)(3,2,1)(3,1,1)(4,2,1)(5,2,1)(5) IIω
(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) III
(1,1,1)(2,2,1)(3,2,1)(3,2) ψI(1,0)(I(1,0))
(1,1,1)(2,2,1)(3,2,1)(3,2)(2,2,1) ΩψI(1,0)(I(1,0))+1
(1,1,1)(2,2,1)(3,2,1)(3,2)(2,2,1)(3,1,1)(4,2,1)(5,2,1)(5,2) ΩψI(1,0)(I(1,0))×2
(1,1,1)(2,2,1)(3,2,1)(3,2)(2,2,1)(3,2) ψψI(1,0)(I(1,0)+1)(ψI(1,0)(I(1,0)+1))
(1,1,1)(2,2,1)(3,2,1)(3,2)(2,2,1)(3,2,1) ψI(1,0)(I(1,0)+1)
(1,1,1)(2,2,1)(3,2,1)(3,2)(2,2,1)(3,2,1)(3,2) ψI(1,0)(I(1,0)×2)
(1,1,1)(2,2,1)(3,2,1)(3,2)(3,2) ψI(1,0)(I(1,0)2)
(1,1,1)(2,2,1)(3,2,1)(3,2)(4,3,1,1) ψI(1,0)(ωproj.)
(1,1,1)(2,2,1)(3,2,1)(3,2,1) I(1,0)=ψM(M3)
(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1) II(1,0)+1
(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)(3,1,1)(4,2,1)(5,2,1)(5,2,1) II(1,0)×2
(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)(3,2) ψI(1,1)(I(1,1))
(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)(3,2)(4,3,1,1) ψI(1,1)(ωproj)
(1,1,1)(2,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)(3,2,1) I(1,1)
(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3) I(1,ω)
(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,1,1)(4,2,1)(5,2,1)(5,2,1) I(1,I(1,0))
(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2) ψI(2,0)(I(2,0))
(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2)(4,3,1,1) ψI(2,0)(ωproj.)
(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1) I(2,0)=ψM(M4)
(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1) II(2,0)+1
(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1)(2,2,1)(3,2,1)(3,2,1) I(1,I(2,0)+1)
(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) I(2,1)
(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1)(3,2) ψI(3,0)(I(3,0))
(1,1,1)(2,2,1)(3,2,1)(3,2,1)(3,2,1)(3,2,1) I(3,0)
(1,1,1)(2,2,1)(3,2,1)(4) I(ω,0)=ψM(Mω)
(1,1,1)(2,2,1)(3,2,1)(4,1,1)(5,2,1)(6,2,1) I(I,0)
(1,1,1)(2,2,1)(3,2,1)(4,2) ψI(1,0,0)(I(1,0,0))

Part 6

TO DO: 非递归 BMS 分析(Part 6)