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This is not the same as the answer obtained by Brian Hopkinsanswer obtained by Brian Hopkins, whose dominoes have an extra $0$, and I must admit that I have not looked carefully the references he gave as yet (and am not convinced that this question should need one to read four papers in Compositio). However, if I tweak my code so that $\lambda$ has core $(1)$ and quotient $(\alpha,\beta)$, then I do seem to get his answer.

This is not the same as the answer obtained by Brian Hopkins, whose dominoes have an extra $0$, and I must admit that I have not looked carefully the references he gave as yet (and am not convinced that this question should need one to read four papers in Compositio). However, if I tweak my code so that $\lambda$ has core $(1)$ and quotient $(\alpha,\beta)$, then I do seem to get his answer.

This is not the same as the answer obtained by Brian Hopkins, whose dominoes have an extra $0$, and I must admit that I have not looked carefully the references he gave as yet (and am not convinced that this question should need one to read four papers in Compositio). However, if I tweak my code so that $\lambda$ has core $(1)$ and quotient $(\alpha,\beta)$, then I do seem to get his answer.

deleted 66 characters in body
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Amritanshu Prasad
Amritanshu Prasad
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[1, 2] ([[1, 2, 2, 32], 3]][1]], [[1, 2, 2, 32], 3]][1]])
[1, -2] ([[1, 2, 2], [3][1, [3]]2]], [[1, 2, 2], [3][1, [3]]2]])
[-1, 2] ([[1, 3, 3]1], [2][2, [2]]2]], [[1, 3, 3]1], [2][2, [2]]2]])
[-1, -2] ([[1, 3], [21, 3]2, [2]]2]], [[1, 3], [21, 3]2, [2]]2]])
[2, 1] ([[1, 2, 2][[1], [3[1], 3]][2], [[1[2]], 2[[1], 2][1], [3[2], 3]][2]])
[2, -1] ([[1, 2, 2], [3][1, [3]]2]], [[1, 3, 3]1], [2][2, [2]]2]])
[-2, 1] ([[1, 3, 3]1], [2][2, [2]]2]], [[1, 2, 2], [3][1, [3]]2]])
[-2, -1] ([[1][[1, [2]1], [2], [3], [3]][2]], [[1][[1, [2]1], [2], [3], [3]][2]])

[1, 2] ([[1, 2, 2, 3, 3]], [[1, 2, 2, 3, 3]])
[1, -2] ([[1, 2, 2], [3], [3]], [[1, 2, 2], [3], [3]])
[-1, 2] ([[1, 3, 3], [2], [2]], [[1, 3, 3], [2], [2]])
[-1, -2] ([[1, 3], [2, 3], [2]], [[1, 3], [2, 3], [2]])
[2, 1] ([[1, 2, 2], [3, 3]], [[1, 2, 2], [3, 3]])
[2, -1] ([[1, 2, 2], [3], [3]], [[1, 3, 3], [2], [2]])
[-2, 1] ([[1, 3, 3], [2], [2]], [[1, 2, 2], [3], [3]])
[-2, -1] ([[1], [2], [2], [3], [3]], [[1], [2], [2], [3], [3]])

[1, 2] ([[1, 2, 2], [1]], [[1, 2, 2], [1]])
[1, -2] ([[1, 2], [1, 2]], [[1, 2], [1, 2]])
[-1, 2] ([[1, 1], [2, 2]], [[1, 1], [2, 2]])
[-1, -2] ([[1, 1, 2, 2]], [[1, 1, 2, 2]])
[2, 1] ([[1], [1], [2], [2]], [[1], [1], [2], [2]])
[2, -1] ([[1, 2], [1, 2]], [[1, 1], [2, 2]])
[-2, 1] ([[1, 1], [2, 2]], [[1, 2], [1, 2]])
[-2, -1] ([[1, 1], [2], [2]], [[1, 1], [2], [2]])
Fixed error in code output example $W(B_2)$.
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Amritanshu Prasad
Amritanshu Prasad
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[1, 2] ([[[1, 2]], []], [[[1, 2]], []])
[1, -2] ([[[2]][[[1]], [[1]]][[2]]], [[[2]][[[1]], [[1]]][[2]]])
[-1, 2] ([[[2]], [[1]]], [[[2]], [[1]]])
[-1, -2] ([[], [[1, 2]]], [[], [[1, 2]]])
[2, 1] ([[[1], [2]], []], [[[1], [2]], []])
[2, -1] ([[[2]][[[1]], [[1]]][[2]]], [[[1]][[[2]], [[2]]][[1]]])
[-2, 1] ([[[2]], [[1]]], [[[1]], [[2]]])
[-2, -1] ([[], [[1], [2]]], [[], [[1], [2]]])

[1, 2] ([[1, 2, 2]2, [1]]3, 3]], [[1, 2, 2]2, [1]]3, 3]])
[1, -2] ([[1, 1]2, [22], 2]][3], [3]], [[1, 1]2, [22], 2]][3], [3]])
[-1, 2] ([[1, 1]3, [23], 2]][2], [2]], [[1, 1]3, [23], 2]][2], [2]])
[-1, -2] ([[1, 13], 2[2, 2]]3], [2]], [[1, 13], 2[2, 2]]3], [2]])
[2, 1] ([[1][[1, [1]2, [2]2], [2]][3, [[1]3]], [1][[1, [2]2, [2]]2], [3, 3]])
[2, -1] ([[1, 1]2, [22], 2]][3], [3]], [[1, 2]3, [13], 2]][2], [2]])
[-2, 1] ([[1, 1]3, [23], 2]][2], [2]], [[1, 2, 2], [1[3], 2]][3]])
[-2, -1] ([[1[[1], 1][2], [2], [2]][3], [[1[3]], 1][[1], [2], [2]][2], [3], [3]])

[1, 2] ([[[1, 2]], []], [[[1, 2]], []])
[1, -2] ([[[2]], [[1]]], [[[2]], [[1]]])
[-1, 2] ([[[2]], [[1]]], [[[2]], [[1]]])
[-1, -2] ([[], [[1, 2]]], [[], [[1, 2]]])
[2, 1] ([[[1], [2]], []], [[[1], [2]], []])
[2, -1] ([[[2]], [[1]]], [[[1]], [[2]]])
[-2, 1] ([[[2]], [[1]]], [[[1]], [[2]]])
[-2, -1] ([[], [[1], [2]]], [[], [[1], [2]]])

[1, 2] ([[1, 2, 2], [1]], [[1, 2, 2], [1]])
[1, -2] ([[1, 1], [2, 2]], [[1, 1], [2, 2]])
[-1, 2] ([[1, 1], [2, 2]], [[1, 1], [2, 2]])
[-1, -2] ([[1, 1, 2, 2]], [[1, 1, 2, 2]])
[2, 1] ([[1], [1], [2], [2]], [[1], [1], [2], [2]])
[2, -1] ([[1, 1], [2, 2]], [[1, 2], [1, 2]])
[-2, 1] ([[1, 1], [2, 2]], [[1, 2], [1, 2]])
[-2, -1] ([[1, 1], [2], [2]], [[1, 1], [2], [2]])

[1, 2] ([[[1, 2]], []], [[[1, 2]], []])
[1, -2] ([[[1]], [[2]]], [[[1]], [[2]]])
[-1, 2] ([[[2]], [[1]]], [[[2]], [[1]]])
[-1, -2] ([[], [[1, 2]]], [[], [[1, 2]]])
[2, 1] ([[[1], [2]], []], [[[1], [2]], []])
[2, -1] ([[[1]], [[2]]], [[[2]], [[1]]])
[-2, 1] ([[[2]], [[1]]], [[[1]], [[2]]])
[-2, -1] ([[], [[1], [2]]], [[], [[1], [2]]])

[1, 2] ([[1, 2, 2, 3, 3]], [[1, 2, 2, 3, 3]])
[1, -2] ([[1, 2, 2], [3], [3]], [[1, 2, 2], [3], [3]])
[-1, 2] ([[1, 3, 3], [2], [2]], [[1, 3, 3], [2], [2]])
[-1, -2] ([[1, 3], [2, 3], [2]], [[1, 3], [2, 3], [2]])
[2, 1] ([[1, 2, 2], [3, 3]], [[1, 2, 2], [3, 3]])
[2, -1] ([[1, 2, 2], [3], [3]], [[1, 3, 3], [2], [2]])
[-2, 1] ([[1, 3, 3], [2], [2]], [[1, 2, 2], [3], [3]])
[-2, -1] ([[1], [2], [2], [3], [3]], [[1], [2], [2], [3], [3]])
Added Sagecode, and comparison with Brian Hopkins answer.
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Amritanshu Prasad
Amritanshu Prasad
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Added domino tableaux example.
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Amritanshu Prasad
Amritanshu Prasad
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added 18 characters in body
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Amritanshu Prasad
Amritanshu Prasad
  • 5.7k
  • 1
  • 38
  • 54
Source Link
Amritanshu Prasad
Amritanshu Prasad
  • 5.7k
  • 1
  • 38
  • 54