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Statistic identifier: St001442
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Collection: Integer partitions
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Description: The number of standard Young tableaux whose major index is divisible by the size of a given integer partition.
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References: [1] Ahlbach, C., Swanson, J. P. Cyclic sieving, necklaces, and branching rules related to Thrall's problem [[arXiv:1808.06043]]
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Code:
def statistic(P):
return sum(1 for T in StandardTableaux(P) if T.standard_major_index() % P.size() == 0)
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Statistic values:
[1] => 1
[2] => 1
[1,1] => 0
[3] => 1
[2,1] => 0
[1,1,1] => 1
[4] => 1
[3,1] => 0
[2,2] => 1
[2,1,1] => 1
[1,1,1,1] => 0
[5] => 1
[4,1] => 0
[3,2] => 1
[3,1,1] => 2
[2,2,1] => 1
[2,1,1,1] => 0
[1,1,1,1,1] => 1
[6] => 1
[5,1] => 0
[4,2] => 2
[4,1,1] => 2
[3,3] => 1
[3,2,1] => 2
[3,1,1,1] => 2
[2,2,2] => 2
[2,2,1,1] => 1
[2,1,1,1,1] => 1
[1,1,1,1,1,1] => 0
[7] => 1
[6,1] => 0
[5,2] => 2
[5,1,1] => 3
[4,3] => 2
[4,2,1] => 5
[4,1,1,1] => 2
[3,3,1] => 3
[3,2,2] => 3
[3,2,1,1] => 5
[3,1,1,1,1] => 3
[2,2,2,1] => 2
[2,2,1,1,1] => 2
[2,1,1,1,1,1] => 0
[1,1,1,1,1,1,1] => 1
[8] => 1
[7,1] => 0
[6,2] => 3
[6,1,1] => 3
[5,3] => 3
[5,2,1] => 8
[5,1,1,1] => 4
[4,4] => 3
[4,3,1] => 8
[4,2,2] => 8
[4,2,1,1] => 11
[4,1,1,1,1] => 5
[3,3,2] => 5
[3,3,1,1] => 8
[3,2,2,1] => 8
[3,2,1,1,1] => 8
[3,1,1,1,1,1] => 2
[2,2,2,2] => 3
[2,2,2,1,1] => 3
[2,2,1,1,1,1] => 3
[2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1] => 0
[9] => 1
[8,1] => 0
[7,2] => 3
[7,1,1] => 4
[6,3] => 6
[6,2,1] => 11
[6,1,1,1] => 6
[5,4] => 4
[5,3,1] => 18
[5,2,2] => 14
[5,2,1,1] => 21
[5,1,1,1,1] => 8
[4,4,1] => 10
[4,3,2] => 18
[4,3,1,1] => 24
[4,2,2,1] => 24
[4,2,1,1,1] => 21
[4,1,1,1,1,1] => 6
[3,3,3] => 6
[3,3,2,1] => 18
[3,3,1,1,1] => 14
[3,2,2,2] => 10
[3,2,2,1,1] => 18
[3,2,1,1,1,1] => 11
[3,1,1,1,1,1,1] => 4
[2,2,2,2,1] => 4
[2,2,2,1,1,1] => 6
[2,2,1,1,1,1,1] => 3
[2,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1] => 1
[10] => 1
[9,1] => 0
[8,2] => 4
[8,1,1] => 4
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Created: Jul 03, 2019 at 22:55 by Martin Rubey
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Last Updated: Jul 03, 2019 at 22:55 by Martin Rubey