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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