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Statistic identifier: St001440
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Collection: Integer partitions
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Description: The number of standard Young tableaux whose major index is congruent one modulo 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):
n = P.size()
return sum(Integer(1) for T in StandardTableaux(P) if T.standard_major_index() % n == 1)
-----------------------------------------------------------------------------
Statistic values:
[1] => 0
[2] => 0
[1,1] => 1
[3] => 0
[2,1] => 1
[1,1,1] => 0
[4] => 0
[3,1] => 1
[2,2] => 0
[2,1,1] => 1
[1,1,1,1] => 0
[5] => 0
[4,1] => 1
[3,2] => 1
[3,1,1] => 1
[2,2,1] => 1
[2,1,1,1] => 1
[1,1,1,1,1] => 0
[6] => 0
[5,1] => 1
[4,2] => 1
[4,1,1] => 2
[3,3] => 1
[3,2,1] => 3
[3,1,1,1] => 1
[2,2,2] => 0
[2,2,1,1] => 2
[2,1,1,1,1] => 1
[1,1,1,1,1,1] => 0
[7] => 0
[6,1] => 1
[5,2] => 2
[5,1,1] => 2
[4,3] => 2
[4,2,1] => 5
[4,1,1,1] => 3
[3,3,1] => 3
[3,2,2] => 3
[3,2,1,1] => 5
[3,1,1,1,1] => 2
[2,2,2,1] => 2
[2,2,1,1,1] => 2
[2,1,1,1,1,1] => 1
[1,1,1,1,1,1,1] => 0
[8] => 0
[7,1] => 1
[6,2] => 2
[6,1,1] => 3
[5,3] => 4
[5,2,1] => 8
[5,1,1,1] => 4
[4,4] => 1
[4,3,1] => 9
[4,2,2] => 6
[4,2,1,1] => 12
[4,1,1,1,1] => 4
[3,3,2] => 6
[3,3,1,1] => 6
[3,2,2,1] => 9
[3,2,1,1,1] => 8
[3,1,1,1,1,1] => 3
[2,2,2,2] => 1
[2,2,2,1,1] => 4
[2,2,1,1,1,1] => 2
[2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1] => 0
[9] => 0
[8,1] => 1
[7,2] => 3
[7,1,1] => 3
[6,3] => 5
[6,2,1] => 12
[6,1,1,1] => 6
[5,4] => 5
[5,3,1] => 18
[5,2,2] => 13
[5,2,1,1] => 21
[5,1,1,1,1] => 8
[4,4,1] => 9
[4,3,2] => 19
[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] => 4
[3,3,2,1] => 19
[3,3,1,1,1] => 13
[3,2,2,2] => 9
[3,2,2,1,1] => 18
[3,2,1,1,1,1] => 12
[3,1,1,1,1,1,1] => 3
[2,2,2,2,1] => 5
[2,2,2,1,1,1] => 5
[2,2,1,1,1,1,1] => 3
[2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1] => 0
[10] => 0
[9,1] => 1
[8,2] => 3
[8,1,1] => 4
[7,3] => 8
[7,2,1] => 16
[7,1,1,1] => 8
[6,4] => 8
[6,3,1] => 32
[6,2,2] => 21
[6,2,1,1] => 36
[6,1,1,1,1] => 12
[5,5] => 5
[5,4,1] => 29
[5,3,2] => 46
[5,3,1,1] => 55
[5,2,2,1] => 53
[5,2,1,1,1] => 45
[5,1,1,1,1,1] => 13
[4,4,2] => 23
[4,4,1,1] => 32
[4,3,3] => 22
[4,3,2,1] => 77
[4,3,1,1,1] => 52
[4,2,2,2] => 28
[4,2,2,1,1] => 58
[4,2,1,1,1,1] => 34
[4,1,1,1,1,1,1] => 9
[3,3,3,1] => 20
[3,3,2,2] => 27
[3,3,2,1,1] => 44
[3,3,1,1,1,1] => 24
[3,2,2,2,1] => 29
[3,2,2,1,1,1] => 31
[3,2,1,1,1,1,1] => 16
[3,1,1,1,1,1,1,1] => 3
[2,2,2,2,2] => 3
[2,2,2,2,1,1] => 10
[2,2,2,1,1,1,1] => 7
[2,2,1,1,1,1,1,1] => 4
[2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1] => 0
[5,4,2] => 90
[5,4,1,1] => 105
[5,3,3] => 60
[5,3,2,1] => 210
[5,3,1,1,1] => 140
[5,2,2,2] => 75
[5,2,2,1,1] => 140
[4,4,3] => 42
[4,4,2,1] => 120
[4,4,1,1,1] => 75
[4,3,3,1] => 108
[4,3,2,2] => 120
[4,3,2,1,1] => 210
[4,2,2,2,1] => 105
[3,3,3,2] => 42
[3,3,3,1,1] => 60
[3,3,2,2,1] => 90
[6,4,2] => 219
[5,4,3] => 177
[5,4,2,1] => 481
[5,4,1,1,1] => 294
[5,3,3,1] => 344
[5,3,2,2] => 375
[5,3,2,1,1] => 640
[5,2,2,2,1] => 294
[4,4,3,1] => 250
[4,4,2,2] => 214
[4,4,2,1,1] => 375
[4,3,3,2] => 250
[4,3,3,1,1] => 344
[4,3,2,2,1] => 481
[3,3,3,2,1] => 177
[3,3,2,2,1,1] => 219
[5,4,3,1] => 1155
[5,4,2,2] => 990
[5,4,2,1,1] => 1650
[5,3,3,2] => 891
[5,3,3,1,1] => 1232
[5,3,2,2,1] => 1650
[4,4,3,2] => 660
[4,4,3,1,1] => 891
[4,4,2,2,1] => 990
[4,3,3,2,1] => 1155
[5,4,3,2] => 3432
[5,4,3,1,1] => 4576
[5,4,2,2,1] => 4903
[5,3,3,2,1] => 4576
[4,4,3,2,1] => 3432
[5,4,3,2,1] => 19522
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Created: Jul 02, 2019 at 14:58 by Martin Rubey
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Last Updated: Jul 02, 2019 at 22:27 by Martin Rubey