Identifier
Identifier
Values
[1] generating graphics... => 0
[2] generating graphics... => 0
[1,1] generating graphics... => 1
[3] generating graphics... => 0
[2,1] generating graphics... => 1
[1,1,1] generating graphics... => 0
[4] generating graphics... => 0
[3,1] generating graphics... => 1
[2,2] generating graphics... => 0
[2,1,1] generating graphics... => 1
[1,1,1,1] generating graphics... => 0
[5] generating graphics... => 0
[4,1] generating graphics... => 1
[3,2] generating graphics... => 1
[3,1,1] generating graphics... => 1
[2,2,1] generating graphics... => 1
[2,1,1,1] generating graphics... => 1
[1,1,1,1,1] generating graphics... => 0
[6] generating graphics... => 0
[5,1] generating graphics... => 1
[4,2] generating graphics... => 1
[4,1,1] generating graphics... => 2
[3,3] generating graphics... => 1
[3,2,1] generating graphics... => 3
[3,1,1,1] generating graphics... => 1
[2,2,2] generating graphics... => 0
[2,2,1,1] generating graphics... => 2
[2,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1] generating graphics... => 0
[7] generating graphics... => 0
[6,1] generating graphics... => 1
[5,2] generating graphics... => 2
[5,1,1] generating graphics... => 2
[4,3] generating graphics... => 2
[4,2,1] generating graphics... => 5
[4,1,1,1] generating graphics... => 3
[3,3,1] generating graphics... => 3
[3,2,2] generating graphics... => 3
[3,2,1,1] generating graphics... => 5
[3,1,1,1,1] generating graphics... => 2
[2,2,2,1] generating graphics... => 2
[2,2,1,1,1] generating graphics... => 2
[2,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1] generating graphics... => 0
[8] generating graphics... => 0
[7,1] generating graphics... => 1
[6,2] generating graphics... => 2
[6,1,1] generating graphics... => 3
[5,3] generating graphics... => 4
[5,2,1] generating graphics... => 8
[5,1,1,1] generating graphics... => 4
[4,4] generating graphics... => 1
[4,3,1] generating graphics... => 9
[4,2,2] generating graphics... => 6
[4,2,1,1] generating graphics... => 12
[4,1,1,1,1] generating graphics... => 4
[3,3,2] generating graphics... => 6
[3,3,1,1] generating graphics... => 6
[3,2,2,1] generating graphics... => 9
[3,2,1,1,1] generating graphics... => 8
[3,1,1,1,1,1] generating graphics... => 3
[2,2,2,2] generating graphics... => 1
[2,2,2,1,1] generating graphics... => 4
[2,2,1,1,1,1] generating graphics... => 2
[2,1,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1,1] generating graphics... => 0
[9] generating graphics... => 0
[8,1] generating graphics... => 1
[7,2] generating graphics... => 3
[7,1,1] generating graphics... => 3
[6,3] generating graphics... => 5
[6,2,1] generating graphics... => 12
[6,1,1,1] generating graphics... => 6
[5,4] generating graphics... => 5
[5,3,1] generating graphics... => 18
[5,2,2] generating graphics... => 13
[5,2,1,1] generating graphics... => 21
[5,1,1,1,1] generating graphics... => 8
[4,4,1] generating graphics... => 9
[4,3,2] generating graphics... => 19
[4,3,1,1] generating graphics... => 24
[4,2,2,1] generating graphics... => 24
[4,2,1,1,1] generating graphics... => 21
[4,1,1,1,1,1] generating graphics... => 6
[3,3,3] generating graphics... => 4
[3,3,2,1] generating graphics... => 19
[3,3,1,1,1] generating graphics... => 13
[3,2,2,2] generating graphics... => 9
[3,2,2,1,1] generating graphics... => 18
[3,2,1,1,1,1] generating graphics... => 12
[3,1,1,1,1,1,1] generating graphics... => 3
[2,2,2,2,1] generating graphics... => 5
[2,2,2,1,1,1] generating graphics... => 5
[2,2,1,1,1,1,1] generating graphics... => 3
[2,1,1,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1,1,1] generating graphics... => 0
[10] generating graphics... => 0
[9,1] generating graphics... => 1
[8,2] generating graphics... => 3
[8,1,1] generating graphics... => 4
[7,3] generating graphics... => 8
[7,2,1] generating graphics... => 16
[7,1,1,1] generating graphics... => 8
[6,4] generating graphics... => 8
[6,3,1] generating graphics... => 32
[6,2,2] generating graphics... => 21
[6,2,1,1] generating graphics... => 36
[6,1,1,1,1] generating graphics... => 12
[5,5] generating graphics... => 5
[5,4,1] generating graphics... => 29
[5,3,2] generating graphics... => 46
[5,3,1,1] generating graphics... => 55
[5,2,2,1] generating graphics... => 53
[5,2,1,1,1] generating graphics... => 45
[5,1,1,1,1,1] generating graphics... => 13
[4,4,2] generating graphics... => 23
[4,4,1,1] generating graphics... => 32
[4,3,3] generating graphics... => 22
[4,3,2,1] generating graphics... => 77
[4,3,1,1,1] generating graphics... => 52
[4,2,2,2] generating graphics... => 28
[4,2,2,1,1] generating graphics... => 58
[4,2,1,1,1,1] generating graphics... => 34
[4,1,1,1,1,1,1] generating graphics... => 9
[3,3,3,1] generating graphics... => 20
[3,3,2,2] generating graphics... => 27
[3,3,2,1,1] generating graphics... => 44
[3,3,1,1,1,1] generating graphics... => 24
[3,2,2,2,1] generating graphics... => 29
[3,2,2,1,1,1] generating graphics... => 31
[3,2,1,1,1,1,1] generating graphics... => 16
[3,1,1,1,1,1,1,1] generating graphics... => 3
[2,2,2,2,2] generating graphics... => 3
[2,2,2,2,1,1] generating graphics... => 10
[2,2,2,1,1,1,1] generating graphics... => 7
[2,2,1,1,1,1,1,1] generating graphics... => 4
[2,1,1,1,1,1,1,1,1] generating graphics... => 1
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[5,4,2] generating graphics... => 90
[5,4,1,1] generating graphics... => 105
[5,3,3] generating graphics... => 60
[5,3,2,1] generating graphics... => 210
[5,3,1,1,1] generating graphics... => 140
[5,2,2,2] generating graphics... => 75
[5,2,2,1,1] generating graphics... => 140
[4,4,3] generating graphics... => 42
[4,4,2,1] generating graphics... => 120
[4,4,1,1,1] generating graphics... => 75
[4,3,3,1] generating graphics... => 108
[4,3,2,2] generating graphics... => 120
[4,3,2,1,1] generating graphics... => 210
[4,2,2,2,1] generating graphics... => 105
[3,3,3,2] generating graphics... => 42
[3,3,3,1,1] generating graphics... => 60
[3,3,2,2,1] generating graphics... => 90
[6,4,2] generating graphics... => 219
[5,4,3] generating graphics... => 177
[5,4,2,1] generating graphics... => 481
[5,4,1,1,1] generating graphics... => 294
[5,3,3,1] generating graphics... => 344
[5,3,2,2] generating graphics... => 375
[5,3,2,1,1] generating graphics... => 640
[5,2,2,2,1] generating graphics... => 294
[4,4,3,1] generating graphics... => 250
[4,4,2,2] generating graphics... => 214
[4,4,2,1,1] generating graphics... => 375
[4,3,3,2] generating graphics... => 250
[4,3,3,1,1] generating graphics... => 344
[4,3,2,2,1] generating graphics... => 481
[3,3,3,2,1] generating graphics... => 177
[3,3,2,2,1,1] generating graphics... => 219
[5,4,3,1] generating graphics... => 1155
[5,4,2,2] generating graphics... => 990
[5,4,2,1,1] generating graphics... => 1650
[5,3,3,2] generating graphics... => 891
[5,3,3,1,1] generating graphics... => 1232
[5,3,2,2,1] generating graphics... => 1650
[4,4,3,2] generating graphics... => 660
[4,4,3,1,1] generating graphics... => 891
[4,4,2,2,1] generating graphics... => 990
[4,3,3,2,1] generating graphics... => 1155
[5,4,3,2] generating graphics... => 3432
[5,4,3,1,1] generating graphics... => 4576
[5,4,2,2,1] generating graphics... => 4903
[5,3,3,2,1] generating graphics... => 4576
[4,4,3,2,1] generating graphics... => 3432
[5,4,3,2,1] generating graphics... => 19522
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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.
References
[1] Ahlbach, C., Swanson, J. P. Cyclic sieving, necklaces, and branching rules related to Thrall's problem arXiv:1808.06043
Code
def statistic(P):
    n = P.size()
    return sum(Integer(1) for T in StandardTableaux(P) if T.standard_major_index() % n == 1)

Created
Jul 02, 2019 at 14:58 by Martin Rubey
Updated
Jul 02, 2019 at 22:27 by Martin Rubey