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Identifier
Values
=>
Cc0002;cc-rep
[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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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