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Identifier
Values
=>
Cc0002;cc-rep
[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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Description
The number of standard Young tableaux whose major index is divisible by 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):
    return sum(1 for T in StandardTableaux(P) if T.standard_major_index() % P.size() == 0)

Created
Jul 03, 2019 at 22:55 by Martin Rubey
Updated
Jul 03, 2019 at 22:55 by Martin Rubey