- FindStat

Identifier

St001442: Integer partitions ⟶ ℤ

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