- FindStat

Identifier

St001440: Integer partitions ⟶ ℤ

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