- FindStat

Identifier

St001629: Integer compositions ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        [1,1,1]=>1
[1,2]=>0
[2,1]=>0
[3]=>1
[1,1,1,1]=>0
[1,1,2]=>1
[1,2,1]=>2
[1,3]=>0
[2,1,1]=>1
[2,2]=>1
[3,1]=>0
[4]=>1
[1,1,1,1,1]=>1
[1,1,1,2]=>0
[1,1,2,1]=>1
[1,1,3]=>2
[1,2,1,1]=>1
[1,2,2]=>4
[1,3,1]=>3
[1,4]=>0
[2,1,1,1]=>0
[2,1,2]=>3
[2,2,1]=>4
[2,3]=>1
[3,1,1]=>2
[3,2]=>1
[4,1]=>0
[5]=>1
[1,1,1,1,1,1]=>0
[1,1,1,1,2]=>1
[1,1,1,2,1]=>2
[1,1,1,3]=>2
[1,1,2,1,1]=>4
[1,1,2,2]=>5
[1,1,3,1]=>4
[1,1,4]=>2
[1,2,1,1,1]=>2
[1,2,1,2]=>7
[1,2,2,1]=>10
[1,2,3]=>6
[1,3,1,1]=>4
[1,3,2]=>7
[1,4,1]=>4
[1,5]=>0
[2,1,1,1,1]=>1
[2,1,1,2]=>3
[2,1,2,1]=>7
[2,1,3]=>4
[2,2,1,1]=>5
[2,2,2]=>11
[2,3,1]=>7
[2,4]=>2
[3,1,1,1]=>2
[3,1,2]=>4
[3,2,1]=>6
[3,3]=>3
[4,1,1]=>2
[4,2]=>2
[5,1]=>0
[6]=>1
[1,1,1,1,1,1,1]=>1
[1,1,1,1,1,2]=>0
[1,1,1,1,2,1]=>2
[1,1,1,1,3]=>3
[1,1,1,2,1,1]=>4
[1,1,1,2,2]=>10
[1,1,1,3,1]=>8
[1,1,1,4]=>2
[1,1,2,1,1,1]=>4
[1,1,2,1,2]=>15
[1,1,2,2,1]=>23
[1,1,2,3]=>12
[1,1,3,1,1]=>11
[1,1,3,2]=>15
[1,1,4,1]=>7
[1,1,5]=>3
[1,2,1,1,1,1]=>2
[1,2,1,1,2]=>12
[1,2,1,2,1]=>25
[1,2,1,3]=>15
[1,2,2,1,1]=>23
[1,2,2,2]=>38
[1,2,3,1]=>25
[1,2,4]=>10
[1,3,1,1,1]=>8
[1,3,1,2]=>18
[1,3,2,1]=>25
[1,3,3]=>15
[1,4,1,1]=>7
[1,4,2]=>12
[1,5,1]=>5
[1,6]=>0
[2,1,1,1,1,1]=>0
[2,1,1,1,2]=>5
[2,1,1,2,1]=>12
[2,1,1,3]=>7
[2,1,2,1,1]=>15
[2,1,2,2]=>25
[2,1,3,1]=>18
[2,1,4]=>8
[2,2,1,1,1]=>10
[2,2,1,2]=>25
[2,2,2,1]=>38
[2,2,3]=>23
[2,3,1,1]=>15
[2,3,2]=>25
[2,4,1]=>12
[2,5]=>2
[3,1,1,1,1]=>3
[3,1,1,2]=>7
[3,1,2,1]=>15
[3,1,3]=>11
[3,2,1,1]=>12
[3,2,2]=>23
[3,3,1]=>15
[3,4]=>4
[4,1,1,1]=>2
[4,1,2]=>8
[4,2,1]=>10
[4,3]=>4
[5,1,1]=>3
[5,2]=>2
[6,1]=>0
[7]=>1
[1,1,1,1,1,1,1,1]=>0
[1,1,1,1,1,1,2]=>1
[1,1,1,1,1,2,1]=>4
[1,1,1,1,1,3]=>2
[1,1,1,1,2,1,1]=>7
[1,1,1,1,2,2]=>13
[1,1,1,1,3,1]=>10
[1,1,1,1,4]=>5
[1,1,1,2,1,1,1]=>10
[1,1,1,2,1,2]=>24
[1,1,1,2,2,1]=>40
[1,1,1,2,3]=>24
[1,1,1,3,1,1]=>18
[1,1,1,3,2]=>32
[1,1,1,4,1]=>16
[1,1,1,5]=>4
[1,1,2,1,1,1,1]=>7
[1,1,2,1,1,2]=>27
[1,1,2,1,2,1]=>59
[1,1,2,1,3]=>40
[1,1,2,2,1,1]=>56
[1,1,2,2,2]=>99
[1,1,2,3,1]=>67
[1,1,2,4]=>23
[1,1,3,1,1,1]=>18
[1,1,3,1,2]=>53
[1,1,3,2,1]=>72
[1,1,3,3]=>39
[1,1,4,1,1]=>24
[1,1,4,2]=>31
[1,1,5,1]=>12
[1,1,6]=>3
[1,2,1,1,1,1,1]=>4
[1,2,1,1,1,2]=>16
[1,2,1,1,2,1]=>46
[1,2,1,1,3]=>32
[1,2,1,2,1,1]=>59
[1,2,1,2,2]=>110
[1,2,1,3,1]=>80
[1,2,1,4]=>31
[1,2,2,1,1,1]=>40
[1,2,2,1,2]=>115
[1,2,2,2,1]=>174
[1,2,2,3]=>98
[1,2,3,1,1]=>72
[1,2,3,2]=>109
[1,2,4,1]=>50
[1,2,5]=>14
[1,3,1,1,1,1]=>10
[1,3,1,1,2]=>40
[1,3,1,2,1]=>80
[1,3,1,3]=>52
[1,3,2,1,1]=>67
[1,3,2,2]=>114
[1,3,3,1]=>74
[1,3,4]=>25
[1,4,1,1,1]=>16
[1,4,1,2]=>39
[1,4,2,1]=>50
[1,4,3]=>28
[1,5,1,1]=>12
[1,5,2]=>17
[1,6,1]=>6
[1,7]=>0
[2,1,1,1,1,1,1]=>1
[2,1,1,1,1,2]=>5
[2,1,1,1,2,1]=>16
[2,1,1,1,3]=>13
[2,1,1,2,1,1]=>27
[2,1,1,2,2]=>51
[2,1,1,3,1]=>40
[2,1,1,4]=>15
[2,1,2,1,1,1]=>24
[2,1,2,1,2]=>75
[2,1,2,2,1]=>115
[2,1,2,3]=>66
[2,1,3,1,1]=>53
[2,1,3,2]=>79
[2,1,4,1]=>39
[2,1,5]=>11
[2,2,1,1,1,1]=>13
[2,2,1,1,2]=>51
[2,2,1,2,1]=>110
[2,2,1,3]=>71
[2,2,2,1,1]=>99
[2,2,2,2]=>173
[2,2,3,1]=>114
[2,2,4]=>41
[2,3,1,1,1]=>32
[2,3,1,2]=>79
[2,3,2,1]=>109
[2,3,3]=>60
[2,4,1,1]=>31
[2,4,2]=>47
[2,5,1]=>17
[2,6]=>3
[3,1,1,1,1,1]=>2
[3,1,1,1,2]=>13
[3,1,1,2,1]=>32
[3,1,1,3]=>23
[3,1,2,1,1]=>40
[3,1,2,2]=>71
[3,1,3,1]=>52
[3,1,4]=>19
[3,2,1,1,1]=>24
[3,2,1,2]=>66
[3,2,2,1]=>98
[3,2,3]=>57
[3,3,1,1]=>39
[3,3,2]=>60
[3,4,1]=>28
[3,5]=>6
[4,1,1,1,1]=>5
[4,1,1,2]=>15
[4,1,2,1]=>31
[4,1,3]=>19
[4,2,1,1]=>23
[4,2,2]=>41
[4,3,1]=>25
[4,4]=>9
[5,1,1,1]=>4
[5,1,2]=>11
[5,2,1]=>14
[5,3]=>6
[6,1,1]=>3
[6,2]=>3
[7,1]=>0
[8]=>1
                    

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Description

The coefficient of the integer composition in the quasisymmetric expansion of the relabelling action of the symmetric group on cycles.

Code

def statistic(a):
    F = QuasiSymmetricFunctions(QQ).F()
    S = species.CycleSpecies().cycle_index_series()
    return F(S.coefficient(a.size())).coefficient(a)

Created

Oct 02, 2020 at 07:18 by Martin Rubey

Updated

Oct 02, 2020 at 07:18 by Martin Rubey