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Identifier
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