- FindStat

Identifier

St001628: Integer partitions ⟶ ℤ

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

                        [1]=>1
[2]=>1
[1,1]=>0
[3]=>2
[2,1]=>1
[1,1,1]=>0
[4]=>6
[3,1]=>5
[2,2]=>5
[2,1,1]=>2
[1,1,1,1]=>1
[5]=>21
[4,1]=>37
[3,2]=>40
[3,1,1]=>27
[2,2,1]=>28
[2,1,1,1]=>13
[1,1,1,1,1]=>5
[6]=>112
[5,1]=>295
[4,2]=>472
[4,1,1]=>375
[3,3]=>208
[3,2,1]=>583
[3,1,1,1]=>292
[2,2,2]=>198
[2,2,1,1]=>242
[2,1,1,1,1]=>128
[1,1,1,1,1,1]=>23
                    

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Description

The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs.

Code

def statistic(mu):
    s = SymmetricFunctions(QQ).s()
    F = (species.SimpleGraphSpecies().cycle_index_series()-1).logarithm()
    return F.coefficient(mu.size()).scalar(s(mu))

Created

Oct 01, 2020 at 22:40 by Martin Rubey

Updated

Oct 01, 2020 at 22:40 by Martin Rubey