- FindStat

Identifier

St001600: Integer partitions ⟶ ℤ

Values

=>
                            Cc0002;cc-rep
                            
                            
                            

                        [1]=>1
[2]=>2
[1,1]=>0
[3]=>4
[2,1]=>2
[1,1,1]=>0
[4]=>11
[3,1]=>9
[2,2]=>8
[2,1,1]=>3
[1,1,1,1]=>1
[5]=>34
[4,1]=>56
[3,2]=>58
[3,1,1]=>36
[2,2,1]=>38
[2,1,1,1]=>16
[1,1,1,1,1]=>6
[6]=>156
[5,1]=>388
[4,2]=>600
[4,1,1]=>460
[3,3]=>264
[3,2,1]=>712
[3,1,1,1]=>340
[2,2,2]=>240
[2,2,1,1]=>288
[2,1,1,1,1]=>148
[1,1,1,1,1,1]=>28
[7]=>1044
[6,1]=>4052
[5,2]=>8032
[5,1,1]=>7236
[4,3]=>7236
[4,2,1]=>15788
[4,1,1,1]=>7720
[3,3,1]=>8844
[3,2,2]=>8788
[3,2,1,1]=>12948
[3,1,1,1,1]=>5036
[2,2,2,1]=>5052
[2,2,1,1,1]=>4416
[2,1,1,1,1,1]=>1788
[1,1,1,1,1,1,1]=>252
                    

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Description

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

Code

def statistic(mu):
    s = SymmetricFunctions(QQ).s()
    F = LazyCombinatorialSpecies(QQ, "X").Graphs().cycle_index_series()
    return F.coefficient(mu.size()).scalar(s(mu))

Created

Sep 26, 2020 at 23:20 by Martin Rubey

Updated

Sep 26, 2025 at 17:07 by Martin Rubey