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Identifier
Values
[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