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Statistic identifier: St001628

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Collection: Integer partitions

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

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References: 

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


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Statistic 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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Created: Oct 01, 2020 at 22:40 by Martin Rubey

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Last Updated: Oct 01, 2020 at 22:40 by Martin Rubey