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Identifier
Values
[1] => 1
[2] => 1
[1,1] => 1
[3] => 2
[2,1] => 3
[1,1,1] => 4
[4] => 6
[3,1] => 11
[2,2] => 16
[2,1,1] => 23
[1,1,1,1] => 38
[5] => 21
[4,1] => 58
[3,2] => 98
[3,1,1] => 162
[2,2,1] => 230
[2,1,1,1] => 402
[1,1,1,1,1] => 728
[6] => 112
[5,1] => 407
[4,2] => 879
[4,1,1] => 1549
[3,3] => 1087
[3,2,1] => 2812
[3,1,1,1] => 5204
[2,2,2] => 4065
[2,2,1,1] => 7490
[2,1,1,1,1] => 14080
[1,1,1,1,1,1] => 26704
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Description
The number of coloured connected graphs such that the multiplicities of colours are given by a partition.
In particular, the value on the partition $(n)$ is the number of unlabelled connected graphs on $n$ vertices, oeis:A001349, whereas the value on the partition $(1^n)$ is the number of labelled connected graphs oeis:A001187.
Code
def statistic(mu):
    h = SymmetricFunctions(QQ).h()
    F = (species.SimpleGraphSpecies().cycle_index_series()-1).logarithm()
    return F.coefficient(mu.size()).scalar(h(mu))
Created
Oct 01, 2020 at 22:08 by Martin Rubey
Updated
Oct 01, 2020 at 22:08 by Martin Rubey