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Identifier
Values
[1] => 1
[2] => 2
[1,1] => 2
[3] => 4
[2,1] => 6
[1,1,1] => 8
[4] => 11
[3,1] => 20
[2,2] => 28
[2,1,1] => 40
[1,1,1,1] => 64
[5] => 34
[4,1] => 90
[3,2] => 148
[3,1,1] => 240
[2,2,1] => 336
[2,1,1,1] => 576
[1,1,1,1,1] => 1024
[6] => 156
[5,1] => 544
[4,2] => 1144
[4,1,1] => 1992
[3,3] => 1408
[3,2,1] => 3568
[3,1,1,1] => 6528
[2,2,2] => 5120
[2,2,1,1] => 9344
[2,1,1,1,1] => 17408
[1,1,1,1,1,1] => 32768
[7] => 1044
[6,1] => 5096
[5,2] => 13128
[5,1,1] => 24416
[4,3] => 20364
[4,2,1] => 55472
[4,1,1,1] => 105536
[3,3,1] => 71552
[3,2,2] => 104160
[3,2,1,1] => 199040
[3,1,1,1,1] => 382976
[2,2,2,1] => 290304
[2,2,1,1,1] => 559104
[2,1,1,1,1,1] => 1081344
[1,1,1,1,1,1,1] => 2097152
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Description
The number of coloured 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 graphs on $n$ vertices, oeis:A000088, whereas the value on the partition $(1^n)$ is the number of labelled graphs oeis:A006125.
Code
def statistic(mu):
    h = SymmetricFunctions(QQ).h()
    F = species.SimpleGraphSpecies().cycle_index_series()
    return F.coefficient(mu.size()).scalar(h(mu))
Created
Sep 27, 2020 at 13:19 by Martin Rubey
Updated
Sep 27, 2020 at 13:19 by Martin Rubey