Identifier
-
Mp00323:
Integer partitions
—Loehr-Warrington inverse⟶
Integer partitions
St001627: Integer partitions ⟶ ℤ
Values
[1] => [1] => 1
[2] => [1,1] => 1
[1,1] => [2] => 1
[3] => [2,1] => 3
[2,1] => [1,1,1] => 4
[1,1,1] => [3] => 2
[4] => [2,2] => 16
[3,1] => [1,1,1,1] => 38
[2,2] => [2,1,1] => 23
[2,1,1] => [3,1] => 11
[1,1,1,1] => [4] => 6
[5] => [3,2] => 98
[4,1] => [3,1,1] => 162
[3,2] => [1,1,1,1,1] => 728
[3,1,1] => [2,1,1,1] => 402
[2,2,1] => [2,2,1] => 230
[2,1,1,1] => [4,1] => 58
[1,1,1,1,1] => [5] => 21
[6] => [3,3] => 1087
[5,1] => [3,2,1] => 2812
[4,2] => [2,1,1,1,1] => 14080
[4,1,1] => [2,2,1,1] => 7490
[3,3] => [3,1,1,1] => 5204
[3,2,1] => [1,1,1,1,1,1] => 26704
[3,1,1,1] => [4,1,1] => 1549
[2,2,2] => [2,2,2] => 4065
[2,2,1,1] => [4,2] => 879
[2,1,1,1,1] => [5,1] => 407
[1,1,1,1,1,1] => [6] => 112
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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.
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.
Map
Loehr-Warrington inverse
Description
Return a partition whose length is the diagonal inversion number of the preimage.
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