Identifier
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
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
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.
Map
Loehr-Warrington inverse
Description
Return a partition whose length is the diagonal inversion number of the preimage.