Identifier
Values
[1] => [1] => 1
[2] => [2] => 1
[1,1] => [1,1] => 0
[3] => [2,1] => 1
[2,1] => [3] => 2
[1,1,1] => [1,1,1] => 0
[4] => [2,2] => 5
[3,1] => [2,1,1] => 2
[2,2] => [4] => 6
[2,1,1] => [3,1] => 5
[1,1,1,1] => [1,1,1,1] => 1
[5] => [2,2,1] => 28
[4,1] => [3,2] => 40
[3,2] => [4,1] => 37
[3,1,1] => [2,1,1,1] => 13
[2,2,1] => [5] => 21
[2,1,1,1] => [3,1,1] => 27
[1,1,1,1,1] => [1,1,1,1,1] => 5
[6] => [2,2,2] => 198
[5,1] => [2,2,1,1] => 242
[4,2] => [4,2] => 472
[4,1,1] => [4,1,1] => 375
[3,3] => [3,2,1] => 583
[3,2,1] => [3,3] => 208
[3,1,1,1] => [2,1,1,1,1] => 128
[2,2,2] => [6] => 112
[2,2,1,1] => [5,1] => 295
[2,1,1,1,1] => [3,1,1,1] => 292
[1,1,1,1,1,1] => [1,1,1,1,1,1] => 23
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Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on simple connected graphs.
Map
2-conjugate
Description
Return a partition with the same number of odd parts and number of even parts interchanged with the number of cells with zero leg and odd arm length.
This is a special case of an involution that preserves the sequence of non-zero remainders of the parts under division by $s$ and interchanges the number of parts divisible by $s$ and the number of cells with zero leg length and arm length congruent to $s-1$ modulo $s$.
In particular, for $s=1$ the involution is conjugation, hence the name.