Identifier
Values
['A',1] => ([],1) => ([],1) => [1] => 1
['A',2] => ([(0,2),(1,2)],3) => ([(1,2)],3) => [2,1] => 3
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(2,3)],4) => [2,1,1] => 5
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(4,5)],6) => [2,1,1,1,1] => 9
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => [5,1] => 1
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Description
The number of permutations such that conjugation with a permutation of given cycle type yields the squared permutation.
Let $\alpha$ be any permutation of cycle type $\lambda$. This statistic is the number of permutations $\pi$ such that
$$ \alpha\pi\alpha^{-1} = \pi^2.$$
Map
incomparability graph
Description
The incomparability graph of a poset.
Map
to partition of connected components
Description
Return the partition of the sizes of the connected components of the graph.
Map
to root poset
Description
The root poset of a finite Cartan type.
This is the poset on the set of positive roots of its root system where $\alpha \prec \beta$ if $\beta - \alpha$ is a simple root.