Identifier
Values
['A',1] => ([],1) => [2] => 1
['A',2] => ([(0,2),(1,2)],3) => [3,2] => 6
['B',2] => ([(0,3),(1,3),(3,2)],4) => [4,2] => 8
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [6,2] => 12
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => [8,4,2] => 960
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 transitive factorisations of a permutation of given cycle type into star transpositions.
Let $\pi$ be a permutation of cycle type $\lambda\vdash n$ and let $r=n + \ell(\lambda) - 2$. A minimal factorization of $\pi$ into star transpositions is an $r$-tuple of transpositions $(1, a_1)\dots(1, a_r)$ whose product (in this order) equals $\pi$.
The number of such factorizations equals [1]
$$ \frac{r!}{n!} \lambda_1\dots\lambda_{\ell(\lambda)}. $$
Map
rowmotion cycle type
Description
The cycle type of rowmotion on the order ideals of a poset.
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.