Identifier
Values
['A',1] => ([],1) => [2] => 2
['A',2] => ([(0,2),(1,2)],3) => [3,2] => 4
['B',2] => ([(0,3),(1,3),(3,2)],4) => [4,2] => 7
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [6,2] => 15
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => [8,4,2] => 50
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Description
The number of ordered refinements of an integer partition.
This is, for an integer partition $\mu = (\mu_1,\ldots,\mu_n)$ the number of integer partition $\lambda = (\lambda_1,\ldots,\lambda_m)$ such that there are indices $1 = a_0 < \ldots < a_n = m$ with $\mu_j = \lambda_{a_{j-1}} + \ldots + \lambda_{a_j-1}$.
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.