Identifier
Values
=>
Cc0022;cc-rep-0 Cc0014;cc-rep-1 Cc0002;cc-rep
['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]=>6 ['G',2]=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>[6,2]=>10
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Description
The leading coefficient of the rook polynomial of an integer partition.
Let $m$ be the minimum of the number of parts and the size of the first part of an integer partition $\lambda$. Then this statistic yields the number of ways to place $m$ non-attacking rooks on the Ferrers board of $\lambda$.
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.
Map
rowmotion cycle type
Description
The cycle type of rowmotion on the order ideals of a poset.