Identifier
-
Mp00148:
Finite Cartan types
—to root poset⟶
Posets
Mp00306: Posets —rowmotion cycle type⟶ Integer partitions
St000531: Integer partitions ⟶ ℤ
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] => 6
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [6,2] => 10
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
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 $\lambda$.
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.
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.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!