Identifier
-
Mp00148:
Finite Cartan types
—to root poset⟶
Posets
St000307: Posets ⟶ ℤ
Values
['A',1] => ([],1) => 1
['A',2] => ([(0,2),(1,2)],3) => 2
['B',2] => ([(0,3),(1,3),(3,2)],4) => 2
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 2
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 3
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Description
The number of rowmotion orbits of a poset.
Rowmotion is an operation on order ideals in a poset $P$. It sends an order ideal $I$ to the order ideal generated by the minimal antichain of $P \setminus I$.
Rowmotion is an operation on order ideals in a poset $P$. It sends an order ideal $I$ to the order ideal generated by the minimal antichain of $P \setminus I$.
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.
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