Identifier
Values
=>
Cc0022;cc-rep-0 Cc0014;cc-rep
['A',1]=>([],1)=>2 ['A',2]=>([(0,2),(1,2)],3)=>5 ['B',2]=>([(0,3),(1,3),(3,2)],4)=>6 ['G',2]=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>8 ['A',3]=>([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)=>14 ['B',3]=>([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)=>20 ['C',3]=>([(0,7),(1,8),(2,7),(2,8),(4,5),(5,3),(6,5),(7,6),(8,4),(8,6)],9)=>20
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Description
The number of antichains in a poset.
An antichain in a poset $P$ is a subset of elements of $P$ which are pairwise incomparable.
An order ideal is a subset $I$ of $P$ such that $a\in I$ and $b \leq_P a$ implies $b \in I$. Since there is a one-to-one correspondence between antichains and order ideals, this statistic is also the number of order ideals in 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.