Identifier
Values
['A',1] => ([],1) => 0
['A',2] => ([(0,2),(1,2)],3) => 0
['B',2] => ([(0,3),(1,3),(3,2)],4) => 0
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 0
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 0
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Description
The first Betti number of the order complex associated with the poset.
The order complex of a poset is the simplicial complex whose faces are the chains of the poset. This statistic is the rank of the first homology group of the order complex.
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.