Identifier
Values
['A',1] => ([],1) => [2] => 0
['A',2] => ([(0,2),(1,2)],3) => [3,2] => 1
['B',2] => ([(0,3),(1,3),(3,2)],4) => [4,2] => 3
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => [6,2] => 15
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Description
Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight.
Given $\lambda$ count how many integer compositions $w$ (weight) there are, such that
$P_{\lambda,w}$ is non-integral, i.e., $w$ such that the Gelfand-Tsetlin polytope $P_{\lambda,w}$ has at least one non-integral vertex.
See also St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight..
Each value in this statistic is greater than or equal to corresponding value in St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight..
Map
rowmotion cycle type
Description
The cycle type of rowmotion on the order ideals of 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.