Identifier
Values
['A',1] => ([],1) => ([],1) => 1
['A',2] => ([(0,2),(1,2)],3) => ([(0,2),(1,2)],3) => 2
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(0,3),(1,3),(2,3)],4) => 3
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => 5
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 10
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Description
The order of toric promotion on the set of labellings of a graph.
In the context of toric promotion, a labelling of a graph $(V, E)$ with $n=|V|$ vertices is a bijection $\sigma: V \to [n]$. In particular, any graph has $n!$ labellings.
In the context of toric promotion, a labelling of a graph $(V, E)$ with $n=|V|$ vertices is a bijection $\sigma: V \to [n]$. In particular, any graph has $n!$ labellings.
Map
to graph
Description
Returns the Hasse diagram of the poset as an undirected graph.
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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