Identifier
Values
['A',1] => ([],1) => ([],1) => 1
['A',2] => ([(0,2),(1,2)],3) => ([(1,2)],3) => 0
['B',2] => ([(0,3),(1,3),(3,2)],4) => ([(2,3)],4) => 1
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => ([(4,5)],6) => 1
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) => 1
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Description
The Grundy value of the game of creating an independent set in a graph.
Two players alternately add a vertex to an initially empty set, which is not adjacent to any of the vertices it already contains.
Alternatively, the game can be described as starting with a graph, the players remove vertices together with their neighbors, until the graph is empty.
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.
Map
incomparability graph
Description
The incomparability graph of a poset.