Identifier
Values
['A',2] => ([(0,2),(1,2)],3) => 2
['B',2] => ([(0,3),(1,3),(3,2)],4) => 3
['G',2] => ([(0,5),(1,5),(3,2),(4,3),(5,4)],6) => 5
['A',3] => ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6) => 4
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Description
The Grundy value for Hackendot on posets.
Two players take turns and remove an order filter. The player who is faced with the one element poset looses. This game is a slight variation of Chomp.
This statistic is the Grundy value of the poset, that is, the smallest non-negative integer which does not occur as value of a poset obtained by a single move.
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.