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Identifier

St000680: Posets ⟶ ℤ

Values

([],2) => 0

([(0,1)],2) => 2

([],3) => 1

([(1,2)],3) => 3

([(0,1),(0,2)],3) => 1

([(0,2),(2,1)],3) => 3

([(0,2),(1,2)],3) => 2

([],4) => 0

([(2,3)],4) => 2

([(1,2),(1,3)],4) => 0

([(0,1),(0,2),(0,3)],4) => 2

([(0,2),(0,3),(3,1)],4) => 4

([(0,1),(0,2),(1,3),(2,3)],4) => 3

([(1,2),(2,3)],4) => 2

([(0,3),(3,1),(3,2)],4) => 2

([(1,3),(2,3)],4) => 3

([(0,3),(1,3),(3,2)],4) => 3

([(0,3),(1,3),(2,3)],4) => 2

([(0,3),(1,2)],4) => 0

([(0,3),(1,2),(1,3)],4) => 0

([(0,2),(0,3),(1,2),(1,3)],4) => 0

([(0,3),(2,1),(3,2)],4) => 4

([(0,3),(1,2),(2,3)],4) => 4

([],5) => 1

([(3,4)],5) => 3

([(2,3),(2,4)],5) => 1

([(1,2),(1,3),(1,4)],5) => 3

([(0,1),(0,2),(0,3),(0,4)],5) => 1

([(0,2),(0,3),(0,4),(4,1)],5) => 3

([(0,1),(0,2),(0,3),(2,4),(3,4)],5) => 4

([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 3

([(1,3),(1,4),(4,2)],5) => 5

([(0,3),(0,4),(4,1),(4,2)],5) => 1

([(1,2),(1,3),(2,4),(3,4)],5) => 2

([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 4

([(0,3),(0,4),(3,2),(4,1)],5) => 1

([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => 1

([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) => 1

([(2,3),(3,4)],5) => 3

([(1,4),(4,2),(4,3)],5) => 3

([(0,4),(4,1),(4,2),(4,3)],5) => 3

([(2,4),(3,4)],5) => 2

([(1,4),(2,4),(4,3)],5) => 2

([(0,4),(1,4),(4,2),(4,3)],5) => 2

([(1,4),(2,4),(3,4)],5) => 3

([(0,4),(1,4),(2,4),(4,3)],5) => 3

([(0,4),(1,4),(2,4),(3,4)],5) => 2

([(0,4),(1,4),(2,3)],5) => 0

([(0,4),(1,3),(2,3),(2,4)],5) => 1

([(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 1

([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 1

([(0,4),(1,4),(2,3),(4,2)],5) => 4

([(0,4),(1,3),(2,3),(3,4)],5) => 4

([(0,4),(1,4),(2,3),(2,4)],5) => 1

([(0,4),(1,4),(2,3),(3,4)],5) => 4

([(1,4),(2,3)],5) => 1

([(1,4),(2,3),(2,4)],5) => 1

([(0,4),(1,2),(1,4),(2,3)],5) => 4

([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => 4

([(1,3),(1,4),(2,3),(2,4)],5) => 1

([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => 4

([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) => 3

([(0,4),(1,2),(1,4),(4,3)],5) => 4

([(0,4),(1,2),(1,3)],5) => 3

([(0,4),(1,2),(1,3),(1,4)],5) => 2

([(0,2),(0,4),(3,1),(4,3)],5) => 3

([(0,4),(1,2),(1,3),(3,4)],5) => 2

([(0,2),(0,3),(1,4),(2,4),(3,1)],5) => 5

([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 2

([(0,3),(0,4),(1,2),(1,4)],5) => 1

([(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 3

([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) => 2

([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => 3

([(0,3),(1,2),(1,4),(3,4)],5) => 1

([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => 3

([(1,4),(3,2),(4,3)],5) => 5

([(0,3),(3,4),(4,1),(4,2)],5) => 3

([(1,4),(2,3),(3,4)],5) => 5

([(0,4),(1,2),(2,4),(4,3)],5) => 5

([(0,3),(1,4),(4,2)],5) => 1

([(0,4),(3,2),(4,1),(4,3)],5) => 5

([(0,4),(1,2),(2,3),(2,4)],5) => 5

([(0,4),(2,3),(3,1),(4,2)],5) => 5

([(0,3),(1,2),(2,4),(3,4)],5) => 1

([(0,4),(1,2),(2,3),(3,4)],5) => 4

([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 4

([],6) => 0

([(4,5)],6) => 2

([(3,4),(3,5)],6) => 0

([(2,3),(2,4),(2,5)],6) => 2

([(1,2),(1,3),(1,4),(1,5)],6) => 0

([(0,1),(0,2),(0,3),(0,4),(0,5)],6) => 2

([(0,2),(0,3),(0,4),(0,5),(5,1)],6) => 4

([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6) => 3

([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6) => 4

([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6) => 3

([(1,3),(1,4),(1,5),(5,2)],6) => 2

([(0,3),(0,4),(0,5),(5,1),(5,2)],6) => 2

([(1,2),(1,3),(1,4),(3,5),(4,5)],6) => 5

([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) => 2

([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],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.

References

[1] wikipedia:Chomp

Code

@cached_function
def statistic(P):
    """Return the Grundy value of the poset for Chomp.
    """
    def children(Q):
        for q in Q:
            F = Q.order_filter([q])
            yield Q.subposet([e for e in Q if e not in F])

    P = Poset(P)
    l = [statistic(Q) for Q in children(P)]
    i = 0
    while i in l:
        i += 1
    return i

Created

Jan 05, 2017 at 21:22 by Martin Rubey

Updated

Jan 05, 2017 at 22:00 by Martin Rubey