Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000680
Mapping
St000680: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
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
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.