Identifier
-
Mp00253:
Decorated permutations
—permutation⟶
Permutations
Mp00209: Permutations —pattern poset⟶ Posets
St000680: Posets ⟶ ℤ
Values
[+,+] => [1,2] => ([(0,1)],2) => 2
[-,+] => [1,2] => ([(0,1)],2) => 2
[+,-] => [1,2] => ([(0,1)],2) => 2
[-,-] => [1,2] => ([(0,1)],2) => 2
[2,1] => [2,1] => ([(0,1)],2) => 2
[+,+,+] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[-,+,+] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[+,-,+] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[+,+,-] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[-,-,+] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[-,+,-] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[+,-,-] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[-,-,-] => [1,2,3] => ([(0,2),(2,1)],3) => 3
[+,3,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
[-,3,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
[2,1,+] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
[2,1,-] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
[2,3,1] => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
[3,1,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 3
[3,+,1] => [3,2,1] => ([(0,2),(2,1)],3) => 3
[3,-,1] => [3,2,1] => ([(0,2),(2,1)],3) => 3
[+,+,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[-,+,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[+,-,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[+,+,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[+,+,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[-,-,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[-,+,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[-,+,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[+,-,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[+,-,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[+,+,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[-,-,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[-,-,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[-,+,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[+,-,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[-,-,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 4
[+,+,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[-,+,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[+,-,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[-,-,4,3] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[+,3,2,+] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[-,3,2,+] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[+,3,2,-] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[-,3,2,-] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[+,3,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[-,3,4,2] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[+,4,2,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[-,4,2,3] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[+,4,+,2] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[-,4,+,2] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[+,4,-,2] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[-,4,-,2] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[2,1,+,+] => [2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[2,1,-,+] => [2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[2,1,+,-] => [2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[2,1,-,-] => [2,1,3,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[2,1,4,3] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 4
[2,3,1,+] => [2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[2,3,1,-] => [2,3,1,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[2,3,4,1] => [2,3,4,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[2,4,+,1] => [2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[2,4,-,1] => [2,4,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[3,1,2,+] => [3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[3,1,2,-] => [3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[3,+,1,+] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[3,-,1,+] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[3,+,1,-] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[3,-,1,-] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[3,+,4,1] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[3,-,4,1] => [3,2,4,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[3,4,1,2] => [3,4,1,2] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 4
[3,4,2,1] => [3,4,2,1] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[4,1,2,3] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[4,1,+,2] => [4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[4,1,-,2] => [4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[4,+,1,3] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[4,-,1,3] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[4,+,+,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[4,-,+,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[4,+,-,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[4,-,-,1] => [4,2,3,1] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 5
[4,3,1,2] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 5
[4,3,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 4
[+,+,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,-,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,+,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,-,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[+,+,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
[-,-,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 5
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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.
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
permutation
Description
The underlying permutation of the decorated permutation.
Map
pattern poset
Description
The pattern poset of a permutation.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.
This is the poset of all non-empty permutations that occur in the given permutation as a pattern, ordered by pattern containment.
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