Processing math: 100%

Identifier
Values
[+,+] => [1,2] => ([(0,1)],2) => 1
[-,+] => [1,2] => ([(0,1)],2) => 1
[+,-] => [1,2] => ([(0,1)],2) => 1
[-,-] => [1,2] => ([(0,1)],2) => 1
[2,1] => [2,1] => ([(0,1)],2) => 1
[+,+,+] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[-,+,+] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[+,-,+] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[+,+,-] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[-,-,+] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[-,+,-] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[+,-,-] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[-,-,-] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[+,3,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[-,3,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[2,1,+] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[2,1,-] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[2,3,1] => [2,3,1] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[3,1,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[3,+,1] => [3,2,1] => ([(0,2),(2,1)],3) => 1
[3,-,1] => [3,2,1] => ([(0,2),(2,1)],3) => 1
[+,+,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[-,+,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[+,-,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[+,+,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[+,+,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[-,-,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[-,+,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[-,+,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[+,-,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[+,-,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[+,+,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[-,-,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[-,-,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[-,+,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[+,-,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[-,-,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[4,3,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 1
[+,+,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,+,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,-,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,+,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,+,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,+,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,-,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,+,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,+,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,+,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,-,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,-,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,-,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,+,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,+,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,+,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,-,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,-,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,-,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,+,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,+,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,+,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,-,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,-,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,-,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,+,-,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,-,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,-,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,-,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,+,-,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[+,-,-,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[-,-,-,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,4,+,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,4,-,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
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Description
The maximum magnitude of the Möbius function of a poset.
The Möbius function of a poset is the multiplicative inverse of the zeta function in the incidence algebra. The Möbius value μ(x,y) is equal to the signed sum of chains from x to y, where odd-length chains are counted with a minus sign, so this statistic is bounded above by the total number of chains in the poset.
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.
Map
permutation
Description
The underlying permutation of the decorated permutation.