Identifier
Values
[1,2] => [1,2] => ([(0,1)],2) => 1
[2,1] => [2,1] => ([(0,1)],2) => 1
[1,2,3] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[1,3,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[2,1,3] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[2,3,1] => [3,2,1] => ([(0,2),(2,1)],3) => 1
[3,1,2] => [3,2,1] => ([(0,2),(2,1)],3) => 1
[3,2,1] => [3,2,1] => ([(0,2),(2,1)],3) => 1
[1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[2,4,3,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 1
[3,4,1,2] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 1
[3,4,2,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 1
[4,2,1,3] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 1
[4,2,3,1] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 1
[4,3,1,2] => [4,3,2,1] => ([(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] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,4,5,3,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,5,3,4,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,5,4,3,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,4,5,1,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,4,5,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,5,1,4,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,5,2,4,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,5,4,1,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,5,4,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,2,5,1,3] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,2,5,3,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,3,5,1,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,3,5,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,5,1,2,3] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,5,1,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,5,2,1,3] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,5,2,3,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,5,3,1,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,5,3,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,2,3,1,4] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,2,3,4,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,2,4,1,3] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,2,4,3,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,3,1,2,4] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,3,1,4,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,3,2,1,4] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,3,2,4,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,3,4,1,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,3,4,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,4,1,2,3] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,4,1,3,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,4,2,1,3] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,4,2,3,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,4,3,1,2] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,4,3,2,1] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
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 $\mu(x, y)$ 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
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.