Identifier
Values
[1,2] => [1,2] => ([(0,1)],2) => 1
[2,1] => [1,2] => ([(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] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[2,3,1] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[3,1,2] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[3,2,1] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[3,4,1,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[3,4,2,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[4,1,2,3] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[4,2,3,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[4,3,1,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[4,3,2,1] => [1,2,3,4] => ([(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
[2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,4,5,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,4,5,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,5,1,2,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,5,2,3,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,5,3,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,5,3,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,1,2,3,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,2,3,4,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,3,4,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,3,4,2,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,4,1,2,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,4,2,3,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,4,3,1,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,4,3,2,1] => [1,2,3,4,5] => ([(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
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
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.