Identifier
Values
[1] => [1] => [1] => ([],1) => 1
[1,2] => [2,1] => [1,2] => ([(0,1)],2) => 1
[2,1] => [1,2] => [1,2] => ([(0,1)],2) => 1
[1,2,3] => [2,3,1] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[1,3,2] => [3,2,1] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[2,1,3] => [1,3,2] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[2,3,1] => [1,2,3] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[3,1,2] => [3,1,2] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 1
[3,2,1] => [2,1,3] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[1,2,3,4] => [2,3,4,1] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[2,1,3,4] => [1,3,4,2] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[2,3,1,4] => [1,2,4,3] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[2,3,4,1] => [1,2,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[2,4,3,1] => [1,3,2,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[3,2,1,4] => [2,1,4,3] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[3,2,4,1] => [2,1,3,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[4,2,3,1] => [2,3,1,4] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => 1
[1,2,3,4,5] => [2,3,4,5,1] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,1,3,4,5] => [1,3,4,5,2] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,3,1,4,5] => [1,2,4,5,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,3,4,1,5] => [1,2,3,5,4] => [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] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,3,5,4,1] => [1,2,4,3,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,4,3,1,5] => [1,3,2,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,4,3,5,1] => [1,3,2,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[2,5,3,4,1] => [1,3,4,2,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,2,1,4,5] => [2,1,4,5,3] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,2,4,1,5] => [2,1,3,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,2,4,5,1] => [2,1,3,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[3,2,5,4,1] => [2,1,4,3,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,2,3,1,5] => [2,3,1,5,4] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[4,2,3,5,1] => [2,3,1,4,5] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,2,3,4,1] => [2,3,4,1,5] => [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 number of connected components of the Hasse diagram for the poset.
Map
Inverse Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.
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
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.