Identifier
Values
[1] => [1] => ([],1) => 1
[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 number of connected components of the Hasse diagram for 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 $\pi = \pi^{-1}$.