Processing math: 100%

Identifier
Values
[1,2] => [1,2] => [2,1] => ([(0,1)],2) => 1
[2,1] => [2,1] => [1,2] => ([(0,1)],2) => 1
[1,2,3] => [1,3,2] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,3,2] => [1,3,2] => [2,1,3] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[2,1,3] => [2,1,3] => [3,2,1] => ([(0,2),(2,1)],3) => 1
[2,3,1] => [2,3,1] => [1,2,3] => ([(0,2),(2,1)],3) => 1
[3,1,2] => [3,1,2] => [3,1,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[3,2,1] => [3,2,1] => [1,3,2] => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[1,2,3,4] => [1,4,3,2] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 4
[1,2,4,3] => [1,4,3,2] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 4
[1,3,2,4] => [1,4,3,2] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 4
[1,3,4,2] => [1,4,3,2] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 4
[1,4,2,3] => [1,4,3,2] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 4
[1,4,3,2] => [1,4,3,2] => [2,1,4,3] => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 4
[2,1,3,4] => [2,1,4,3] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
[2,1,4,3] => [2,1,4,3] => [3,2,1,4] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
[2,3,1,4] => [2,4,1,3] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 2
[2,3,4,1] => [2,4,3,1] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
[2,4,1,3] => [2,4,1,3] => [4,2,1,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 2
[2,4,3,1] => [2,4,3,1] => [1,2,4,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
[3,1,2,4] => [3,1,4,2] => [3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 2
[3,1,4,2] => [3,1,4,2] => [3,1,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 2
[3,2,1,4] => [3,2,1,4] => [4,3,2,1] => ([(0,3),(2,1),(3,2)],4) => 1
[3,2,4,1] => [3,2,4,1] => [1,3,2,4] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 2
[3,4,1,2] => [3,4,1,2] => [4,1,2,3] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
[3,4,2,1] => [3,4,2,1] => [1,4,2,3] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 2
[4,2,1,3] => [4,2,1,3] => [4,3,1,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
[4,2,3,1] => [4,2,3,1] => [1,3,4,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 2
[4,3,1,2] => [4,3,1,2] => [4,1,3,2] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) => 2
[4,3,2,1] => [4,3,2,1] => [1,4,3,2] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1
[4,3,2,1,5] => [4,3,2,1,5] => [5,4,3,2,1] => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[5,4,3,2,1,6] => [5,4,3,2,1,6] => [6,5,4,3,2,1] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 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 size of the automorphism group of a poset.
A poset automorphism is a permutation of the elements of the poset preserving the order relation.
Map
Simion-Schmidt map
Description
The Simion-Schmidt map sends any permutation to a 123-avoiding permutation.
Details can be found in [1].
In particular, this is a bijection between 132-avoiding permutations and 123-avoiding permutations, see [1, Proposition 19].
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
Kreweras complement
Description
Sends the permutation π∈Sn to the permutation π−1c where c=(1,…,n) is the long cycle.