Identifier
Values
{{1,2}} => [2,1] => [1,2] => [1,2] => 1
{{1},{2}} => [1,2] => [2,1] => [2,1] => 0
{{1,2,3}} => [2,3,1] => [1,3,2] => [1,3,2] => 1
{{1,2},{3}} => [2,1,3] => [3,1,2] => [3,1,2] => 1
{{1,3},{2}} => [3,2,1] => [1,2,3] => [1,3,2] => 1
{{1},{2,3}} => [1,3,2] => [2,3,1] => [2,3,1] => 1
{{1},{2},{3}} => [1,2,3] => [3,2,1] => [3,2,1] => 0
{{1,2,3,4}} => [2,3,4,1] => [1,4,3,2] => [1,4,3,2] => 1
{{1,2,3},{4}} => [2,3,1,4] => [4,1,3,2] => [4,1,3,2] => 1
{{1,2,4},{3}} => [2,4,3,1] => [1,3,4,2] => [1,4,3,2] => 1
{{1,2},{3,4}} => [2,1,4,3] => [3,4,1,2] => [3,4,1,2] => 2
{{1,2},{3},{4}} => [2,1,3,4] => [4,3,1,2] => [4,3,1,2] => 1
{{1,3,4},{2}} => [3,2,4,1] => [1,4,2,3] => [1,4,3,2] => 1
{{1,3},{2,4}} => [3,4,1,2] => [2,1,4,3] => [2,1,4,3] => 1
{{1,3},{2},{4}} => [3,2,1,4] => [4,1,2,3] => [4,1,3,2] => 1
{{1,4},{2,3}} => [4,3,2,1] => [1,2,3,4] => [1,4,3,2] => 1
{{1},{2,3,4}} => [1,3,4,2] => [2,4,3,1] => [2,4,3,1] => 1
{{1},{2,3},{4}} => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 1
{{1,4},{2},{3}} => [4,2,3,1] => [1,3,2,4] => [1,4,3,2] => 1
{{1},{2,4},{3}} => [1,4,3,2] => [2,3,4,1] => [2,4,3,1] => 1
{{1},{2},{3,4}} => [1,2,4,3] => [3,4,2,1] => [3,4,2,1] => 1
{{1},{2},{3},{4}} => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
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
click to show known generating functions       
Description
The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
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].