Identifier
Values
[1,2] => [1,2] => [1,2] => [2,1] => 0
[2,1] => [2,1] => [1,2] => [2,1] => 0
[1,2,3] => [1,2,3] => [1,2,3] => [3,2,1] => 0
[1,3,2] => [3,1,2] => [1,2,3] => [3,2,1] => 0
[2,1,3] => [2,1,3] => [1,3,2] => [2,3,1] => 1
[2,3,1] => [2,3,1] => [1,2,3] => [3,2,1] => 0
[3,1,2] => [1,3,2] => [1,3,2] => [2,3,1] => 1
[3,2,1] => [3,2,1] => [1,2,3] => [3,2,1] => 0
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [4,3,2,1] => 0
[1,2,4,3] => [4,1,2,3] => [1,2,3,4] => [4,3,2,1] => 0
[1,3,2,4] => [3,1,2,4] => [1,2,4,3] => [3,4,2,1] => 1
[1,3,4,2] => [3,4,1,2] => [1,2,3,4] => [4,3,2,1] => 0
[1,4,2,3] => [1,4,2,3] => [1,4,2,3] => [3,2,4,1] => 1
[1,4,3,2] => [4,3,1,2] => [1,2,3,4] => [4,3,2,1] => 0
[2,1,3,4] => [2,1,3,4] => [1,3,4,2] => [2,4,3,1] => 1
[2,1,4,3] => [2,4,1,3] => [1,3,2,4] => [4,2,3,1] => 1
[2,3,1,4] => [2,3,1,4] => [1,4,2,3] => [3,2,4,1] => 1
[2,3,4,1] => [2,3,4,1] => [1,2,3,4] => [4,3,2,1] => 0
[2,4,1,3] => [4,2,1,3] => [1,3,2,4] => [4,2,3,1] => 1
[2,4,3,1] => [4,2,3,1] => [1,2,3,4] => [4,3,2,1] => 0
[3,1,2,4] => [1,3,2,4] => [1,3,2,4] => [4,2,3,1] => 1
[3,1,4,2] => [1,3,4,2] => [1,3,4,2] => [2,4,3,1] => 1
[3,2,1,4] => [3,2,1,4] => [1,4,2,3] => [3,2,4,1] => 1
[3,2,4,1] => [3,2,4,1] => [1,2,4,3] => [3,4,2,1] => 1
[3,4,1,2] => [3,1,4,2] => [1,4,2,3] => [3,2,4,1] => 1
[3,4,2,1] => [3,4,2,1] => [1,2,3,4] => [4,3,2,1] => 0
[4,1,2,3] => [1,2,4,3] => [1,2,4,3] => [3,4,2,1] => 1
[4,1,3,2] => [4,1,3,2] => [1,3,2,4] => [4,2,3,1] => 1
[4,2,1,3] => [2,1,4,3] => [1,4,2,3] => [3,2,4,1] => 1
[4,2,3,1] => [2,4,3,1] => [1,2,4,3] => [3,4,2,1] => 1
[4,3,1,2] => [1,4,3,2] => [1,4,2,3] => [3,2,4,1] => 1
[4,3,2,1] => [4,3,2,1] => [1,2,3,4] => [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
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
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.