Identifier
Values
[[1]] => [1] => 0
[[1,2]] => [1,2] => 0
[[1],[2]] => [2,1] => 1
[[1,2,3]] => [1,2,3] => 0
[[1,3],[2]] => [2,1,3] => 1
[[1,2],[3]] => [3,1,2] => 1
[[1],[2],[3]] => [3,2,1] => 2
[[1,2,3,4]] => [1,2,3,4] => 0
[[1,3,4],[2]] => [2,1,3,4] => 1
[[1,2,4],[3]] => [3,1,2,4] => 1
[[1,2,3],[4]] => [4,1,2,3] => 1
[[1,3],[2,4]] => [2,4,1,3] => 2
[[1,2],[3,4]] => [3,4,1,2] => 1
[[1,4],[2],[3]] => [3,2,1,4] => 2
[[1,3],[2],[4]] => [4,2,1,3] => 2
[[1,2],[3],[4]] => [4,3,1,2] => 2
[[1],[2],[3],[4]] => [4,3,2,1] => 3
[[1,2,3,4,5]] => [1,2,3,4,5] => 0
[[1,3,4,5],[2]] => [2,1,3,4,5] => 1
[[1,2,4,5],[3]] => [3,1,2,4,5] => 1
[[1,2,3,5],[4]] => [4,1,2,3,5] => 1
[[1,2,3,4],[5]] => [5,1,2,3,4] => 1
[[1,3,5],[2,4]] => [2,4,1,3,5] => 2
[[1,2,5],[3,4]] => [3,4,1,2,5] => 1
[[1,3,4],[2,5]] => [2,5,1,3,4] => 2
[[1,2,4],[3,5]] => [3,5,1,2,4] => 2
[[1,2,3],[4,5]] => [4,5,1,2,3] => 1
[[1,4,5],[2],[3]] => [3,2,1,4,5] => 2
[[1,3,5],[2],[4]] => [4,2,1,3,5] => 2
[[1,2,5],[3],[4]] => [4,3,1,2,5] => 2
[[1,3,4],[2],[5]] => [5,2,1,3,4] => 2
[[1,2,4],[3],[5]] => [5,3,1,2,4] => 2
[[1,2,3],[4],[5]] => [5,4,1,2,3] => 2
[[1,4],[2,5],[3]] => [3,2,5,1,4] => 3
[[1,3],[2,5],[4]] => [4,2,5,1,3] => 2
[[1,2],[3,5],[4]] => [4,3,5,1,2] => 2
[[1,3],[2,4],[5]] => [5,2,4,1,3] => 3
[[1,2],[3,4],[5]] => [5,3,4,1,2] => 2
[[1,5],[2],[3],[4]] => [4,3,2,1,5] => 3
[[1,4],[2],[3],[5]] => [5,3,2,1,4] => 3
[[1,3],[2],[4],[5]] => [5,4,2,1,3] => 3
[[1,2],[3],[4],[5]] => [5,4,3,1,2] => 3
[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 4
[[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 0
[[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => 1
[[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => 1
[[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => 1
[[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => 1
[[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 1
[[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => 2
[[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => 1
[[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => 2
[[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => 2
[[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => 1
[[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => 2
[[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => 2
[[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => 2
[[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 1
[[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => 2
[[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => 2
[[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => 2
[[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => 2
[[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => 2
[[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => 2
[[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => 2
[[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => 2
[[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => 2
[[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 2
[[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => 3
[[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => 2
[[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => 2
[[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => 2
[[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 1
[[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => 3
[[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => 2
[[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => 2
[[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => 3
[[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => 2
[[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => 3
[[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => 3
[[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => 3
[[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => 2
[[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => 2
[[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => 2
[[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => 3
[[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => 2
[[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => 3
[[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => 3
[[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 2
[[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => 3
[[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => 3
[[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => 3
[[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => 3
[[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => 3
[[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => 3
[[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => 3
[[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => 3
[[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => 3
[[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 3
[[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => 4
[[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => 3
>>> Load all 120 entries. <<<
[[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => 3
[[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => 3
[[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 2
[[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => 4
[[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => 3
[[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => 3
[[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => 3
[[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => 4
[[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => 3
[[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => 3
[[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => 4
[[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 3
[[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => 4
[[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => 4
[[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => 4
[[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => 4
[[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 4
[[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 5
[[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => 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 maximum of the number of descents and the number of inverse descents.
This is, the maximum of St000021The number of descents of a permutation. and St000354The number of recoils of a permutation..
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.