Identifier
Values
[1] => [[1]] => [1] => 0
[2] => [[1,2]] => [1,2] => 0
[1,1] => [[1],[2]] => [2,1] => 2
[3] => [[1,2,3]] => [1,2,3] => 0
[2,1] => [[1,2],[3]] => [3,1,2] => 3
[1,1,1] => [[1],[2],[3]] => [3,2,1] => 6
[4] => [[1,2,3,4]] => [1,2,3,4] => 0
[3,1] => [[1,2,3],[4]] => [4,1,2,3] => 4
[2,2] => [[1,2],[3,4]] => [3,4,1,2] => 6
[2,1,1] => [[1,2],[3],[4]] => [4,3,1,2] => 8
[1,1,1,1] => [[1],[2],[3],[4]] => [4,3,2,1] => 12
[5] => [[1,2,3,4,5]] => [1,2,3,4,5] => 0
[4,1] => [[1,2,3,4],[5]] => [5,1,2,3,4] => 5
[3,2] => [[1,2,3],[4,5]] => [4,5,1,2,3] => 8
[3,1,1] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => 10
[2,2,1] => [[1,2],[3,4],[5]] => [5,3,4,1,2] => 12
[2,1,1,1] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => 15
[1,1,1,1,1] => [[1],[2],[3],[4],[5]] => [5,4,3,2,1] => 20
[6] => [[1,2,3,4,5,6]] => [1,2,3,4,5,6] => 0
[5,1] => [[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => 6
[4,2] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => 10
[4,1,1] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => 12
[3,3] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 12
[3,2,1] => [[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => 15
[3,1,1,1] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => 18
[2,2,2] => [[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => 18
[2,2,1,1] => [[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => 20
[2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => 24
[1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => 30
[7] => [[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => 0
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Description
The number of inversions plus the major index of a permutation.
This is, the sum of St000004The major index of a permutation. and St000018The number of inversions 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.
Map
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers $1$ through $n$ row by row.