Identifier
Values
[[1]] => [1] => [1] => [1] => 0
[[1,2]] => [1,2] => [2,1] => [2,1] => 1
[[1],[2]] => [2,1] => [1,2] => [1,2] => 0
[[1,2,3]] => [1,2,3] => [3,2,1] => [2,3,1] => 1
[[1,3],[2]] => [2,1,3] => [3,1,2] => [3,1,2] => 2
[[1,2],[3]] => [3,1,2] => [2,1,3] => [2,1,3] => 1
[[1],[2],[3]] => [3,2,1] => [1,2,3] => [1,2,3] => 0
[[1,2,3,4]] => [1,2,3,4] => [4,3,2,1] => [3,4,1,2] => 2
[[1,3,4],[2]] => [2,1,3,4] => [4,3,1,2] => [3,4,2,1] => 1
[[1,2,4],[3]] => [3,1,2,4] => [4,2,1,3] => [2,4,1,3] => 2
[[1,2,3],[4]] => [4,1,2,3] => [3,2,1,4] => [2,3,1,4] => 1
[[1,3],[2,4]] => [2,4,1,3] => [3,1,4,2] => [4,1,3,2] => 2
[[1,2],[3,4]] => [3,4,1,2] => [2,1,4,3] => [2,1,4,3] => 2
[[1,4],[2],[3]] => [3,2,1,4] => [4,1,2,3] => [4,1,2,3] => 3
[[1,3],[2],[4]] => [4,2,1,3] => [3,1,2,4] => [3,1,2,4] => 2
[[1,2],[3],[4]] => [4,3,1,2] => [2,1,3,4] => [2,1,3,4] => 1
[[1],[2],[3],[4]] => [4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 0
[[1,2,3,4,5]] => [1,2,3,4,5] => [5,4,3,2,1] => [3,4,5,1,2] => 2
[[1,3,4,5],[2]] => [2,1,3,4,5] => [5,4,3,1,2] => [3,4,5,2,1] => 1
[[1,2,4,5],[3]] => [3,1,2,4,5] => [5,4,2,1,3] => [4,5,1,3,2] => 2
[[1,2,3,5],[4]] => [4,1,2,3,5] => [5,3,2,1,4] => [3,5,1,2,4] => 3
[[1,2,3,4],[5]] => [5,1,2,3,4] => [4,3,2,1,5] => [3,4,1,2,5] => 2
[[1,3,5],[2,4]] => [2,4,1,3,5] => [5,3,1,4,2] => [3,4,2,5,1] => 1
[[1,2,5],[3,4]] => [3,4,1,2,5] => [5,2,1,4,3] => [2,4,1,5,3] => 2
[[1,3,4],[2,5]] => [2,5,1,3,4] => [4,3,1,5,2] => [3,5,2,4,1] => 1
[[1,2,4],[3,5]] => [3,5,1,2,4] => [4,2,1,5,3] => [2,5,1,4,3] => 2
[[1,2,3],[4,5]] => [4,5,1,2,3] => [3,2,1,5,4] => [2,3,1,5,4] => 2
[[1,4,5],[2],[3]] => [3,2,1,4,5] => [5,4,1,2,3] => [4,5,2,3,1] => 1
[[1,3,5],[2],[4]] => [4,2,1,3,5] => [5,3,1,2,4] => [3,5,2,1,4] => 2
[[1,2,5],[3],[4]] => [4,3,1,2,5] => [5,2,1,3,4] => [2,5,1,3,4] => 3
[[1,3,4],[2],[5]] => [5,2,1,3,4] => [4,3,1,2,5] => [3,4,2,1,5] => 1
[[1,2,4],[3],[5]] => [5,3,1,2,4] => [4,2,1,3,5] => [2,4,1,3,5] => 2
[[1,2,3],[4],[5]] => [5,4,1,2,3] => [3,2,1,4,5] => [2,3,1,4,5] => 1
[[1,4],[2,5],[3]] => [3,2,5,1,4] => [4,1,5,2,3] => [5,1,4,3,2] => 2
[[1,3],[2,5],[4]] => [4,2,5,1,3] => [3,1,5,2,4] => [5,1,3,2,4] => 3
[[1,2],[3,5],[4]] => [4,3,5,1,2] => [2,1,5,3,4] => [2,1,5,3,4] => 3
[[1,3],[2,4],[5]] => [5,2,4,1,3] => [3,1,4,2,5] => [4,1,3,2,5] => 2
[[1,2],[3,4],[5]] => [5,3,4,1,2] => [2,1,4,3,5] => [2,1,4,3,5] => 2
[[1,5],[2],[3],[4]] => [4,3,2,1,5] => [5,1,2,3,4] => [5,1,2,3,4] => 4
[[1,4],[2],[3],[5]] => [5,3,2,1,4] => [4,1,2,3,5] => [4,1,2,3,5] => 3
[[1,3],[2],[4],[5]] => [5,4,2,1,3] => [3,1,2,4,5] => [3,1,2,4,5] => 2
[[1,2],[3],[4],[5]] => [5,4,3,1,2] => [2,1,3,4,5] => [2,1,3,4,5] => 1
[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => 3
[[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => [6,5,4,3,1,2] => [4,5,6,1,3,2] => 2
[[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => [6,5,4,2,1,3] => [4,5,6,2,3,1] => 1
[[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => [6,5,3,2,1,4] => [3,5,6,1,4,2] => 2
[[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => [6,4,3,2,1,5] => [3,4,6,1,2,5] => 3
[[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [5,4,3,2,1,6] => [3,4,5,1,2,6] => 2
[[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => [6,5,3,1,4,2] => [3,5,6,2,1,4] => 2
[[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => [6,5,2,1,4,3] => [5,6,1,3,2,4] => 3
[[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => [6,4,3,1,5,2] => [3,4,5,2,6,1] => 1
[[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => [6,4,2,1,5,3] => [4,5,1,3,6,2] => 2
[[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => [6,3,2,1,5,4] => [3,5,1,2,6,4] => 3
[[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => [5,4,3,1,6,2] => [3,4,6,2,5,1] => 1
[[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => [5,4,2,1,6,3] => [4,6,1,3,5,2] => 2
[[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => [5,3,2,1,6,4] => [3,6,1,2,5,4] => 3
[[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [4,3,2,1,6,5] => [3,4,1,2,6,5] => 3
[[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => [6,5,4,1,2,3] => [4,5,6,3,2,1] => 1
[[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => [6,5,3,1,2,4] => [3,5,6,2,4,1] => 1
[[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => [6,5,2,1,3,4] => [5,6,1,3,4,2] => 2
[[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => [6,4,3,1,2,5] => [3,4,6,2,1,5] => 2
[[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => [6,4,2,1,3,5] => [4,6,1,3,2,5] => 3
[[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => [6,3,2,1,4,5] => [3,6,1,2,4,5] => 4
[[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => [5,4,3,1,2,6] => [3,4,5,2,1,6] => 1
[[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => [5,4,2,1,3,6] => [4,5,1,3,2,6] => 2
[[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => [5,3,2,1,4,6] => [3,5,1,2,4,6] => 3
[[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [4,3,2,1,5,6] => [3,4,1,2,5,6] => 2
[[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [5,3,1,6,4,2] => [3,6,2,5,1,4] => 2
[[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [5,2,1,6,4,3] => [2,6,1,5,3,4] => 3
[[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [4,3,1,6,5,2] => [3,5,2,4,6,1] => 1
[[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [4,2,1,6,5,3] => [2,5,1,4,6,3] => 2
[[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [2,3,1,5,6,4] => 2
[[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [6,4,1,5,2,3] => [4,6,2,5,3,1] => 1
[[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [6,3,1,5,2,4] => [3,5,2,6,4,1] => 1
[[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => [6,2,1,5,3,4] => [2,5,1,6,4,3] => 2
[[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => [6,3,1,4,2,5] => [3,4,2,6,1,5] => 2
[[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => [6,2,1,4,3,5] => [2,4,1,6,3,5] => 3
[[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [5,4,1,6,2,3] => [5,6,2,4,3,1] => 1
[[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => [5,3,1,6,2,4] => [3,6,2,5,4,1] => 1
[[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [5,2,1,6,3,4] => [2,6,1,5,4,3] => 2
[[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => [4,3,1,6,2,5] => [3,6,2,4,1,5] => 2
[[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => [4,2,1,6,3,5] => [2,6,1,4,3,5] => 3
[[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => [3,2,1,6,4,5] => [2,3,1,6,4,5] => 3
[[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => [5,3,1,4,2,6] => [3,4,2,5,1,6] => 1
[[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => [5,2,1,4,3,6] => [2,4,1,5,3,6] => 2
[[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => [4,3,1,5,2,6] => [3,5,2,4,1,6] => 1
[[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => [4,2,1,5,3,6] => [2,5,1,4,3,6] => 2
[[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => [3,2,1,5,4,6] => [2,3,1,5,4,6] => 2
[[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => [6,5,1,2,3,4] => [5,6,2,3,4,1] => 1
[[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => [6,4,1,2,3,5] => [4,6,2,3,1,5] => 2
[[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => [6,3,1,2,4,5] => [3,6,2,1,4,5] => 3
[[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => [6,2,1,3,4,5] => [2,6,1,3,4,5] => 4
[[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => [5,4,1,2,3,6] => [4,5,2,3,1,6] => 1
[[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => [5,3,1,2,4,6] => [3,5,2,1,4,6] => 2
[[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => [5,2,1,3,4,6] => [2,5,1,3,4,6] => 3
[[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => 1
[[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => [4,2,1,3,5,6] => [2,4,1,3,5,6] => 2
[[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => [3,2,1,4,5,6] => [2,3,1,4,5,6] => 1
[[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [4,1,5,2,6,3] => [6,1,4,3,5,2] => 2
[[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [3,1,5,2,6,4] => [6,1,3,2,5,4] => 3
>>> Load all 186 entries. <<<
[[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => [2,1,5,3,6,4] => [2,1,6,3,5,4] => 3
[[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => [3,1,4,2,6,5] => [4,1,3,2,6,5] => 3
[[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 3
[[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [5,1,6,2,3,4] => [6,1,5,3,4,2] => 2
[[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [4,1,6,2,3,5] => [6,1,4,3,2,5] => 3
[[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [3,1,6,2,4,5] => [6,1,3,2,4,5] => 4
[[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => [2,1,6,3,4,5] => [2,1,6,3,4,5] => 4
[[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [4,1,5,2,3,6] => [5,1,4,3,2,6] => 2
[[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => [3,1,5,2,4,6] => [5,1,3,2,4,6] => 3
[[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => [2,1,5,3,4,6] => [2,1,5,3,4,6] => 3
[[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => [3,1,4,2,5,6] => [4,1,3,2,5,6] => 2
[[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => [2,1,4,3,5,6] => [2,1,4,3,5,6] => 2
[[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => [6,1,2,3,4,5] => [6,1,2,3,4,5] => 5
[[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => [5,1,2,3,4,6] => [5,1,2,3,4,6] => 4
[[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => [4,1,2,3,5,6] => [4,1,2,3,5,6] => 3
[[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => [3,1,2,4,5,6] => [3,1,2,4,5,6] => 2
[[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 1
[[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => [6,5,4,3,2,1,7] => [4,5,6,1,2,3,7] => 3
[[1,4,5,6],[2],[3],[7]] => [7,3,2,1,4,5,6] => [6,5,4,1,2,3,7] => [4,5,6,3,2,1,7] => 1
[[1,2,3,6],[4],[5],[7]] => [7,5,4,1,2,3,6] => [6,3,2,1,4,5,7] => [3,6,1,2,4,5,7] => 4
[[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => [4,3,2,1,5,6,7] => [3,4,1,2,5,6,7] => 2
[[1,2,7],[3],[4],[5],[6]] => [6,5,4,3,1,2,7] => [7,2,1,3,4,5,6] => [2,7,1,3,4,5,6] => 5
[[1,2,6],[3],[4],[5],[7]] => [7,5,4,3,1,2,6] => [6,2,1,3,4,5,7] => [2,6,1,3,4,5,7] => 4
[[1,2,5],[3],[4],[6],[7]] => [7,6,4,3,1,2,5] => [5,2,1,3,4,6,7] => [2,5,1,3,4,6,7] => 3
[[1,2,4],[3],[5],[6],[7]] => [7,6,5,3,1,2,4] => [4,2,1,3,5,6,7] => [2,4,1,3,5,6,7] => 2
[[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => [3,2,1,4,5,6,7] => [2,3,1,4,5,6,7] => 1
[[1,2],[3,7],[4],[5],[6]] => [6,5,4,3,7,1,2] => [2,1,7,3,4,5,6] => [2,1,7,3,4,5,6] => 5
[[1,2],[3,6],[4],[5],[7]] => [7,5,4,3,6,1,2] => [2,1,6,3,4,5,7] => [2,1,6,3,4,5,7] => 4
[[1,7],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7] => [7,1,2,3,4,5,6] => [7,1,2,3,4,5,6] => 6
[[1,6],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6] => [6,1,2,3,4,5,7] => [6,1,2,3,4,5,7] => 5
[[1,5],[2],[3],[4],[6],[7]] => [7,6,4,3,2,1,5] => [5,1,2,3,4,6,7] => [5,1,2,3,4,6,7] => 4
[[1,4],[2],[3],[5],[6],[7]] => [7,6,5,3,2,1,4] => [4,1,2,3,5,6,7] => [4,1,2,3,5,6,7] => 3
[[1,3],[2],[4],[5],[6],[7]] => [7,6,5,4,2,1,3] => [3,1,2,4,5,6,7] => [3,1,2,4,5,6,7] => 2
[[1,2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 1
[[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[[1,2,3,4,5,6,7,8]] => [1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1] => [5,6,7,8,1,2,3,4] => 4
[[1,2,3,4,5,6,8],[7]] => [7,1,2,3,4,5,6,8] => [8,6,5,4,3,2,1,7] => [4,5,6,8,1,2,3,7] => 4
[[1,2,5,6,7,8],[3,4]] => [3,4,1,2,5,6,7,8] => [8,7,6,5,2,1,4,3] => [5,6,7,8,3,4,1,2] => 2
[[1,2,3,4,5,6],[7,8]] => [7,8,1,2,3,4,5,6] => [6,5,4,3,2,1,8,7] => [4,5,6,1,2,3,8,7] => 4
[[1,2,3,4,5,6],[7],[8]] => [8,7,1,2,3,4,5,6] => [6,5,4,3,2,1,7,8] => [4,5,6,1,2,3,7,8] => 3
[[1,2,6,7,8],[3,4],[5]] => [5,3,4,1,2,6,7,8] => [8,7,6,2,1,4,3,5] => [6,7,8,2,4,3,5,1] => 1
[[1,2,3,4],[5,6,7,8]] => [5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => [3,4,1,2,7,8,5,6] => 4
[[1,2,7,8],[3,4],[5,6]] => [5,6,3,4,1,2,7,8] => [8,7,2,1,4,3,6,5] => [7,8,1,3,2,5,4,6] => 4
[[1,2,3,4],[5,6],[7,8]] => [7,8,5,6,1,2,3,4] => [4,3,2,1,6,5,8,7] => [3,4,1,2,6,5,8,7] => 4
[[1,6,7,8],[2],[3],[4],[5]] => [5,4,3,2,1,6,7,8] => [8,7,6,1,2,3,4,5] => [6,7,8,3,4,5,2,1] => 1
[[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => [4,3,2,1,5,6,7,8] => [3,4,1,2,5,6,7,8] => 2
[[1,4,6],[2,8],[3],[5],[7]] => [7,5,3,2,8,1,4,6] => [6,4,1,8,2,3,5,7] => [6,8,2,4,3,5,1,7] => 2
[[1,2,8],[3],[4],[5],[6],[7]] => [7,6,5,4,3,1,2,8] => [8,2,1,3,4,5,6,7] => [2,8,1,3,4,5,6,7] => 6
[[1,2,7],[3],[4],[5],[6],[8]] => [8,6,5,4,3,1,2,7] => [7,2,1,3,4,5,6,8] => [2,7,1,3,4,5,6,8] => 5
[[1,2,6],[3],[4],[5],[7],[8]] => [8,7,5,4,3,1,2,6] => [6,2,1,3,4,5,7,8] => [2,6,1,3,4,5,7,8] => 4
[[1,2],[3,4],[5,6],[7,8]] => [7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 4
[[1,3],[2,4],[5,8],[6],[7]] => [7,6,5,8,2,4,1,3] => [3,1,4,2,8,5,6,7] => [4,1,3,2,8,5,6,7] => 5
[[1,2],[3,4],[5,8],[6],[7]] => [7,6,5,8,3,4,1,2] => [2,1,4,3,8,5,6,7] => [2,1,4,3,8,5,6,7] => 5
[[1,2],[3,8],[4],[5],[6],[7]] => [7,6,5,4,3,8,1,2] => [2,1,8,3,4,5,6,7] => [2,1,8,3,4,5,6,7] => 6
[[1,8],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7] => [8,1,2,3,4,5,6,7] => 7
[[1,7],[2],[3],[4],[5],[6],[8]] => [8,6,5,4,3,2,1,7] => [7,1,2,3,4,5,6,8] => [7,1,2,3,4,5,6,8] => 6
[[1,6],[2],[3],[4],[5],[7],[8]] => [8,7,5,4,3,2,1,6] => [6,1,2,3,4,5,7,8] => [6,1,2,3,4,5,7,8] => 5
[[1,5],[2],[3],[4],[6],[7],[8]] => [8,7,6,4,3,2,1,5] => [5,1,2,3,4,6,7,8] => [5,1,2,3,4,6,7,8] => 4
[[1,2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8] => [2,1,3,4,5,6,7,8] => 1
[[1],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
[[1,2,3,4,5,6,7,8],[9]] => [9,1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1,9] => [5,6,7,8,1,2,3,4,9] => 4
[[1,2,3,4,5,6],[7],[8],[9]] => [9,8,7,1,2,3,4,5,6] => [6,5,4,3,2,1,7,8,9] => [4,5,6,1,2,3,7,8,9] => 3
[[1,2,3,4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,1,2,3,4] => [4,3,2,1,5,6,7,8,9] => [3,4,1,2,5,6,7,8,9] => 2
[[1,2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8,9] => [2,1,3,4,5,6,7,8,9] => 1
[[1],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => 0
[[1,2,3,4,5,6,7,8,9,10]] => [1,2,3,4,5,6,7,8,9,10] => [10,9,8,7,6,5,4,3,2,1] => [6,7,8,9,10,1,2,3,4,5] => 5
[[1,2,3,4,5,6,7,8],[9],[10]] => [10,9,1,2,3,4,5,6,7,8] => [8,7,6,5,4,3,2,1,9,10] => [5,6,7,8,1,2,3,4,9,10] => 4
[[1,2,3,4,5,6],[7],[8],[9],[10]] => [10,9,8,7,1,2,3,4,5,6] => [6,5,4,3,2,1,7,8,9,10] => [4,5,6,1,2,3,7,8,9,10] => 3
[[1,2,3,4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,1,2,3,4] => [4,3,2,1,5,6,7,8,9,10] => [3,4,1,2,5,6,7,8,9,10] => 2
[[1,2],[3,4],[5,6],[7,8],[9,10]] => [9,10,7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => 5
[[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,1,2] => [2,1,3,4,5,6,7,8,9,10] => [2,1,3,4,5,6,7,8,9,10] => 1
[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [10,9,8,7,6,5,4,3,2,1] => [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => 0
[[1,2,3,4,5,6,7,8,9,10,11,12]] => [1,2,3,4,5,6,7,8,9,10,11,12] => [12,11,10,9,8,7,6,5,4,3,2,1] => [7,8,9,10,11,12,1,2,3,4,5,6] => 6
[[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => [11,12,9,10,7,8,5,6,3,4,1,2] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => 6
[[1,9],[2],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,2,1,9] => [9,1,2,3,4,5,6,7,8] => [9,1,2,3,4,5,6,7,8] => 8
[[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,2,1,10] => [10,1,2,3,4,5,6,7,8,9] => [10,1,2,3,4,5,6,7,8,9] => 9
[[1,2,9],[3],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,1,2,9] => [9,2,1,3,4,5,6,7,8] => [2,9,1,3,4,5,6,7,8] => 7
[[1,2,3,4,5,6,7,8,10],[9]] => [9,1,2,3,4,5,6,7,8,10] => [10,8,7,6,5,4,3,2,1,9] => [5,6,7,8,10,1,2,3,4,9] => 5
[[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [9,8,7,6,5,4,3,1,2,10] => [10,2,1,3,4,5,6,7,8,9] => [2,10,1,3,4,5,6,7,8,9] => 8
[] => [] => [] => [] => 0
[[1,8],[2],[3],[4],[5],[6],[7],[9]] => [9,7,6,5,4,3,2,1,8] => [8,1,2,3,4,5,6,7,9] => [8,1,2,3,4,5,6,7,9] => 7
[[1,9],[2],[3],[4],[5],[6],[7],[8],[10]] => [10,8,7,6,5,4,3,2,1,9] => [9,1,2,3,4,5,6,7,8,10] => [9,1,2,3,4,5,6,7,8,10] => 8
[[1,2,3,4,5,6,7,8,9,10,12],[11]] => [11,1,2,3,4,5,6,7,8,9,10,12] => [12,10,9,8,7,6,5,4,3,2,1,11] => [6,7,8,9,10,12,1,2,3,4,5,11] => 6
[[1,2],[3,9],[4],[5],[6],[7],[8]] => [8,7,6,5,4,3,9,1,2] => [2,1,9,3,4,5,6,7,8] => [2,1,9,3,4,5,6,7,8] => 7
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Description
The number of exclusive right-to-left minima of a permutation.
This is the number of right-to-left minima that are not left-to-right maxima.
This is also the number of non weak exceedences of a permutation that are also not mid-points of a decreasing subsequence of length 3.
Given a permutation $\pi = [\pi_1,\ldots,\pi_n]$, this statistic counts the number of position $j$ such that $\pi_j < j$ and there do not exist indices $i,k$ with $i < j < k$ and $\pi_i > \pi_j > \pi_k$.
See also St000213The number of weak exceedances (also weak excedences) of a permutation. and St000119The number of occurrences of the pattern 321 in a permutation..
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
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
Corteel
Description
Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.