Identifier
Values
{{1}} => [1] => [1] => [1] => 1
{{1,2}} => [2,1] => [1,2] => [1,2] => 1
{{1},{2}} => [1,2] => [1,2] => [1,2] => 1
{{1,2,3}} => [2,3,1] => [1,2,3] => [1,2,3] => 1
{{1,2},{3}} => [2,1,3] => [1,2,3] => [1,2,3] => 1
{{1,3},{2}} => [3,2,1] => [1,3,2] => [1,3,2] => 2
{{1},{2,3}} => [1,3,2] => [1,2,3] => [1,2,3] => 1
{{1},{2},{3}} => [1,2,3] => [1,2,3] => [1,2,3] => 1
{{1,2,3,4}} => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 1
{{1,2,3},{4}} => [2,3,1,4] => [1,2,3,4] => [1,2,3,4] => 1
{{1,2,4},{3}} => [2,4,3,1] => [1,2,4,3] => [1,2,4,3] => 2
{{1,2},{3,4}} => [2,1,4,3] => [1,2,3,4] => [1,2,3,4] => 1
{{1,2},{3},{4}} => [2,1,3,4] => [1,2,3,4] => [1,2,3,4] => 1
{{1,3,4},{2}} => [3,2,4,1] => [1,3,4,2] => [1,4,2,3] => 2
{{1,3},{2,4}} => [3,4,1,2] => [1,3,2,4] => [1,3,2,4] => 2
{{1,3},{2},{4}} => [3,2,1,4] => [1,3,2,4] => [1,3,2,4] => 2
{{1,4},{2,3}} => [4,3,2,1] => [1,4,2,3] => [1,3,4,2] => 2
{{1},{2,3,4}} => [1,3,4,2] => [1,2,3,4] => [1,2,3,4] => 1
{{1},{2,3},{4}} => [1,3,2,4] => [1,2,3,4] => [1,2,3,4] => 1
{{1,4},{2},{3}} => [4,2,3,1] => [1,4,2,3] => [1,3,4,2] => 2
{{1},{2,4},{3}} => [1,4,3,2] => [1,2,4,3] => [1,2,4,3] => 2
{{1},{2},{3,4}} => [1,2,4,3] => [1,2,3,4] => [1,2,3,4] => 1
{{1},{2},{3},{4}} => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 1
{{1,2,3,4,5}} => [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1,2,3,4},{5}} => [2,3,4,1,5] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1,2,3,5},{4}} => [2,3,5,4,1] => [1,2,3,5,4] => [1,2,3,5,4] => 2
{{1,2,3},{4,5}} => [2,3,1,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1,2,4,5},{3}} => [2,4,3,5,1] => [1,2,4,5,3] => [1,2,5,3,4] => 2
{{1,2,4},{3,5}} => [2,4,5,1,3] => [1,2,4,3,5] => [1,2,4,3,5] => 2
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [1,2,4,3,5] => [1,2,4,3,5] => 2
{{1,2,5},{3,4}} => [2,5,4,3,1] => [1,2,5,3,4] => [1,2,4,5,3] => 2
{{1,2},{3,4,5}} => [2,1,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1,2},{3,4},{5}} => [2,1,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1,2,5},{3},{4}} => [2,5,3,4,1] => [1,2,5,3,4] => [1,2,4,5,3] => 2
{{1,2},{3,5},{4}} => [2,1,5,4,3] => [1,2,3,5,4] => [1,2,3,5,4] => 2
{{1,2},{3},{4,5}} => [2,1,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1,3,4,5},{2}} => [3,2,4,5,1] => [1,3,4,5,2] => [1,5,2,3,4] => 2
{{1,3,4},{2,5}} => [3,5,4,1,2] => [1,3,4,2,5] => [1,4,2,3,5] => 2
{{1,3,4},{2},{5}} => [3,2,4,1,5] => [1,3,4,2,5] => [1,4,2,3,5] => 2
{{1,3,5},{2,4}} => [3,4,5,2,1] => [1,3,5,2,4] => [1,4,2,5,3] => 3
{{1,3},{2,4,5}} => [3,4,1,5,2] => [1,3,2,4,5] => [1,3,2,4,5] => 2
{{1,3},{2,4},{5}} => [3,4,1,2,5] => [1,3,2,4,5] => [1,3,2,4,5] => 2
{{1,3,5},{2},{4}} => [3,2,5,4,1] => [1,3,5,2,4] => [1,4,2,5,3] => 3
{{1,3},{2,5},{4}} => [3,5,1,4,2] => [1,3,2,5,4] => [1,3,2,5,4] => 3
{{1,3},{2},{4,5}} => [3,2,1,5,4] => [1,3,2,4,5] => [1,3,2,4,5] => 2
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 2
{{1,4,5},{2,3}} => [4,3,2,5,1] => [1,4,5,2,3] => [1,4,5,2,3] => 2
{{1,4},{2,3,5}} => [4,3,5,1,2] => [1,4,2,3,5] => [1,3,4,2,5] => 2
{{1,4},{2,3},{5}} => [4,3,2,1,5] => [1,4,2,3,5] => [1,3,4,2,5] => 2
{{1,5},{2,3,4}} => [5,3,4,2,1] => [1,5,2,3,4] => [1,3,4,5,2] => 2
{{1},{2,3,4,5}} => [1,3,4,5,2] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1,5},{2,3},{4}} => [5,3,2,4,1] => [1,5,2,3,4] => [1,3,4,5,2] => 2
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [1,2,3,5,4] => [1,2,3,5,4] => 2
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1,4,5},{2},{3}} => [4,2,3,5,1] => [1,4,5,2,3] => [1,4,5,2,3] => 2
{{1,4},{2,5},{3}} => [4,5,3,1,2] => [1,4,2,5,3] => [1,3,5,2,4] => 2
{{1,4},{2},{3,5}} => [4,2,5,1,3] => [1,4,2,3,5] => [1,3,4,2,5] => 2
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => [1,4,2,3,5] => [1,3,4,2,5] => 2
{{1,5},{2,4},{3}} => [5,4,3,2,1] => [1,5,2,4,3] => [1,3,5,4,2] => 3
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [1,2,4,5,3] => [1,2,5,3,4] => 2
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [1,2,4,3,5] => [1,2,4,3,5] => 2
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [1,2,4,3,5] => [1,2,4,3,5] => 2
{{1,5},{2},{3,4}} => [5,2,4,3,1] => [1,5,2,3,4] => [1,3,4,5,2] => 2
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [1,2,5,3,4] => [1,2,4,5,3] => 2
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => [1,5,2,3,4] => [1,3,4,5,2] => 2
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [1,2,5,3,4] => [1,2,4,5,3] => 2
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [1,2,3,5,4] => [1,2,3,5,4] => 2
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 1
{{1,2,3,4,5,6}} => [2,3,4,5,6,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 2
{{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => 2
{{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 2
{{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 2
{{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 2
{{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 2
{{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 2
{{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => 2
{{1,2,4,5},{3,6}} => [2,4,6,5,1,3] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => 2
{{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => 2
{{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => 3
{{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 2
{{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 2
{{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => 3
{{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 3
{{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 2
{{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 2
{{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => [1,2,5,6,3,4] => [1,2,5,6,3,4] => 2
>>> Load all 278 entries. <<<
{{1,2,5},{3,4,6}} => [2,5,4,6,1,3] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 2
{{1,2,5},{3,4},{6}} => [2,5,4,3,1,6] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 2
{{1,2,6},{3,4,5}} => [2,6,4,5,3,1] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 2
{{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,2,6},{3,4},{5}} => [2,6,4,3,5,1] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 2
{{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 2
{{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => [1,2,5,6,3,4] => [1,2,5,6,3,4] => 2
{{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => [1,2,5,3,6,4] => [1,2,4,6,3,5] => 2
{{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 2
{{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 2
{{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => [1,2,6,3,5,4] => [1,2,4,6,5,3] => 3
{{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => 2
{{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 2
{{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 2
{{1,2,6},{3},{4,5}} => [2,6,3,5,4,1] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 2
{{1,2},{3,6},{4,5}} => [2,1,6,5,4,3] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 2
{{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 2
{{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 2
{{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 2
{{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => [1,3,4,5,6,2] => [1,6,2,3,4,5] => 2
{{1,3,4,5},{2,6}} => [3,6,4,5,1,2] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => 2
{{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => [1,3,4,5,2,6] => [1,5,2,3,4,6] => 2
{{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => [1,3,4,6,2,5] => [1,5,2,3,6,4] => 3
{{1,3,4},{2,5,6}} => [3,5,4,1,6,2] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => 2
{{1,3,4},{2,5},{6}} => [3,5,4,1,2,6] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => 2
{{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => [1,3,4,6,2,5] => [1,5,2,3,6,4] => 3
{{1,3,4},{2,6},{5}} => [3,6,4,1,5,2] => [1,3,4,2,6,5] => [1,4,2,3,6,5] => 3
{{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => 2
{{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => [1,3,4,2,5,6] => [1,4,2,3,5,6] => 2
{{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => [1,3,5,6,2,4] => [1,5,2,6,3,4] => 3
{{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => [1,3,5,2,4,6] => [1,4,2,5,3,6] => 3
{{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => [1,3,5,2,4,6] => [1,4,2,5,3,6] => 3
{{1,3,6},{2,4,5}} => [3,4,6,5,2,1] => [1,3,6,2,4,5] => [1,4,2,5,6,3] => 3
{{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 2
{{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 2
{{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => [1,3,6,2,4,5] => [1,4,2,5,6,3] => 3
{{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 3
{{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 2
{{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 2
{{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => [1,3,5,6,2,4] => [1,5,2,6,3,4] => 3
{{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => [1,3,5,2,6,4] => [1,4,2,6,3,5] => 3
{{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => [1,3,5,2,4,6] => [1,4,2,5,3,6] => 3
{{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => [1,3,5,2,4,6] => [1,4,2,5,3,6] => 3
{{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => [1,3,6,2,5,4] => [1,4,2,6,5,3] => 4
{{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => [1,3,2,5,6,4] => [1,3,2,6,4,5] => 3
{{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 3
{{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => [1,3,2,5,4,6] => [1,3,2,5,4,6] => 3
{{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => [1,3,6,2,4,5] => [1,4,2,5,6,3] => 3
{{1,3},{2,6},{4,5}} => [3,6,1,5,4,2] => [1,3,2,6,4,5] => [1,3,2,5,6,4] => 3
{{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 2
{{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 2
{{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => [1,3,6,2,4,5] => [1,4,2,5,6,3] => 3
{{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => [1,3,2,6,4,5] => [1,3,2,5,6,4] => 3
{{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => [1,3,2,4,6,5] => [1,3,2,4,6,5] => 3
{{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 2
{{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => [1,3,2,4,5,6] => [1,3,2,4,5,6] => 2
{{1,4,5,6},{2,3}} => [4,3,2,5,6,1] => [1,4,5,6,2,3] => [1,5,6,2,3,4] => 2
{{1,4,5},{2,3,6}} => [4,3,6,5,1,2] => [1,4,5,2,3,6] => [1,4,5,2,3,6] => 2
{{1,4,5},{2,3},{6}} => [4,3,2,5,1,6] => [1,4,5,2,3,6] => [1,4,5,2,3,6] => 2
{{1,4,6},{2,3,5}} => [4,3,5,6,2,1] => [1,4,6,2,3,5] => [1,4,5,2,6,3] => 3
{{1,4},{2,3,5,6}} => [4,3,5,1,6,2] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 2
{{1,4},{2,3,5},{6}} => [4,3,5,1,2,6] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 2
{{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => [1,4,6,2,3,5] => [1,4,5,2,6,3] => 3
{{1,4},{2,3,6},{5}} => [4,3,6,1,5,2] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => 3
{{1,4},{2,3},{5,6}} => [4,3,2,1,6,5] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 2
{{1,4},{2,3},{5},{6}} => [4,3,2,1,5,6] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 2
{{1,5,6},{2,3,4}} => [5,3,4,2,6,1] => [1,5,6,2,3,4] => [1,4,5,6,2,3] => 2
{{1,5},{2,3,4,6}} => [5,3,4,6,1,2] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 2
{{1,5},{2,3,4},{6}} => [5,3,4,2,1,6] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 2
{{1,6},{2,3,4,5}} => [6,3,4,5,2,1] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 2
{{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 2
{{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 2
{{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,5,6},{2,3},{4}} => [5,3,2,4,6,1] => [1,5,6,2,3,4] => [1,4,5,6,2,3] => 2
{{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => [1,5,2,3,6,4] => [1,3,4,6,2,5] => 2
{{1,5},{2,3},{4,6}} => [5,3,2,6,1,4] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 2
{{1,5},{2,3},{4},{6}} => [5,3,2,4,1,6] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 2
{{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => [1,6,2,3,5,4] => [1,3,4,6,5,2] => 3
{{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => 2
{{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 2
{{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 2
{{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 2
{{1},{2,3,6},{4,5}} => [1,3,6,5,4,2] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 2
{{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 2
{{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 2
{{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 2
{{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => [1,4,5,6,2,3] => [1,5,6,2,3,4] => 2
{{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => [1,4,5,2,6,3] => [1,4,6,2,3,5] => 2
{{1,4,5},{2},{3,6}} => [4,2,6,5,1,3] => [1,4,5,2,3,6] => [1,4,5,2,3,6] => 2
{{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => [1,4,5,2,3,6] => [1,4,5,2,3,6] => 2
{{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => [1,4,6,2,5,3] => [1,4,6,2,5,3] => 3
{{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => [1,4,2,5,6,3] => [1,3,6,2,4,5] => 2
{{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => [1,4,2,5,3,6] => [1,3,5,2,4,6] => 2
{{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => [1,4,2,5,3,6] => [1,3,5,2,4,6] => 2
{{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => [1,4,6,2,3,5] => [1,4,5,2,6,3] => 3
{{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => [1,4,2,6,3,5] => [1,3,5,2,6,4] => 3
{{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 2
{{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 2
{{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => [1,4,6,2,3,5] => [1,4,5,2,6,3] => 3
{{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => [1,4,2,6,3,5] => [1,3,5,2,6,4] => 3
{{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => [1,4,2,3,6,5] => [1,3,4,2,6,5] => 3
{{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 2
{{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => [1,4,2,3,5,6] => [1,3,4,2,5,6] => 2
{{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => [1,5,6,2,4,3] => [1,4,6,5,2,3] => 3
{{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => [1,5,2,4,6,3] => [1,3,6,4,2,5] => 3
{{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => [1,5,2,4,3,6] => [1,3,5,4,2,6] => 3
{{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => [1,5,2,4,3,6] => [1,3,5,4,2,6] => 3
{{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => [1,6,2,4,5,3] => [1,3,6,4,5,2] => 3
{{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => [1,2,4,5,6,3] => [1,2,6,3,4,5] => 2
{{1},{2,4,5},{3,6}} => [1,4,6,5,2,3] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => 2
{{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => [1,2,4,5,3,6] => [1,2,5,3,4,6] => 2
{{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => [1,6,2,4,3,5] => [1,3,5,4,6,2] => 3
{{1},{2,4,6},{3,5}} => [1,4,5,6,3,2] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => 3
{{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 2
{{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 2
{{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => [1,6,2,4,3,5] => [1,3,5,4,6,2] => 3
{{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => [1,2,4,6,3,5] => [1,2,5,3,6,4] => 3
{{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => [1,2,4,3,6,5] => [1,2,4,3,6,5] => 3
{{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 2
{{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => [1,2,4,3,5,6] => [1,2,4,3,5,6] => 2
{{1,5,6},{2},{3,4}} => [5,2,4,3,6,1] => [1,5,6,2,3,4] => [1,4,5,6,2,3] => 2
{{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => [1,5,2,6,3,4] => [1,3,5,6,2,4] => 2
{{1,5},{2},{3,4,6}} => [5,2,4,6,1,3] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 2
{{1,5},{2},{3,4},{6}} => [5,2,4,3,1,6] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 2
{{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => [1,6,2,5,3,4] => [1,3,5,6,4,2] => 3
{{1},{2,5,6},{3,4}} => [1,5,4,3,6,2] => [1,2,5,6,3,4] => [1,2,5,6,3,4] => 2
{{1},{2,5},{3,4,6}} => [1,5,4,6,2,3] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 2
{{1},{2,5},{3,4},{6}} => [1,5,4,3,2,6] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 2
{{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 2
{{1},{2,6},{3,4,5}} => [1,6,4,5,3,2] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 2
{{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 2
{{1},{2,6},{3,4},{5}} => [1,6,4,3,5,2] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 2
{{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 2
{{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => [1,5,6,2,3,4] => [1,4,5,6,2,3] => 2
{{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => [1,5,2,6,3,4] => [1,3,5,6,2,4] => 2
{{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => [1,5,2,3,6,4] => [1,3,4,6,2,5] => 2
{{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 2
{{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => [1,5,2,3,4,6] => [1,3,4,5,2,6] => 2
{{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => [1,6,2,5,3,4] => [1,3,5,6,4,2] => 3
{{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => [1,2,5,6,3,4] => [1,2,5,6,3,4] => 2
{{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => [1,2,5,3,6,4] => [1,2,4,6,3,5] => 2
{{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 2
{{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => [1,2,5,3,4,6] => [1,2,4,5,3,6] => 2
{{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => [1,6,2,3,5,4] => [1,3,4,6,5,2] => 3
{{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => [1,2,6,3,5,4] => [1,2,4,6,5,3] => 3
{{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => [1,2,3,5,6,4] => [1,2,3,6,4,5] => 2
{{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 2
{{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => [1,2,3,5,4,6] => [1,2,3,5,4,6] => 2
{{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 2
{{1},{2,6},{3},{4,5}} => [1,6,3,5,4,2] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 2
{{1},{2},{3,6},{4,5}} => [1,2,6,5,4,3] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 2
{{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => [1,6,2,3,4,5] => [1,3,4,5,6,2] => 2
{{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => [1,2,6,3,4,5] => [1,2,4,5,6,3] => 2
{{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => [1,2,3,6,4,5] => [1,2,3,5,6,4] => 2
{{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => [1,2,3,4,6,5] => [1,2,3,4,6,5] => 2
{{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
{{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
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 width of the tree associated to a permutation.
A permutation can be mapped to a rooted tree with vertices $\{0,1,2,\ldots,n\}$ and root $0$ in the following way. Entries of the permutations are inserted one after the other, each child is larger than its parent and the children are in strict order from left to right. Details of the construction are found in [1].
The width of the tree is given by the number of leaves of this tree.
Note that, due to the construction of this tree, the width of the tree is always one more than the number of descents St000021The number of descents of a permutation.. This also matches the number of runs in a permutation St000470The number of runs in a permutation..
See also St000308The height of the tree associated to a permutation. for the height of this tree.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
Map
inverse
Description
Sends a permutation to its inverse.