Identifier
Values
{{1}} => [1] => [1] => 0
{{1,2}} => [2,1] => [2,1] => 0
{{1},{2}} => [1,2] => [1,2] => 0
{{1,2,3}} => [2,3,1] => [1,3,2] => 0
{{1,2},{3}} => [2,1,3] => [3,1,2] => 0
{{1,3},{2}} => [3,2,1] => [1,2,3] => 0
{{1},{2,3}} => [1,3,2] => [2,3,1] => 0
{{1},{2},{3}} => [1,2,3] => [3,2,1] => 1
{{1,2,3,4}} => [2,3,4,1] => [1,3,4,2] => 0
{{1,2,3},{4}} => [2,3,1,4] => [3,4,1,2] => 0
{{1,2,4},{3}} => [2,4,3,1] => [3,1,2,4] => 0
{{1,2},{3,4}} => [2,1,4,3] => [3,2,4,1] => 1
{{1,2},{3},{4}} => [2,1,3,4] => [3,4,2,1] => 1
{{1,3,4},{2}} => [3,2,4,1] => [4,1,3,2] => 1
{{1,3},{2,4}} => [3,4,1,2] => [1,4,2,3] => 0
{{1,3},{2},{4}} => [3,2,1,4] => [4,3,1,2] => 1
{{1,4},{2,3}} => [4,3,2,1] => [2,4,1,3] => 0
{{1},{2,3,4}} => [1,3,4,2] => [4,2,1,3] => 1
{{1},{2,3},{4}} => [1,3,2,4] => [4,3,2,1] => 2
{{1,4},{2},{3}} => [4,2,3,1] => [1,2,3,4] => 0
{{1},{2,4},{3}} => [1,4,3,2] => [2,4,3,1] => 1
{{1},{2},{3,4}} => [1,2,4,3] => [3,2,1,4] => 1
{{1},{2},{3},{4}} => [1,2,3,4] => [3,1,4,2] => 0
{{1,2,3,4,5}} => [2,3,4,5,1] => [1,3,4,5,2] => 0
{{1,2,3,4},{5}} => [2,3,4,1,5] => [3,4,5,1,2] => 0
{{1,2,3,5},{4}} => [2,3,5,4,1] => [3,4,1,2,5] => 0
{{1,2,3},{4,5}} => [2,3,1,5,4] => [3,4,2,5,1] => 1
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [3,4,5,2,1] => 1
{{1,2,4,5},{3}} => [2,4,3,5,1] => [3,5,1,4,2] => 1
{{1,2,4},{3,5}} => [2,4,5,1,3] => [1,3,5,2,4] => 0
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [3,5,4,1,2] => 1
{{1,2,5},{3,4}} => [2,5,4,3,1] => [3,2,5,1,4] => 1
{{1,2},{3,4,5}} => [2,1,4,5,3] => [3,5,2,1,4] => 1
{{1,2},{3,4},{5}} => [2,1,4,3,5] => [3,5,4,2,1] => 2
{{1,2,5},{3},{4}} => [2,5,3,4,1] => [3,1,2,4,5] => 0
{{1,2},{3,5},{4}} => [2,1,5,4,3] => [3,2,5,4,1] => 2
{{1,2},{3},{4,5}} => [2,1,3,5,4] => [3,4,2,1,5] => 1
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [3,4,1,5,2] => 0
{{1,3,4,5},{2}} => [3,2,4,5,1] => [4,1,3,5,2] => 1
{{1,3,4},{2,5}} => [3,5,4,1,2] => [4,1,2,5,3] => 0
{{1,3,4},{2},{5}} => [3,2,4,1,5] => [4,3,5,1,2] => 1
{{1,3,5},{2,4}} => [3,4,5,2,1] => [4,5,1,2,3] => 0
{{1,3},{2,4,5}} => [3,4,1,5,2] => [4,5,2,3,1] => 2
{{1,3},{2,4},{5}} => [3,4,1,2,5] => [1,4,5,3,2] => 1
{{1,3,5},{2},{4}} => [3,2,5,4,1] => [4,3,1,2,5] => 1
{{1,3},{2,5},{4}} => [3,5,1,4,2] => [1,4,2,5,3] => 0
{{1,3},{2},{4,5}} => [3,2,1,5,4] => [4,3,2,5,1] => 2
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => [4,3,5,2,1] => 2
{{1,4,5},{2,3}} => [4,3,2,5,1] => [5,4,1,3,2] => 2
{{1,4},{2,3,5}} => [4,3,5,1,2] => [5,1,4,2,3] => 1
{{1,4},{2,3},{5}} => [4,3,2,1,5] => [5,4,3,1,2] => 3
{{1,5},{2,3,4}} => [5,3,4,2,1] => [2,4,5,1,3] => 0
{{1},{2,3,4,5}} => [1,3,4,5,2] => [4,1,5,2,3] => 0
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [4,1,5,3,2] => 1
{{1,5},{2,3},{4}} => [5,3,2,4,1] => [2,4,1,3,5] => 0
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [4,2,1,5,3] => 1
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [4,3,2,1,5] => 2
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [4,3,1,5,2] => 1
{{1,4,5},{2},{3}} => [4,2,3,5,1] => [5,1,3,4,2] => 2
{{1,4},{2,5},{3}} => [4,5,3,1,2] => [5,1,2,4,3] => 1
{{1,4},{2},{3,5}} => [4,2,5,1,3] => [5,1,3,2,4] => 1
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => [5,3,4,1,2] => 2
{{1,5},{2,4},{3}} => [5,4,3,2,1] => [2,5,4,1,3] => 1
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [5,4,2,1,3] => 2
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [5,2,1,3,4] => 1
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [5,4,3,2,1] => 4
{{1,5},{2},{3,4}} => [5,2,4,3,1] => [2,3,5,1,4] => 0
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [2,5,4,3,1] => 2
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [3,1,5,2,4] => 0
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [3,1,5,4,2] => 1
{{1,5},{2},{3},{4}} => [5,2,3,4,1] => [1,2,3,4,5] => 0
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [2,4,1,5,3] => 0
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [3,2,1,5,4] => 1
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [3,1,4,2,5] => 0
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [3,1,4,5,2] => 0
{{1,2,3,4,5,6}} => [2,3,4,5,6,1] => [1,3,4,5,6,2] => 0
{{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => [3,4,5,6,1,2] => 0
{{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => [3,4,5,1,2,6] => 0
{{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => [3,4,5,2,6,1] => 1
{{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => [3,4,5,6,2,1] => 1
{{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => [3,4,6,1,5,2] => 1
{{1,2,3,5},{4,6}} => [2,3,5,6,1,4] => [1,3,4,6,2,5] => 0
{{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => [3,4,6,5,1,2] => 1
{{1,2,3,6},{4,5}} => [2,3,6,5,4,1] => [3,4,2,6,1,5] => 1
{{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => [3,4,6,2,1,5] => 1
{{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => [3,4,6,5,2,1] => 2
{{1,2,3,6},{4},{5}} => [2,3,6,4,5,1] => [3,4,1,2,5,6] => 0
{{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => [3,4,2,6,5,1] => 2
{{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => [3,4,5,2,1,6] => 1
{{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => [3,4,5,1,6,2] => 0
{{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => [3,5,1,4,6,2] => 1
{{1,2,4,5},{3,6}} => [2,4,6,5,1,3] => [3,5,1,2,6,4] => 0
{{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => [3,5,4,6,1,2] => 1
{{1,2,4,6},{3,5}} => [2,4,5,6,3,1] => [3,5,6,1,2,4] => 0
{{1,2,4},{3,5,6}} => [2,4,5,1,6,3] => [3,5,6,2,4,1] => 2
{{1,2,4},{3,5},{6}} => [2,4,5,1,3,6] => [1,3,5,6,4,2] => 1
{{1,2,4,6},{3},{5}} => [2,4,3,6,5,1] => [3,5,4,1,2,6] => 1
{{1,2,4},{3,6},{5}} => [2,4,6,1,5,3] => [1,3,5,2,6,4] => 0
{{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => [3,5,4,2,6,1] => 2
{{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => [3,5,4,6,2,1] => 2
{{1,2,5,6},{3,4}} => [2,5,4,3,6,1] => [3,6,5,1,4,2] => 2
>>> Load all 315 entries. <<<
{{1,2,5},{3,4,6}} => [2,5,4,6,1,3] => [3,6,1,5,2,4] => 1
{{1,2,5},{3,4},{6}} => [2,5,4,3,1,6] => [3,6,5,4,1,2] => 3
{{1,2,6},{3,4,5}} => [2,6,4,5,3,1] => [3,2,5,6,1,4] => 1
{{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => [3,5,1,6,2,4] => 0
{{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => [3,5,1,6,4,2] => 1
{{1,2,6},{3,4},{5}} => [2,6,4,3,5,1] => [3,2,5,1,4,6] => 1
{{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => [3,5,2,1,6,4] => 1
{{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => [3,5,4,2,1,6] => 2
{{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => [3,5,4,1,6,2] => 1
{{1,2,5,6},{3},{4}} => [2,5,3,4,6,1] => [3,6,1,4,5,2] => 2
{{1,2,5},{3,6},{4}} => [2,5,6,4,1,3] => [3,6,1,2,5,4] => 1
{{1,2,5},{3},{4,6}} => [2,5,3,6,1,4] => [3,6,1,4,2,5] => 1
{{1,2,5},{3},{4},{6}} => [2,5,3,4,1,6] => [3,6,4,5,1,2] => 2
{{1,2,6},{3,5},{4}} => [2,6,5,4,3,1] => [3,2,6,5,1,4] => 2
{{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => [3,6,5,2,1,4] => 2
{{1,2},{3,5},{4,6}} => [2,1,5,6,3,4] => [3,6,2,1,4,5] => 1
{{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => [3,6,5,4,2,1] => 4
{{1,2,6},{3},{4,5}} => [2,6,3,5,4,1] => [3,2,4,6,1,5] => 1
{{1,2},{3,6},{4,5}} => [2,1,6,5,4,3] => [3,2,6,5,4,1] => 3
{{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => [3,4,1,6,2,5] => 0
{{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => [3,4,1,6,5,2] => 1
{{1,2,6},{3},{4},{5}} => [2,6,3,4,5,1] => [3,1,2,4,5,6] => 0
{{1,2},{3,6},{4},{5}} => [2,1,6,4,5,3] => [3,2,5,1,6,4] => 1
{{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => [3,4,2,1,6,5] => 1
{{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => [3,4,1,5,2,6] => 0
{{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => [3,4,1,5,6,2] => 0
{{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => [4,1,3,5,6,2] => 1
{{1,3,4,5},{2,6}} => [3,6,4,5,1,2] => [4,1,2,5,6,3] => 0
{{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => [4,3,5,6,1,2] => 1
{{1,3,4,6},{2,5}} => [3,5,4,6,2,1] => [4,6,5,1,2,3] => 1
{{1,3,4},{2,5,6}} => [3,5,4,1,6,2] => [4,6,5,2,3,1] => 3
{{1,3,4},{2,5},{6}} => [3,5,4,1,2,6] => [4,6,1,5,3,2] => 2
{{1,3,4,6},{2},{5}} => [3,2,4,6,5,1] => [4,3,5,1,2,6] => 1
{{1,3,4},{2,6},{5}} => [3,6,4,1,5,2] => [4,2,5,6,3,1] => 2
{{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => [4,3,5,2,6,1] => 2
{{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => [4,3,5,6,2,1] => 2
{{1,3,5,6},{2,4}} => [3,4,5,2,6,1] => [4,5,6,1,3,2] => 1
{{1,3,5},{2,4,6}} => [3,4,5,6,1,2] => [1,4,5,6,2,3] => 0
{{1,3,5},{2,4},{6}} => [3,4,5,2,1,6] => [4,5,6,3,1,2] => 2
{{1,3,6},{2,4,5}} => [3,4,6,5,2,1] => [4,5,2,6,1,3] => 1
{{1,3},{2,4,5,6}} => [3,4,1,5,6,2] => [4,5,6,2,1,3] => 1
{{1,3},{2,4,5},{6}} => [3,4,1,5,2,6] => [4,5,6,3,2,1] => 3
{{1,3,6},{2,4},{5}} => [3,4,6,2,5,1] => [4,5,1,2,3,6] => 0
{{1,3},{2,4,6},{5}} => [3,4,1,6,5,2] => [4,5,2,6,3,1] => 2
{{1,3},{2,4},{5,6}} => [3,4,1,2,6,5] => [1,4,5,3,2,6] => 1
{{1,3},{2,4},{5},{6}} => [3,4,1,2,5,6] => [1,4,5,3,6,2] => 1
{{1,3,5,6},{2},{4}} => [3,2,5,4,6,1] => [4,3,6,1,5,2] => 2
{{1,3,5},{2,6},{4}} => [3,6,5,4,1,2] => [4,2,6,1,5,3] => 2
{{1,3,5},{2},{4,6}} => [3,2,5,6,1,4] => [4,1,3,6,2,5] => 1
{{1,3,5},{2},{4},{6}} => [3,2,5,4,1,6] => [4,3,6,5,1,2] => 2
{{1,3,6},{2,5},{4}} => [3,5,6,4,2,1] => [4,6,2,5,1,3] => 2
{{1,3},{2,5,6},{4}} => [3,5,1,4,6,2] => [1,4,6,5,2,3] => 1
{{1,3},{2,5},{4,6}} => [3,5,1,6,2,4] => [4,6,2,3,1,5] => 2
{{1,3},{2,5},{4},{6}} => [3,5,1,4,2,6] => [1,4,6,5,3,2] => 2
{{1,3,6},{2},{4,5}} => [3,2,6,5,4,1] => [4,3,2,6,1,5] => 2
{{1,3},{2,6},{4,5}} => [3,6,1,5,4,2] => [1,4,2,6,5,3] => 1
{{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => [4,3,6,2,1,5] => 2
{{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => [4,3,6,5,2,1] => 3
{{1,3,6},{2},{4},{5}} => [3,2,6,4,5,1] => [4,3,1,2,5,6] => 1
{{1,3},{2,6},{4},{5}} => [3,6,1,4,5,2] => [1,4,2,5,6,3] => 0
{{1,3},{2},{4,6},{5}} => [3,2,1,6,5,4] => [4,3,2,6,5,1] => 3
{{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => [4,3,5,2,1,6] => 2
{{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => [4,3,5,1,6,2] => 1
{{1,4,5,6},{2,3}} => [4,3,2,5,6,1] => [5,4,1,3,6,2] => 2
{{1,4,5},{2,3,6}} => [4,3,6,5,1,2] => [5,4,1,2,6,3] => 1
{{1,4,5},{2,3},{6}} => [4,3,2,5,1,6] => [5,4,3,6,1,2] => 3
{{1,4,6},{2,3,5}} => [4,3,5,6,2,1] => [5,4,6,1,2,3] => 1
{{1,4},{2,3,5,6}} => [4,3,5,1,6,2] => [5,4,6,2,3,1] => 3
{{1,4},{2,3,5},{6}} => [4,3,5,1,2,6] => [5,1,4,6,3,2] => 2
{{1,4,6},{2,3},{5}} => [4,3,2,6,5,1] => [5,4,3,1,2,6] => 3
{{1,4},{2,3,6},{5}} => [4,3,6,1,5,2] => [5,1,4,2,6,3] => 1
{{1,4},{2,3},{5,6}} => [4,3,2,1,6,5] => [5,4,3,2,6,1] => 4
{{1,4},{2,3},{5},{6}} => [4,3,2,1,5,6] => [5,4,3,6,2,1] => 4
{{1,5,6},{2,3,4}} => [5,3,4,2,6,1] => [6,4,5,1,3,2] => 3
{{1,5},{2,3,4,6}} => [5,3,4,6,1,2] => [6,1,4,5,2,3] => 2
{{1,5},{2,3,4},{6}} => [5,3,4,2,1,6] => [6,4,5,3,1,2] => 4
{{1,6},{2,3,4,5}} => [6,3,4,5,2,1] => [2,4,5,6,1,3] => 0
{{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => [4,1,5,6,2,3] => 0
{{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => [4,1,5,6,3,2] => 1
{{1,6},{2,3,4},{5}} => [6,3,4,2,5,1] => [2,4,5,1,3,6] => 0
{{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => [4,1,5,2,6,3] => 0
{{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => [4,1,5,3,2,6] => 1
{{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => [4,1,5,3,6,2] => 1
{{1,5,6},{2,3},{4}} => [5,3,2,4,6,1] => [6,4,1,3,5,2] => 3
{{1,5},{2,3,6},{4}} => [5,3,6,4,1,2] => [6,4,1,2,5,3] => 2
{{1,5},{2,3},{4,6}} => [5,3,2,6,1,4] => [6,4,1,3,2,5] => 2
{{1,5},{2,3},{4},{6}} => [5,3,2,4,1,6] => [6,4,3,5,1,2] => 4
{{1,6},{2,3,5},{4}} => [6,3,5,4,2,1] => [2,4,6,5,1,3] => 1
{{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => [4,1,6,5,2,3] => 1
{{1},{2,3,5},{4,6}} => [1,3,5,6,2,4] => [4,1,6,2,3,5] => 0
{{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => [4,1,6,5,3,2] => 2
{{1,6},{2,3},{4,5}} => [6,3,2,5,4,1] => [2,4,3,6,1,5] => 1
{{1},{2,3,6},{4,5}} => [1,3,6,5,4,2] => [4,2,1,6,5,3] => 2
{{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => [4,3,1,6,2,5] => 1
{{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => [4,3,1,6,5,2] => 2
{{1,6},{2,3},{4},{5}} => [6,3,2,4,5,1] => [2,4,1,3,5,6] => 0
{{1},{2,3,6},{4},{5}} => [1,3,6,4,5,2] => [4,2,1,5,6,3] => 1
{{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => [4,3,2,1,6,5] => 2
{{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => [4,3,1,5,2,6] => 1
{{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => [4,3,1,5,6,2] => 1
{{1,4,5,6},{2},{3}} => [4,2,3,5,6,1] => [5,1,3,4,6,2] => 2
{{1,4,5},{2,6},{3}} => [4,6,3,5,1,2] => [5,1,2,4,6,3] => 1
{{1,4,5},{2},{3,6}} => [4,2,6,5,1,3] => [5,3,1,2,6,4] => 1
{{1,4,5},{2},{3},{6}} => [4,2,3,5,1,6] => [5,3,4,6,1,2] => 2
{{1,4,6},{2,5},{3}} => [4,5,3,6,2,1] => [5,6,4,1,2,3] => 2
{{1,4},{2,5,6},{3}} => [4,5,3,1,6,2] => [5,6,4,2,3,1] => 4
{{1,4},{2,5},{3,6}} => [4,5,6,1,2,3] => [1,5,6,2,3,4] => 0
{{1,4},{2,5},{3},{6}} => [4,5,3,1,2,6] => [5,6,1,4,3,2] => 3
{{1,4,6},{2},{3,5}} => [4,2,5,6,3,1] => [5,3,6,1,2,4] => 1
{{1,4},{2,6},{3,5}} => [4,6,5,1,3,2] => [5,1,2,6,4,3] => 1
{{1,4},{2},{3,5,6}} => [4,2,5,1,6,3] => [5,3,6,2,4,1] => 3
{{1,4},{2},{3,5},{6}} => [4,2,5,1,3,6] => [5,1,3,6,4,2] => 2
{{1,4,6},{2},{3},{5}} => [4,2,3,6,5,1] => [5,3,4,1,2,6] => 2
{{1,4},{2,6},{3},{5}} => [4,6,3,1,5,2] => [5,2,4,6,3,1] => 3
{{1,4},{2},{3,6},{5}} => [4,2,6,1,5,3] => [5,1,3,2,6,4] => 1
{{1,4},{2},{3},{5,6}} => [4,2,3,1,6,5] => [5,3,4,2,6,1] => 3
{{1,4},{2},{3},{5},{6}} => [4,2,3,1,5,6] => [5,3,4,6,2,1] => 3
{{1,5,6},{2,4},{3}} => [5,4,3,2,6,1] => [6,5,4,1,3,2] => 4
{{1,5},{2,4,6},{3}} => [5,4,3,6,1,2] => [6,5,1,4,2,3] => 3
{{1,5},{2,4},{3,6}} => [5,4,6,2,1,3] => [6,5,2,3,4,1] => 4
{{1,5},{2,4},{3},{6}} => [5,4,3,2,1,6] => [6,5,4,3,1,2] => 5
{{1,6},{2,4,5},{3}} => [6,4,3,5,2,1] => [2,5,4,6,1,3] => 1
{{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => [5,4,1,6,2,3] => 1
{{1},{2,4,5},{3,6}} => [1,4,6,5,2,3] => [5,2,1,6,3,4] => 1
{{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => [5,4,1,6,3,2] => 2
{{1,6},{2,4},{3,5}} => [6,4,5,2,3,1] => [2,5,6,1,3,4] => 0
{{1},{2,4,6},{3,5}} => [1,4,5,6,3,2] => [5,1,6,2,4,3] => 1
{{1},{2,4},{3,5,6}} => [1,4,5,2,6,3] => [5,1,6,3,2,4] => 1
{{1},{2,4},{3,5},{6}} => [1,4,5,2,3,6] => [5,1,6,3,4,2] => 2
{{1,6},{2,4},{3},{5}} => [6,4,3,2,5,1] => [2,5,4,1,3,6] => 1
{{1},{2,4,6},{3},{5}} => [1,4,3,6,5,2] => [5,4,2,1,6,3] => 2
{{1},{2,4},{3,6},{5}} => [1,4,6,2,5,3] => [5,2,1,3,6,4] => 1
{{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => [5,4,3,2,1,6] => 4
{{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => [5,4,3,1,6,2] => 3
{{1,5,6},{2},{3,4}} => [5,2,4,3,6,1] => [6,3,5,1,4,2] => 3
{{1,5},{2,6},{3,4}} => [5,6,4,3,1,2] => [6,2,5,1,4,3] => 3
{{1,5},{2},{3,4,6}} => [5,2,4,6,1,3] => [6,1,3,5,2,4] => 2
{{1,5},{2},{3,4},{6}} => [5,2,4,3,1,6] => [6,3,5,4,1,2] => 4
{{1,6},{2,5},{3,4}} => [6,5,4,3,2,1] => [2,6,5,4,1,3] => 3
{{1},{2,5,6},{3,4}} => [1,5,4,3,6,2] => [6,5,4,2,1,3] => 4
{{1},{2,5},{3,4,6}} => [1,5,4,6,2,3] => [6,5,2,1,3,4] => 2
{{1},{2,5},{3,4},{6}} => [1,5,4,3,2,6] => [6,5,4,3,2,1] => 6
{{1,6},{2},{3,4,5}} => [6,2,4,5,3,1] => [2,3,5,6,1,4] => 0
{{1},{2,6},{3,4,5}} => [1,6,4,5,3,2] => [2,5,1,6,4,3] => 1
{{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => [3,1,5,6,2,4] => 0
{{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => [3,1,5,6,4,2] => 1
{{1,6},{2},{3,4},{5}} => [6,2,4,3,5,1] => [2,3,5,1,4,6] => 0
{{1},{2,6},{3,4},{5}} => [1,6,4,3,5,2] => [2,5,4,1,6,3] => 1
{{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => [3,1,5,2,6,4] => 0
{{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => [3,1,5,4,2,6] => 1
{{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => [3,1,5,4,6,2] => 1
{{1,5,6},{2},{3},{4}} => [5,2,3,4,6,1] => [6,1,3,4,5,2] => 3
{{1,5},{2,6},{3},{4}} => [5,6,3,4,1,2] => [6,1,2,4,5,3] => 2
{{1,5},{2},{3,6},{4}} => [5,2,6,4,1,3] => [6,3,1,2,5,4] => 2
{{1,5},{2},{3},{4,6}} => [5,2,3,6,1,4] => [6,1,3,4,2,5] => 2
{{1,5},{2},{3},{4},{6}} => [5,2,3,4,1,6] => [6,3,4,5,1,2] => 3
{{1,6},{2,5},{3},{4}} => [6,5,3,4,2,1] => [2,6,4,5,1,3] => 2
{{1},{2,5,6},{3},{4}} => [1,5,3,4,6,2] => [6,4,1,5,2,3] => 2
{{1},{2,5},{3,6},{4}} => [1,5,6,4,2,3] => [6,2,1,5,3,4] => 2
{{1},{2,5},{3},{4,6}} => [1,5,3,6,2,4] => [6,4,2,1,3,5] => 2
{{1},{2,5},{3},{4},{6}} => [1,5,3,4,2,6] => [6,4,1,5,3,2] => 3
{{1,6},{2},{3,5},{4}} => [6,2,5,4,3,1] => [2,3,6,5,1,4] => 1
{{1},{2,6},{3,5},{4}} => [1,6,5,4,3,2] => [2,6,5,4,3,1] => 4
{{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => [3,1,6,5,2,4] => 1
{{1},{2},{3,5},{4,6}} => [1,2,5,6,3,4] => [3,1,6,2,4,5] => 0
{{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => [3,1,6,5,4,2] => 2
{{1,6},{2},{3},{4,5}} => [6,2,3,5,4,1] => [2,3,4,6,1,5] => 0
{{1},{2,6},{3},{4,5}} => [1,6,3,5,4,2] => [2,4,1,6,5,3] => 1
{{1},{2},{3,6},{4,5}} => [1,2,6,5,4,3] => [3,2,1,6,5,4] => 2
{{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => [3,1,4,6,2,5] => 0
{{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => [3,1,4,6,5,2] => 1
{{1,6},{2},{3},{4},{5}} => [6,2,3,4,5,1] => [1,2,3,4,5,6] => 0
{{1},{2,6},{3},{4},{5}} => [1,6,3,4,5,2] => [2,4,1,5,6,3] => 0
{{1},{2},{3,6},{4},{5}} => [1,2,6,4,5,3] => [3,2,1,5,6,4] => 1
{{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => [3,1,4,2,6,5] => 0
{{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => [3,1,4,5,2,6] => 0
{{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => [3,1,4,5,6,2] => 0
{{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => [3,4,5,6,7,1,2] => 0
{{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => [3,4,5,6,2,7,1] => 1
{{1,2,3,7},{4},{5},{6}} => [2,3,7,4,5,6,1] => [3,4,1,2,5,6,7] => 0
{{1,2,4,7},{3,5},{6}} => [2,4,5,7,3,6,1] => [3,5,6,1,2,4,7] => 0
{{1,2},{3,5},{4},{6,7}} => [2,1,5,4,3,7,6] => [3,6,5,4,2,1,7] => 4
{{1,2,7},{3},{4},{5},{6}} => [2,7,3,4,5,6,1] => [3,1,2,4,5,6,7] => 0
{{1,3},{2,4,5},{6,7}} => [3,4,1,5,2,7,6] => [4,5,6,3,2,1,7] => 3
{{1,3},{2,6},{4,5},{7}} => [3,6,1,5,4,2,7] => [1,4,7,6,5,3,2] => 4
{{1,3},{2},{4,5},{6,7}} => [3,2,1,5,4,7,6] => [4,3,6,5,2,1,7] => 3
{{1,4},{2,3},{5},{6,7}} => [4,3,2,1,5,7,6] => [5,4,3,6,2,1,7] => 4
{{1,5,7},{2,3,4,6}} => [5,3,4,6,7,2,1] => [6,4,5,7,1,2,3] => 2
{{1,7},{2,3},{4},{5},{6}} => [7,3,2,4,5,6,1] => [2,4,1,3,5,6,7] => 0
{{1,4},{2,5,6},{3,7}} => [4,5,7,1,6,2,3] => [1,5,6,2,7,3,4] => 0
{{1,4,7},{2,5},{3,6}} => [4,5,6,7,2,3,1] => [5,6,7,1,2,3,4] => 0
{{1,6},{2,4},{3,5},{7}} => [6,4,5,2,3,1,7] => [7,5,6,3,4,1,2] => 6
{{1},{2,4},{3},{5,7},{6}} => [1,4,3,2,7,6,5] => [5,4,3,2,1,7,6] => 4
{{1,6},{2,5},{3,4},{7}} => [6,5,4,3,2,1,7] => [7,6,5,4,3,1,2] => 8
{{1},{2,5},{3,4},{6,7}} => [1,5,4,3,2,7,6] => [6,5,4,3,2,1,7] => 6
{{1,7},{2},{3,4,5,6}} => [7,2,4,5,6,3,1] => [2,3,5,6,7,1,4] => 0
{{1,5,7},{2,6},{3},{4}} => [5,6,3,4,7,2,1] => [6,7,4,5,1,2,3] => 4
{{1,5,7},{2},{3},{4,6}} => [5,2,3,6,7,4,1] => [6,3,4,7,1,2,5] => 2
{{1},{2,6},{3,5},{4},{7}} => [1,6,5,4,3,2,7] => [7,6,5,4,3,2,1] => 9
{{1,7},{2},{3},{4,5,6}} => [7,2,3,5,6,4,1] => [2,3,4,6,7,1,5] => 0
{{1,7},{2},{3},{4},{5,6}} => [7,2,3,4,6,5,1] => [2,3,4,5,7,1,6] => 0
{{1,7},{2},{3},{4},{5},{6}} => [7,2,3,4,5,6,1] => [1,2,3,4,5,6,7] => 0
{{1,6},{2,5},{3,4},{7,8}} => [6,5,4,3,2,1,8,7] => [7,6,5,4,3,2,8,1] => 9
{{1,8},{2,5},{3,6},{4,7}} => [8,5,6,7,2,3,4,1] => [2,6,7,8,1,3,4,5] => 0
{{1,5},{2,6},{3,7},{4,8}} => [5,6,7,8,1,2,3,4] => [1,6,7,8,2,3,4,5] => 0
{{1},{2},{3,4},{5,6},{7},{8}} => [1,2,4,3,6,5,7,8] => [3,1,5,4,7,6,8,2] => 2
{{1},{2,4},{3},{5,8},{6,7}} => [1,4,3,2,8,7,6,5] => [5,4,3,2,1,8,7,6] => 5
{{1,3},{2},{4},{5},{6,8},{7}} => [3,2,1,4,5,8,7,6] => [4,3,5,1,6,2,8,7] => 1
{{1,3},{2},{4,6,8},{5},{7}} => [3,2,1,6,5,8,7,4] => [4,3,7,6,2,1,8,5] => 3
{{1,3,5,6},{2},{4},{7,8}} => [3,2,5,4,6,1,8,7] => [4,3,6,5,7,2,8,1] => 3
{{1,4},{2,3},{5,8},{6},{7}} => [4,3,2,1,8,6,7,5] => [5,4,3,2,7,1,8,6] => 4
{{1,7},{2,6},{3,5},{4},{8}} => [7,6,5,4,3,2,1,8] => [8,7,6,5,4,3,1,2] => 11
{{1,5},{2,6,7},{3},{4,8}} => [5,6,3,8,1,7,2,4] => [6,7,1,4,2,8,3,5] => 2
{{1,2},{3,5,7},{4,6,8}} => [2,1,5,6,7,8,3,4] => [3,6,1,7,8,2,4,5] => 0
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Description
The number of nestings in the permutation.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
inverse toric promotion
Description
Toric promotion of a permutation.
Let $\sigma\in\mathfrak S_n$ be a permutation and let
$ \tau_{i, j}(\sigma) = \begin{cases} \sigma & \text{if $|\sigma^{-1}(i) - \sigma^{-1}(j)| = 1$}\\ (i, j)\circ\sigma & \text{otherwise}. \end{cases} $
The toric promotion operator is the product $\tau_{n,1}\tau_{n-1,n}\dots\tau_{1,2}$.
This is the special case of toric promotion on graphs for the path graph. Its order is $n-1$.