Identifier
Values
{{1}} => [1] => [1,0] => [[1],[]] => 0
{{1,2}} => [2,1] => [1,1,0,0] => [[2],[]] => 0
{{1},{2}} => [1,2] => [1,0,1,0] => [[1,1],[]] => 0
{{1,2,3}} => [2,3,1] => [1,1,0,1,0,0] => [[3],[]] => 0
{{1,2},{3}} => [2,1,3] => [1,1,0,0,1,0] => [[2,2],[1]] => 0
{{1,3},{2}} => [3,2,1] => [1,1,1,0,0,0] => [[2,2],[]] => 1
{{1},{2,3}} => [1,3,2] => [1,0,1,1,0,0] => [[2,1],[]] => 0
{{1},{2},{3}} => [1,2,3] => [1,0,1,0,1,0] => [[1,1,1],[]] => 0
{{1,2,3,4}} => [2,3,4,1] => [1,1,0,1,0,1,0,0] => [[4],[]] => 0
{{1,2,3},{4}} => [2,3,1,4] => [1,1,0,1,0,0,1,0] => [[3,3],[2]] => 0
{{1,2,4},{3}} => [2,4,3,1] => [1,1,0,1,1,0,0,0] => [[3,3],[1]] => 1
{{1,2},{3,4}} => [2,1,4,3] => [1,1,0,0,1,1,0,0] => [[3,2],[1]] => 0
{{1,2},{3},{4}} => [2,1,3,4] => [1,1,0,0,1,0,1,0] => [[2,2,2],[1,1]] => 0
{{1,3,4},{2}} => [3,2,4,1] => [1,1,1,0,0,1,0,0] => [[3,2],[]] => 1
{{1,3},{2,4}} => [3,4,1,2] => [1,1,1,0,1,0,0,0] => [[2,2,2],[]] => 2
{{1,3},{2},{4}} => [3,2,1,4] => [1,1,1,0,0,0,1,0] => [[2,2,2],[1]] => 1
{{1,4},{2,3}} => [4,3,2,1] => [1,1,1,1,0,0,0,0] => [[3,3],[]] => 2
{{1},{2,3,4}} => [1,3,4,2] => [1,0,1,1,0,1,0,0] => [[3,1],[]] => 0
{{1},{2,3},{4}} => [1,3,2,4] => [1,0,1,1,0,0,1,0] => [[2,2,1],[1]] => 0
{{1,4},{2},{3}} => [4,2,3,1] => [1,1,1,1,0,0,0,0] => [[3,3],[]] => 2
{{1},{2,4},{3}} => [1,4,3,2] => [1,0,1,1,1,0,0,0] => [[2,2,1],[]] => 1
{{1},{2},{3,4}} => [1,2,4,3] => [1,0,1,0,1,1,0,0] => [[2,1,1],[]] => 0
{{1},{2},{3},{4}} => [1,2,3,4] => [1,0,1,0,1,0,1,0] => [[1,1,1,1],[]] => 0
{{1,2,3,4,5}} => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [[5],[]] => 0
{{1,2,3,4},{5}} => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => [[4,4],[3]] => 0
{{1,2,3,5},{4}} => [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => [[4,4],[2]] => 1
{{1,2,3},{4,5}} => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => [[4,3],[2]] => 0
{{1,2,3},{4},{5}} => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => [[3,3,3],[2,2]] => 0
{{1,2,4,5},{3}} => [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => [[4,3],[1]] => 1
{{1,2,4},{3,5}} => [2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => [[3,3,3],[1,1]] => 2
{{1,2,4},{3},{5}} => [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => [[3,3,3],[2,1]] => 1
{{1,2,5},{3,4}} => [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0] => [[4,4],[1]] => 2
{{1,2},{3,4,5}} => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => [[4,2],[1]] => 0
{{1,2},{3,4},{5}} => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => [[3,3,2],[2,1]] => 0
{{1,2,5},{3},{4}} => [2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0] => [[4,4],[1]] => 2
{{1,2},{3,5},{4}} => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => [[3,3,2],[1,1]] => 1
{{1,2},{3},{4,5}} => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => [[3,2,2],[1,1]] => 0
{{1,2},{3},{4},{5}} => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2],[1,1,1]] => 0
{{1,3,4,5},{2}} => [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => [[4,2],[]] => 1
{{1,3,4},{2},{5}} => [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => [[3,3,2],[2]] => 1
{{1,3},{2,4,5}} => [3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0] => [[3,2,2],[]] => 2
{{1,3},{2,4},{5}} => [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2],[1]] => 2
{{1,3,5},{2},{4}} => [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => [[3,3,2],[1]] => 2
{{1,3},{2},{4,5}} => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => [[3,2,2],[1]] => 1
{{1,3},{2},{4},{5}} => [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2],[1,1]] => 1
{{1,4,5},{2,3}} => [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0] => [[4,3],[]] => 2
{{1,4},{2,3},{5}} => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0] => [[3,3,3],[2]] => 2
{{1},{2,3,4,5}} => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => [[4,1],[]] => 0
{{1},{2,3,4},{5}} => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => [[3,3,1],[2]] => 0
{{1},{2,3,5},{4}} => [1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0] => [[3,3,1],[1]] => 1
{{1},{2,3},{4,5}} => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => [[3,2,1],[1]] => 0
{{1},{2,3},{4},{5}} => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1],[1,1]] => 0
{{1,4,5},{2},{3}} => [4,2,3,5,1] => [1,1,1,1,0,0,0,1,0,0] => [[4,3],[]] => 2
{{1,4},{2},{3},{5}} => [4,2,3,1,5] => [1,1,1,1,0,0,0,0,1,0] => [[3,3,3],[2]] => 2
{{1},{2,4,5},{3}} => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => [[3,2,1],[]] => 1
{{1},{2,4},{3,5}} => [1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1],[]] => 2
{{1},{2,4},{3},{5}} => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1],[1]] => 1
{{1},{2,5},{3,4}} => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0] => [[3,3,1],[]] => 2
{{1},{2},{3,4,5}} => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => [[3,1,1],[]] => 0
{{1},{2},{3,4},{5}} => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1],[1]] => 0
{{1},{2,5},{3},{4}} => [1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0] => [[3,3,1],[]] => 2
{{1},{2},{3,5},{4}} => [1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1],[]] => 1
{{1},{2},{3},{4,5}} => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1],[]] => 0
{{1},{2},{3},{4},{5}} => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1],[]] => 0
{{1,2,3,4,5,6}} => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [[6],[]] => 0
{{1,2,3,4,5},{6}} => [2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5],[4]] => 0
{{1,2,3,4,6},{5}} => [2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => [[5,5],[3]] => 1
{{1,2,3,4},{5,6}} => [2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4],[3]] => 0
{{1,2,3,4},{5},{6}} => [2,3,4,1,5,6] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4],[3,3]] => 0
{{1,2,3,5,6},{4}} => [2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => [[5,4],[2]] => 1
{{1,2,3,5},{4},{6}} => [2,3,5,4,1,6] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[4,4,4],[3,2]] => 1
{{1,2,3},{4,5,6}} => [2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3],[2]] => 0
{{1,2,3},{4,5},{6}} => [2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3],[3,2]] => 0
{{1,2,3},{4,6},{5}} => [2,3,1,6,5,4] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[4,4,3],[2,2]] => 1
{{1,2,3},{4},{5,6}} => [2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3],[2,2]] => 0
{{1,2,3},{4},{5},{6}} => [2,3,1,4,5,6] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3],[2,2,2]] => 0
{{1,2,4,5,6},{3}} => [2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => [[5,3],[1]] => 1
{{1,2,4,5},{3},{6}} => [2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[4,4,3],[3,1]] => 1
{{1,2,4},{3},{5,6}} => [2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[4,3,3],[2,1]] => 1
{{1,2,4},{3},{5},{6}} => [2,4,3,1,5,6] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2,1]] => 1
{{1,2},{3,4,5,6}} => [2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2],[1]] => 0
{{1,2},{3,4,5},{6}} => [2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2],[3,1]] => 0
{{1,2},{3,4,6},{5}} => [2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[4,4,2],[2,1]] => 1
{{1,2},{3,4},{5,6}} => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2],[2,1]] => 0
{{1,2},{3,4},{5},{6}} => [2,1,4,3,5,6] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2,1]] => 0
{{1,2},{3,5,6},{4}} => [2,1,5,4,6,3] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[4,3,2],[1,1]] => 1
{{1,2},{3,5},{4},{6}} => [2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1,1]] => 1
{{1,2},{3},{4,5,6}} => [2,1,3,5,6,4] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2],[1,1]] => 0
{{1,2},{3},{4,5},{6}} => [2,1,3,5,4,6] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1,1]] => 0
{{1,2},{3},{4,6},{5}} => [2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1,1]] => 1
{{1,2},{3},{4},{5,6}} => [2,1,3,4,6,5] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1,1]] => 0
{{1,2},{3},{4},{5},{6}} => [2,1,3,4,5,6] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1,1]] => 0
{{1,3,4,5,6},{2}} => [3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2],[]] => 1
{{1,3,4,5},{2},{6}} => [3,2,4,5,1,6] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[4,4,2],[3]] => 1
{{1,3,4},{2},{5,6}} => [3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[4,3,2],[2]] => 1
{{1,3,4},{2},{5},{6}} => [3,2,4,1,5,6] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2]] => 1
{{1,3},{2},{4,5,6}} => [3,2,1,5,6,4] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[4,2,2],[1]] => 1
{{1,3},{2},{4,5},{6}} => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1]] => 1
{{1,3},{2},{4},{5,6}} => [3,2,1,4,6,5] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1]] => 1
{{1,3},{2},{4},{5},{6}} => [3,2,1,4,5,6] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1]] => 1
{{1},{2,3,4,5,6}} => [1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1],[]] => 0
>>> Load all 192 entries. <<<
{{1},{2,3,4,5},{6}} => [1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1],[3]] => 0
{{1},{2,3,4,6},{5}} => [1,3,4,6,5,2] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[4,4,1],[2]] => 1
{{1},{2,3,4},{5,6}} => [1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1],[2]] => 0
{{1},{2,3,4},{5},{6}} => [1,3,4,2,5,6] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1],[2,2]] => 0
{{1},{2,3,5,6},{4}} => [1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[4,3,1],[1]] => 1
{{1},{2,3,5},{4},{6}} => [1,3,5,4,2,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[3,3,3,1],[2,1]] => 1
{{1},{2,3},{4,5,6}} => [1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1],[1]] => 0
{{1},{2,3},{4,5},{6}} => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1],[2,1]] => 0
{{1},{2,3},{4,6},{5}} => [1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[3,3,2,1],[1,1]] => 1
{{1},{2,3},{4},{5,6}} => [1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1],[1,1]] => 0
{{1},{2,3},{4},{5},{6}} => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1],[1,1,1]] => 0
{{1},{2,4,5,6},{3}} => [1,4,3,5,6,2] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1],[]] => 1
{{1},{2,4,5},{3},{6}} => [1,4,3,5,2,6] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[3,3,2,1],[2]] => 1
{{1},{2,4},{3},{5,6}} => [1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[3,2,2,1],[1]] => 1
{{1},{2,4},{3},{5},{6}} => [1,4,3,2,5,6] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2,1],[1,1]] => 1
{{1},{2},{3,4,5,6}} => [1,2,4,5,6,3] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1],[]] => 0
{{1},{2},{3,4,5},{6}} => [1,2,4,5,3,6] => [1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1],[2]] => 0
{{1},{2},{3,4,6},{5}} => [1,2,4,6,5,3] => [1,0,1,0,1,1,0,1,1,0,0,0] => [[3,3,1,1],[1]] => 1
{{1},{2},{3,4},{5,6}} => [1,2,4,3,6,5] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1],[1]] => 0
{{1},{2},{3,4},{5},{6}} => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1],[1,1]] => 0
{{1},{2},{3,5,6},{4}} => [1,2,5,4,6,3] => [1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1],[]] => 1
{{1},{2},{3,5},{4},{6}} => [1,2,5,4,3,6] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1,1],[1]] => 1
{{1},{2},{3},{4,5,6}} => [1,2,3,5,6,4] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1],[]] => 0
{{1},{2},{3},{4,5},{6}} => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1],[1]] => 0
{{1},{2},{3},{4,6},{5}} => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1],[]] => 1
{{1},{2},{3},{4},{5,6}} => [1,2,3,4,6,5] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1],[]] => 0
{{1},{2},{3},{4},{5},{6}} => [1,2,3,4,5,6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1],[]] => 0
{{1,2,3,4,5,6,7}} => [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7],[]] => 0
{{1,2,3,4,5,6},{7}} => [2,3,4,5,6,1,7] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[6,6],[5]] => 0
{{1,2,3,4,5},{6,7}} => [2,3,4,5,1,7,6] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[6,5],[4]] => 0
{{1,2,3,4,5},{6},{7}} => [2,3,4,5,1,6,7] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5],[4,4]] => 0
{{1,2,3,4},{5,6,7}} => [2,3,4,1,6,7,5] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[6,4],[3]] => 0
{{1,2,3,4},{5,6},{7}} => [2,3,4,1,6,5,7] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4],[4,3]] => 0
{{1,2,3,4},{5},{6,7}} => [2,3,4,1,5,7,6] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4],[3,3]] => 0
{{1,2,3,4},{5},{6},{7}} => [2,3,4,1,5,6,7] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4],[3,3,3]] => 0
{{1,2,3},{4,5,6,7}} => [2,3,1,5,6,7,4] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[6,3],[2]] => 0
{{1,2,3},{4,5,6},{7}} => [2,3,1,5,6,4,7] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3],[4,2]] => 0
{{1,2,3},{4,5},{6,7}} => [2,3,1,5,4,7,6] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3],[3,2]] => 0
{{1,2,3},{4,5},{6},{7}} => [2,3,1,5,4,6,7] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3,2]] => 0
{{1,2,3},{4},{5,6,7}} => [2,3,1,4,6,7,5] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3],[2,2]] => 0
{{1,2,3},{4},{5,6},{7}} => [2,3,1,4,6,5,7] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2,2]] => 0
{{1,2,3},{4},{5},{6,7}} => [2,3,1,4,5,7,6] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3],[2,2,2]] => 0
{{1,2,3},{4},{5},{6},{7}} => [2,3,1,4,5,6,7] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2,2]] => 0
{{1,2},{3,4,5,6,7}} => [2,1,4,5,6,7,3] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[6,2],[1]] => 0
{{1,2},{3,4,5,6},{7}} => [2,1,4,5,6,3,7] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[5,5,2],[4,1]] => 0
{{1,2},{3,4,5},{6,7}} => [2,1,4,5,3,7,6] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2],[3,1]] => 0
{{1,2},{3,4,5},{6},{7}} => [2,1,4,5,3,6,7] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2],[3,3,1]] => 0
{{1,2},{3,4},{5,6,7}} => [2,1,4,3,6,7,5] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2],[2,1]] => 0
{{1,2},{3,4},{5,6},{7}} => [2,1,4,3,6,5,7] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2],[3,2,1]] => 0
{{1,2},{3,4},{5},{6,7}} => [2,1,4,3,5,7,6] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2],[2,2,1]] => 0
{{1,2},{3,4},{5},{6},{7}} => [2,1,4,3,5,6,7] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2],[2,2,2,1]] => 0
{{1,2},{3},{4,5,6,7}} => [2,1,3,5,6,7,4] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[5,2,2],[1,1]] => 0
{{1,2},{3},{4,5,6},{7}} => [2,1,3,5,6,4,7] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2],[3,1,1]] => 0
{{1,2},{3},{4,5},{6,7}} => [2,1,3,5,4,7,6] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2],[2,1,1]] => 0
{{1,2},{3},{4,5},{6},{7}} => [2,1,3,5,4,6,7] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2],[2,2,1,1]] => 0
{{1,2},{3},{4},{5,6,7}} => [2,1,3,4,6,7,5] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2],[1,1,1]] => 0
{{1,2},{3},{4},{5,6},{7}} => [2,1,3,4,6,5,7] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2],[2,1,1,1]] => 0
{{1,2},{3},{4},{5},{6,7}} => [2,1,3,4,5,7,6] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2],[1,1,1,1]] => 0
{{1,2},{3},{4},{5},{6},{7}} => [2,1,3,4,5,6,7] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1,1,1]] => 0
{{1},{2,3,4,5,6,7}} => [1,3,4,5,6,7,2] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1],[]] => 0
{{1},{2,3,4,5,6},{7}} => [1,3,4,5,6,2,7] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5,1],[4]] => 0
{{1},{2,3,4,5},{6,7}} => [1,3,4,5,2,7,6] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4,1],[3]] => 0
{{1},{2,3,4,5},{6},{7}} => [1,3,4,5,2,6,7] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4,1],[3,3]] => 0
{{1},{2,3,4},{5,6,7}} => [1,3,4,2,6,7,5] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3,1],[2]] => 0
{{1},{2,3,4},{5,6},{7}} => [1,3,4,2,6,5,7] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,1],[3,2]] => 0
{{1},{2,3,4},{5},{6,7}} => [1,3,4,2,5,7,6] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,1],[2,2]] => 0
{{1},{2,3,4},{5},{6},{7}} => [1,3,4,2,5,6,7] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,1],[2,2,2]] => 0
{{1},{2,3},{4,5,6,7}} => [1,3,2,5,6,7,4] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2,1],[1]] => 0
{{1},{2,3},{4,5,6},{7}} => [1,3,2,5,6,4,7] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1],[3,1]] => 0
{{1},{2,3},{4,5},{6,7}} => [1,3,2,5,4,7,6] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,1],[2,1]] => 0
{{1},{2,3},{4,5},{6},{7}} => [1,3,2,5,4,6,7] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,1],[2,2,1]] => 0
{{1},{2,3},{4},{5,6,7}} => [1,3,2,4,6,7,5] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,1],[1,1]] => 0
{{1},{2,3},{4},{5,6},{7}} => [1,3,2,4,6,5,7] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,1],[2,1,1]] => 0
{{1},{2,3},{4},{5},{6,7}} => [1,3,2,4,5,7,6] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,1],[1,1,1]] => 0
{{1},{2,3},{4},{5},{6},{7}} => [1,3,2,4,5,6,7] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1,1,1]] => 0
{{1},{2},{3,4,5,6,7}} => [1,2,4,5,6,7,3] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1],[]] => 0
{{1},{2},{3,4,5,6},{7}} => [1,2,4,5,6,3,7] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1,1],[3]] => 0
{{1},{2},{3,4,5},{6,7}} => [1,2,4,5,3,7,6] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1,1],[2]] => 0
{{1},{2},{3,4,5},{6},{7}} => [1,2,4,5,3,6,7] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1,1],[2,2]] => 0
{{1},{2},{3,4},{5,6,7}} => [1,2,4,3,6,7,5] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1,1],[1]] => 0
{{1},{2},{3,4},{5,6},{7}} => [1,2,4,3,6,5,7] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1],[2,1]] => 0
{{1},{2},{3,4},{5},{6,7}} => [1,2,4,3,5,7,6] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1],[1,1]] => 0
{{1},{2},{3,4},{5},{6},{7}} => [1,2,4,3,5,6,7] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1],[1,1,1]] => 0
{{1},{2},{3},{4,5,6,7}} => [1,2,3,5,6,7,4] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1],[]] => 0
{{1},{2},{3},{4,5,6},{7}} => [1,2,3,5,6,4,7] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1,1],[2]] => 0
{{1},{2},{3},{4,5},{6,7}} => [1,2,3,5,4,7,6] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1],[1]] => 0
{{1},{2},{3},{4,5},{6},{7}} => [1,2,3,5,4,6,7] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1],[1,1]] => 0
{{1},{2},{3},{4},{5,6,7}} => [1,2,3,4,6,7,5] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1],[]] => 0
{{1},{2},{3},{4},{5,6},{7}} => [1,2,3,4,6,5,7] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1,1],[1]] => 0
{{1},{2},{3},{4},{5},{6,7}} => [1,2,3,4,5,7,6] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1],[]] => 0
{{1},{2},{3},{4},{5},{6},{7}} => [1,2,3,4,5,6,7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1],[]] => 0
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Description
The number of two-by-two squares inside a skew partition.
This is, the number of cells $(i,j)$ in a skew partition for which the box $(i+1,j+1)$ is also a cell inside the skew partition.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
skew partition
Description
The parallelogram polyomino corresponding to a Dyck path, interpreted as a skew partition.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
This map returns the skew partition definded by the diagram of $\gamma(D)$.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.