Processing math: 100%

Identifier
Values
[1,0] => [1] => {{1}} => 1
[1,0,1,0] => [1,2] => {{1},{2}} => 2
[1,1,0,0] => [2,1] => {{1,2}} => 2
[1,0,1,0,1,0] => [1,2,3] => {{1},{2},{3}} => 3
[1,0,1,1,0,0] => [1,3,2] => {{1},{2,3}} => 3
[1,1,0,0,1,0] => [2,1,3] => {{1,2},{3}} => 3
[1,1,0,1,0,0] => [2,3,1] => {{1,2,3}} => 3
[1,1,1,0,0,0] => [3,2,1] => {{1,3},{2}} => 4
[1,0,1,0,1,0,1,0] => [1,2,3,4] => {{1},{2},{3},{4}} => 4
[1,0,1,0,1,1,0,0] => [1,2,4,3] => {{1},{2},{3,4}} => 4
[1,0,1,1,0,0,1,0] => [1,3,2,4] => {{1},{2,3},{4}} => 4
[1,0,1,1,0,1,0,0] => [1,3,4,2] => {{1},{2,3,4}} => 4
[1,0,1,1,1,0,0,0] => [1,4,3,2] => {{1},{2,4},{3}} => 5
[1,1,0,0,1,0,1,0] => [2,1,3,4] => {{1,2},{3},{4}} => 4
[1,1,0,0,1,1,0,0] => [2,1,4,3] => {{1,2},{3,4}} => 4
[1,1,0,1,0,0,1,0] => [2,3,1,4] => {{1,2,3},{4}} => 4
[1,1,0,1,0,1,0,0] => [2,3,4,1] => {{1,2,3,4}} => 4
[1,1,0,1,1,0,0,0] => [2,4,3,1] => {{1,2,4},{3}} => 5
[1,1,1,0,0,0,1,0] => [3,2,1,4] => {{1,3},{2},{4}} => 5
[1,1,1,0,0,1,0,0] => [3,2,4,1] => {{1,3,4},{2}} => 5
[1,1,1,0,1,0,0,0] => [4,2,3,1] => {{1,4},{2},{3}} => 6
[1,1,1,1,0,0,0,0] => [4,3,2,1] => {{1,4},{2,3}} => 6
[1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}} => 5
[1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => {{1},{2},{3},{4,5}} => 5
[1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => {{1},{2},{3,4},{5}} => 5
[1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => {{1},{2},{3,4,5}} => 5
[1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => {{1},{2},{3,5},{4}} => 6
[1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => {{1},{2,3},{4},{5}} => 5
[1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => {{1},{2,3},{4,5}} => 5
[1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => {{1},{2,3,4},{5}} => 5
[1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => {{1},{2,3,4,5}} => 5
[1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => {{1},{2,3,5},{4}} => 6
[1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => {{1},{2,4},{3},{5}} => 6
[1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => {{1},{2,4,5},{3}} => 6
[1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => {{1},{2,5},{3},{4}} => 7
[1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => {{1},{2,5},{3,4}} => 7
[1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => {{1,2},{3},{4},{5}} => 5
[1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => {{1,2},{3},{4,5}} => 5
[1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => {{1,2},{3,4},{5}} => 5
[1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => {{1,2},{3,4,5}} => 5
[1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => {{1,2},{3,5},{4}} => 6
[1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => {{1,2,3},{4},{5}} => 5
[1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => {{1,2,3},{4,5}} => 5
[1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => {{1,2,3,4},{5}} => 5
[1,1,0,1,0,1,0,1,0,0] => [2,3,4,5,1] => {{1,2,3,4,5}} => 5
[1,1,0,1,0,1,1,0,0,0] => [2,3,5,4,1] => {{1,2,3,5},{4}} => 6
[1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => {{1,2,4},{3},{5}} => 6
[1,1,0,1,1,0,0,1,0,0] => [2,4,3,5,1] => {{1,2,4,5},{3}} => 6
[1,1,0,1,1,0,1,0,0,0] => [2,5,3,4,1] => {{1,2,5},{3},{4}} => 7
[1,1,0,1,1,1,0,0,0,0] => [2,5,4,3,1] => {{1,2,5},{3,4}} => 7
[1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => {{1,3},{2},{4},{5}} => 6
[1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => {{1,3},{2},{4,5}} => 6
[1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => {{1,3,4},{2},{5}} => 6
[1,1,1,0,0,1,0,1,0,0] => [3,2,4,5,1] => {{1,3,4,5},{2}} => 6
[1,1,1,0,0,1,1,0,0,0] => [3,2,5,4,1] => {{1,3,5},{2},{4}} => 7
[1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => {{1,4},{2},{3},{5}} => 7
[1,1,1,0,1,0,0,1,0,0] => [4,2,3,5,1] => {{1,4,5},{2},{3}} => 7
[1,1,1,0,1,0,1,0,0,0] => [5,2,3,4,1] => {{1,5},{2},{3},{4}} => 8
[1,1,1,0,1,1,0,0,0,0] => [5,2,4,3,1] => {{1,5},{2},{3,4}} => 8
[1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => {{1,4},{2,3},{5}} => 7
[1,1,1,1,0,0,0,1,0,0] => [4,3,2,5,1] => {{1,4,5},{2,3}} => 7
[1,1,1,1,0,0,1,0,0,0] => [5,3,2,4,1] => {{1,5},{2,3},{4}} => 8
[1,1,1,1,0,1,0,0,0,0] => [5,3,4,2,1] => {{1,5},{2,3,4}} => 8
[1,1,1,1,1,0,0,0,0,0] => [5,4,3,2,1] => {{1,5},{2,4},{3}} => 9
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}} => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}} => 6
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}} => 6
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,2,3,5,6,4] => {{1},{2},{3},{4,5,6}} => 6
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,2,3,6,5,4] => {{1},{2},{3},{4,6},{5}} => 7
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}} => 6
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}} => 6
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,2,4,5,3,6] => {{1},{2},{3,4,5},{6}} => 6
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,2,4,5,6,3] => {{1},{2},{3,4,5,6}} => 6
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,2,4,6,5,3] => {{1},{2},{3,4,6},{5}} => 7
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,2,5,4,3,6] => {{1},{2},{3,5},{4},{6}} => 7
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,2,5,4,6,3] => {{1},{2},{3,5,6},{4}} => 7
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,2,6,4,5,3] => {{1},{2},{3,6},{4},{5}} => 8
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,2,6,5,4,3] => {{1},{2},{3,6},{4,5}} => 8
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}} => 6
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}} => 6
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}} => 6
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,3,2,5,6,4] => {{1},{2,3},{4,5,6}} => 6
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,3,2,6,5,4] => {{1},{2,3},{4,6},{5}} => 7
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,3,4,2,5,6] => {{1},{2,3,4},{5},{6}} => 6
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,3,4,2,6,5] => {{1},{2,3,4},{5,6}} => 6
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,3,4,5,2,6] => {{1},{2,3,4,5},{6}} => 6
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,3,4,5,6,2] => {{1},{2,3,4,5,6}} => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,3,4,6,5,2] => {{1},{2,3,4,6},{5}} => 7
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,3,5,4,2,6] => {{1},{2,3,5},{4},{6}} => 7
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,3,5,4,6,2] => {{1},{2,3,5,6},{4}} => 7
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,3,6,4,5,2] => {{1},{2,3,6},{4},{5}} => 8
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,3,6,5,4,2] => {{1},{2,3,6},{4,5}} => 8
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,4,3,2,5,6] => {{1},{2,4},{3},{5},{6}} => 7
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,4,3,2,6,5] => {{1},{2,4},{3},{5,6}} => 7
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,4,3,5,2,6] => {{1},{2,4,5},{3},{6}} => 7
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,4,3,5,6,2] => {{1},{2,4,5,6},{3}} => 7
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,4,3,6,5,2] => {{1},{2,4,6},{3},{5}} => 8
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,5,3,4,2,6] => {{1},{2,5},{3},{4},{6}} => 8
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,5,3,4,6,2] => {{1},{2,5,6},{3},{4}} => 8
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,6,3,4,5,2] => {{1},{2,6},{3},{4},{5}} => 9
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,6,3,5,4,2] => {{1},{2,6},{3},{4,5}} => 9
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,5,4,3,2,6] => {{1},{2,5},{3,4},{6}} => 8
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,5,4,3,6,2] => {{1},{2,5,6},{3,4}} => 8
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,6,4,3,5,2] => {{1},{2,6},{3,4},{5}} => 9
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,6,4,5,3,2] => {{1},{2,6},{3,4,5}} => 9
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,6,5,4,3,2] => {{1},{2,6},{3,5},{4}} => 10
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,3,4,5,6] => {{1,2},{3},{4},{5},{6}} => 6
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,1,3,4,6,5] => {{1,2},{3},{4},{5,6}} => 6
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,3,5,4,6] => {{1,2},{3},{4,5},{6}} => 6
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,1,3,5,6,4] => {{1,2},{3},{4,5,6}} => 6
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,1,3,6,5,4] => {{1,2},{3},{4,6},{5}} => 7
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => {{1,2},{3,4},{5},{6}} => 6
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,1,4,3,6,5] => {{1,2},{3,4},{5,6}} => 6
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => {{1,2},{3,4,5},{6}} => 6
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,1,4,5,6,3] => {{1,2},{3,4,5,6}} => 6
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,1,4,6,5,3] => {{1,2},{3,4,6},{5}} => 7
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,4,3,6] => {{1,2},{3,5},{4},{6}} => 7
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,1,5,4,6,3] => {{1,2},{3,5,6},{4}} => 7
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,1,6,4,5,3] => {{1,2},{3,6},{4},{5}} => 8
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,1,6,5,4,3] => {{1,2},{3,6},{4,5}} => 8
[1,1,0,1,0,0,1,0,1,0,1,0] => [2,3,1,4,5,6] => {{1,2,3},{4},{5},{6}} => 6
[1,1,0,1,0,0,1,0,1,1,0,0] => [2,3,1,4,6,5] => {{1,2,3},{4},{5,6}} => 6
[1,1,0,1,0,0,1,1,0,0,1,0] => [2,3,1,5,4,6] => {{1,2,3},{4,5},{6}} => 6
[1,1,0,1,0,0,1,1,0,1,0,0] => [2,3,1,5,6,4] => {{1,2,3},{4,5,6}} => 6
[1,1,0,1,0,0,1,1,1,0,0,0] => [2,3,1,6,5,4] => {{1,2,3},{4,6},{5}} => 7
[1,1,0,1,0,1,0,0,1,0,1,0] => [2,3,4,1,5,6] => {{1,2,3,4},{5},{6}} => 6
[1,1,0,1,0,1,0,0,1,1,0,0] => [2,3,4,1,6,5] => {{1,2,3,4},{5,6}} => 6
[1,1,0,1,0,1,0,1,0,0,1,0] => [2,3,4,5,1,6] => {{1,2,3,4,5},{6}} => 6
[1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}} => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,4,6,5,1] => {{1,2,3,4,6},{5}} => 7
[1,1,0,1,0,1,1,0,0,0,1,0] => [2,3,5,4,1,6] => {{1,2,3,5},{4},{6}} => 7
[1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,5,4,6,1] => {{1,2,3,5,6},{4}} => 7
[1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,6,4,5,1] => {{1,2,3,6},{4},{5}} => 8
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,6,5,4,1] => {{1,2,3,6},{4,5}} => 8
[1,1,0,1,1,0,0,0,1,0,1,0] => [2,4,3,1,5,6] => {{1,2,4},{3},{5},{6}} => 7
[1,1,0,1,1,0,0,0,1,1,0,0] => [2,4,3,1,6,5] => {{1,2,4},{3},{5,6}} => 7
[1,1,0,1,1,0,0,1,0,0,1,0] => [2,4,3,5,1,6] => {{1,2,4,5},{3},{6}} => 7
[1,1,0,1,1,0,0,1,0,1,0,0] => [2,4,3,5,6,1] => {{1,2,4,5,6},{3}} => 7
[1,1,0,1,1,0,0,1,1,0,0,0] => [2,4,3,6,5,1] => {{1,2,4,6},{3},{5}} => 8
[1,1,0,1,1,0,1,0,0,0,1,0] => [2,5,3,4,1,6] => {{1,2,5},{3},{4},{6}} => 8
[1,1,0,1,1,0,1,0,0,1,0,0] => [2,5,3,4,6,1] => {{1,2,5,6},{3},{4}} => 8
[1,1,0,1,1,0,1,0,1,0,0,0] => [2,6,3,4,5,1] => {{1,2,6},{3},{4},{5}} => 9
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,6,3,5,4,1] => {{1,2,6},{3},{4,5}} => 9
[1,1,0,1,1,1,0,0,0,0,1,0] => [2,5,4,3,1,6] => {{1,2,5},{3,4},{6}} => 8
[1,1,0,1,1,1,0,0,0,1,0,0] => [2,5,4,3,6,1] => {{1,2,5,6},{3,4}} => 8
[1,1,0,1,1,1,0,0,1,0,0,0] => [2,6,4,3,5,1] => {{1,2,6},{3,4},{5}} => 9
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,6,4,5,3,1] => {{1,2,6},{3,4,5}} => 9
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,6,5,4,3,1] => {{1,2,6},{3,5},{4}} => 10
[1,1,1,0,0,0,1,0,1,0,1,0] => [3,2,1,4,5,6] => {{1,3},{2},{4},{5},{6}} => 7
[1,1,1,0,0,0,1,0,1,1,0,0] => [3,2,1,4,6,5] => {{1,3},{2},{4},{5,6}} => 7
[1,1,1,0,0,0,1,1,0,0,1,0] => [3,2,1,5,4,6] => {{1,3},{2},{4,5},{6}} => 7
[1,1,1,0,0,0,1,1,0,1,0,0] => [3,2,1,5,6,4] => {{1,3},{2},{4,5,6}} => 7
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,2,1,6,5,4] => {{1,3},{2},{4,6},{5}} => 8
[1,1,1,0,0,1,0,0,1,0,1,0] => [3,2,4,1,5,6] => {{1,3,4},{2},{5},{6}} => 7
[1,1,1,0,0,1,0,0,1,1,0,0] => [3,2,4,1,6,5] => {{1,3,4},{2},{5,6}} => 7
[1,1,1,0,0,1,0,1,0,0,1,0] => [3,2,4,5,1,6] => {{1,3,4,5},{2},{6}} => 7
[1,1,1,0,0,1,0,1,0,1,0,0] => [3,2,4,5,6,1] => {{1,3,4,5,6},{2}} => 7
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,2,4,6,5,1] => {{1,3,4,6},{2},{5}} => 8
[1,1,1,0,0,1,1,0,0,0,1,0] => [3,2,5,4,1,6] => {{1,3,5},{2},{4},{6}} => 8
[1,1,1,0,0,1,1,0,0,1,0,0] => [3,2,5,4,6,1] => {{1,3,5,6},{2},{4}} => 8
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,6,4,5,1] => {{1,3,6},{2},{4},{5}} => 9
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,2,6,5,4,1] => {{1,3,6},{2},{4,5}} => 9
[1,1,1,0,1,0,0,0,1,0,1,0] => [4,2,3,1,5,6] => {{1,4},{2},{3},{5},{6}} => 8
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,2,3,1,6,5] => {{1,4},{2},{3},{5,6}} => 8
[1,1,1,0,1,0,0,1,0,0,1,0] => [4,2,3,5,1,6] => {{1,4,5},{2},{3},{6}} => 8
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,2,3,5,6,1] => {{1,4,5,6},{2},{3}} => 8
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,2,3,6,5,1] => {{1,4,6},{2},{3},{5}} => 9
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,3,4,1,6] => {{1,5},{2},{3},{4},{6}} => 9
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,2,3,4,6,1] => {{1,5,6},{2},{3},{4}} => 9
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,2,3,4,5,1] => {{1,6},{2},{3},{4},{5}} => 10
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,2,3,5,4,1] => {{1,6},{2},{3},{4,5}} => 10
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,2,4,3,1,6] => {{1,5},{2},{3,4},{6}} => 9
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,4,3,6,1] => {{1,5,6},{2},{3,4}} => 9
[1,1,1,0,1,1,0,0,1,0,0,0] => [6,2,4,3,5,1] => {{1,6},{2},{3,4},{5}} => 10
[1,1,1,0,1,1,0,1,0,0,0,0] => [6,2,4,5,3,1] => {{1,6},{2},{3,4,5}} => 10
[1,1,1,0,1,1,1,0,0,0,0,0] => [6,2,5,4,3,1] => {{1,6},{2},{3,5},{4}} => 11
[1,1,1,1,0,0,0,0,1,0,1,0] => [4,3,2,1,5,6] => {{1,4},{2,3},{5},{6}} => 8
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,3,2,1,6,5] => {{1,4},{2,3},{5,6}} => 8
[1,1,1,1,0,0,0,1,0,0,1,0] => [4,3,2,5,1,6] => {{1,4,5},{2,3},{6}} => 8
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3,2,5,6,1] => {{1,4,5,6},{2,3}} => 8
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,3,2,6,5,1] => {{1,4,6},{2,3},{5}} => 9
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,3,2,4,1,6] => {{1,5},{2,3},{4},{6}} => 9
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => {{1,5,6},{2,3},{4}} => 9
[1,1,1,1,0,0,1,0,1,0,0,0] => [6,3,2,4,5,1] => {{1,6},{2,3},{4},{5}} => 10
[1,1,1,1,0,0,1,1,0,0,0,0] => [6,3,2,5,4,1] => {{1,6},{2,3},{4,5}} => 10
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,3,4,2,1,6] => {{1,5},{2,3,4},{6}} => 9
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,3,4,2,6,1] => {{1,5,6},{2,3,4}} => 9
[1,1,1,1,0,1,0,0,1,0,0,0] => [6,3,4,2,5,1] => {{1,6},{2,3,4},{5}} => 10
[1,1,1,1,0,1,0,1,0,0,0,0] => [6,3,4,5,2,1] => {{1,6},{2,3,4,5}} => 10
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,5,4,2,1] => {{1,6},{2,3,5},{4}} => 11
[1,1,1,1,1,0,0,0,0,0,1,0] => [5,4,3,2,1,6] => {{1,5},{2,4},{3},{6}} => 10
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,4,3,2,6,1] => {{1,5,6},{2,4},{3}} => 10
[1,1,1,1,1,0,0,0,1,0,0,0] => [6,4,3,2,5,1] => {{1,6},{2,4},{3},{5}} => 11
[1,1,1,1,1,0,0,1,0,0,0,0] => [6,4,3,5,2,1] => {{1,6},{2,4,5},{3}} => 11
[1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,3,4,2,1] => {{1,6},{2,5},{3},{4}} => 12
[1,1,1,1,1,1,0,0,0,0,0,0] => [6,5,4,3,2,1] => {{1,6},{2,5},{3,4}} => 12
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Description
Sum of the difference between the maximal and the minimal elements of the blocks plus the number of blocks of a set partition.
This is, for a set partition P={B1,,Bk} of {1,,n}, the statistic is
d(P)=i(max(Bi)min(Bi)+1).
This statistic is called dimension index in [2]
Map
to non-crossing permutation
Description
Sends a Dyck path D with valley at positions {(i1,j1),,(ik,jk)} to the unique non-crossing permutation π having descents {i1,,ik} and whose inverse has descents {j1,,jk}.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to n(n1) minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
to cycle type
Description
Let π=c1cr a permutation of size n decomposed in its cyclic parts. The associated set partition of [n] then is S=S1Sr such that Si is the set of integers in the cycle ci.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].