Identifier
Values
[1,0] => [2,1] => [2,1] => {{1,2}} => 1
[1,0,1,0] => [3,1,2] => [2,3,1] => {{1,2,3}} => 2
[1,1,0,0] => [2,3,1] => [3,1,2] => {{1,3},{2}} => 2
[1,0,1,0,1,0] => [4,1,2,3] => [2,3,4,1] => {{1,2,3,4}} => 3
[1,0,1,1,0,0] => [3,1,4,2] => [2,4,1,3] => {{1,2,4},{3}} => 3
[1,1,0,0,1,0] => [2,4,1,3] => [3,1,4,2] => {{1,3,4},{2}} => 3
[1,1,0,1,0,0] => [4,3,1,2] => [3,4,2,1] => {{1,3},{2,4}} => 4
[1,1,1,0,0,0] => [2,3,4,1] => [4,1,2,3] => {{1,4},{2},{3}} => 3
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [2,3,4,5,1] => {{1,2,3,4,5}} => 4
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [2,3,5,1,4] => {{1,2,3,5},{4}} => 4
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [2,4,1,5,3] => {{1,2,4,5},{3}} => 4
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [2,4,5,3,1] => {{1,2,4},{3,5}} => 5
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [2,5,1,3,4] => {{1,2,5},{3},{4}} => 4
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [3,1,4,5,2] => {{1,3,4,5},{2}} => 4
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [3,1,5,2,4] => {{1,3,5},{2},{4}} => 4
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [3,4,2,5,1] => {{1,3},{2,4,5}} => 5
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [3,4,5,2,1] => {{1,3,5},{2,4}} => 6
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [3,5,2,1,4] => {{1,3},{2,5},{4}} => 5
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [4,1,2,5,3] => {{1,4,5},{2},{3}} => 4
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [4,1,5,3,2] => {{1,4},{2},{3,5}} => 5
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [4,5,2,3,1] => {{1,4},{2,5},{3}} => 6
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [5,1,2,3,4] => {{1,5},{2},{3},{4}} => 4
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}} => 5
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [2,3,4,6,1,5] => {{1,2,3,4,6},{5}} => 5
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [2,3,5,1,6,4] => {{1,2,3,5,6},{4}} => 5
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [2,3,5,6,4,1] => {{1,2,3,5},{4,6}} => 6
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [2,3,6,1,4,5] => {{1,2,3,6},{4},{5}} => 5
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [2,4,1,5,6,3] => {{1,2,4,5,6},{3}} => 5
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [2,4,1,6,3,5] => {{1,2,4,6},{3},{5}} => 5
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [2,4,5,3,6,1] => {{1,2,4},{3,5,6}} => 6
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [2,4,5,6,3,1] => {{1,2,4,6},{3,5}} => 7
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [2,4,6,3,1,5] => {{1,2,4},{3,6},{5}} => 6
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [2,5,1,3,6,4] => {{1,2,5,6},{3},{4}} => 5
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [2,5,1,6,4,3] => {{1,2,5},{3},{4,6}} => 6
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [2,5,6,3,4,1] => {{1,2,5},{3,6},{4}} => 7
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [2,6,1,3,4,5] => {{1,2,6},{3},{4},{5}} => 5
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [3,1,4,5,6,2] => {{1,3,4,5,6},{2}} => 5
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [3,1,4,6,2,5] => {{1,3,4,6},{2},{5}} => 5
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [3,1,5,2,6,4] => {{1,3,5,6},{2},{4}} => 5
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [3,1,5,6,4,2] => {{1,3,5},{2},{4,6}} => 6
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [3,1,6,2,4,5] => {{1,3,6},{2},{4},{5}} => 5
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => {{1,3},{2,4,5,6}} => 6
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [3,4,2,6,1,5] => {{1,3},{2,4,6},{5}} => 6
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => {{1,3,5,6},{2,4}} => 7
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [3,4,5,6,1,2] => {{1,3,5},{2,4,6}} => 8
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [3,4,6,2,1,5] => {{1,3,6},{2,4},{5}} => 7
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [3,5,2,1,6,4] => {{1,3},{2,5,6},{4}} => 6
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [3,5,2,6,4,1] => {{1,3},{2,5},{4,6}} => 7
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [3,5,6,2,4,1] => {{1,3,6},{2,5},{4}} => 8
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [3,6,2,1,4,5] => {{1,3},{2,6},{4},{5}} => 6
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [4,1,2,5,6,3] => {{1,4,5,6},{2},{3}} => 5
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [4,1,2,6,3,5] => {{1,4,6},{2},{3},{5}} => 5
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [4,1,5,3,6,2] => {{1,4},{2},{3,5,6}} => 6
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [4,1,5,6,3,2] => {{1,4,6},{2},{3,5}} => 7
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [4,1,6,3,2,5] => {{1,4},{2},{3,6},{5}} => 6
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [4,5,2,3,6,1] => {{1,4},{2,5,6},{3}} => 7
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [4,5,2,6,3,1] => {{1,4,6},{2,5},{3}} => 8
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [4,5,6,3,2,1] => {{1,4},{2,5},{3,6}} => 9
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [4,6,2,3,1,5] => {{1,4},{2,6},{3},{5}} => 7
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [5,1,2,3,6,4] => {{1,5,6},{2},{3},{4}} => 5
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [5,1,2,6,4,3] => {{1,5},{2},{3},{4,6}} => 6
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [5,1,6,3,4,2] => {{1,5},{2},{3,6},{4}} => 7
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [5,6,2,3,4,1] => {{1,5},{2,6},{3},{4}} => 8
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => {{1,6},{2},{3},{4},{5}} => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => {{1,2,3,4,5,6,7}} => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [2,3,4,5,7,1,6] => {{1,2,3,4,5,7},{6}} => 6
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [2,3,4,6,1,7,5] => {{1,2,3,4,6,7},{5}} => 6
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => [2,3,4,6,7,5,1] => {{1,2,3,4,6},{5,7}} => 7
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [2,3,4,7,1,5,6] => {{1,2,3,4,7},{5},{6}} => 6
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [2,3,5,1,6,7,4] => {{1,2,3,5,6,7},{4}} => 6
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [2,3,5,1,7,4,6] => {{1,2,3,5,7},{4},{6}} => 6
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => [2,3,5,6,4,7,1] => {{1,2,3,5},{4,6,7}} => 7
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => [2,3,5,6,7,4,1] => {{1,2,3,5,7},{4,6}} => 8
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => [2,3,5,7,4,1,6] => {{1,2,3,5},{4,7},{6}} => 7
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [2,3,6,1,4,7,5] => {{1,2,3,6,7},{4},{5}} => 6
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => [2,3,6,1,7,5,4] => {{1,2,3,6},{4},{5,7}} => 7
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => [2,3,6,7,4,5,1] => {{1,2,3,6},{4,7},{5}} => 8
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [2,3,7,1,4,5,6] => {{1,2,3,7},{4},{5},{6}} => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [2,4,1,5,6,7,3] => {{1,2,4,5,6,7},{3}} => 6
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [2,4,1,5,7,3,6] => {{1,2,4,5,7},{3},{6}} => 6
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [2,4,1,6,3,7,5] => {{1,2,4,6,7},{3},{5}} => 6
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => [2,4,1,6,7,5,3] => {{1,2,4,6},{3},{5,7}} => 7
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [2,4,1,7,3,5,6] => {{1,2,4,7},{3},{5},{6}} => 6
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => [2,4,5,3,6,7,1] => {{1,2,4},{3,5,6,7}} => 7
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => [2,4,5,3,7,1,6] => {{1,2,4},{3,5,7},{6}} => 7
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => [2,4,5,6,3,7,1] => {{1,2,4,6,7},{3,5}} => 8
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [2,4,5,6,7,1,3] => {{1,2,4,6},{3,5,7}} => 9
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => [2,4,5,7,3,1,6] => {{1,2,4,7},{3,5},{6}} => 8
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => [2,4,6,3,1,7,5] => {{1,2,4},{3,6,7},{5}} => 7
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => [2,4,6,3,7,5,1] => {{1,2,4},{3,6},{5,7}} => 8
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => [2,4,6,7,3,5,1] => {{1,2,4,7},{3,6},{5}} => 9
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => [2,4,7,3,1,5,6] => {{1,2,4},{3,7},{5},{6}} => 7
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [2,5,1,3,6,7,4] => {{1,2,5,6,7},{3},{4}} => 6
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [2,5,1,3,7,4,6] => {{1,2,5,7},{3},{4},{6}} => 6
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => [2,5,1,6,4,7,3] => {{1,2,5},{3},{4,6,7}} => 7
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [2,5,1,6,7,4,3] => {{1,2,5,7},{3},{4,6}} => 8
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => [2,5,1,7,4,3,6] => {{1,2,5},{3},{4,7},{6}} => 7
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => [2,5,6,3,4,7,1] => {{1,2,5},{3,6,7},{4}} => 8
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [2,5,6,3,7,4,1] => {{1,2,5,7},{3,6},{4}} => 9
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => [2,5,6,7,4,3,1] => {{1,2,5},{3,6},{4,7}} => 10
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => [2,5,7,3,4,1,6] => {{1,2,5},{3,7},{4},{6}} => 8
>>> Load all 205 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [2,6,1,3,4,7,5] => {{1,2,6,7},{3},{4},{5}} => 6
[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [2,6,1,3,7,5,4] => {{1,2,6},{3},{4},{5,7}} => 7
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [2,6,1,7,4,5,3] => {{1,2,6},{3},{4,7},{5}} => 8
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => [2,6,7,3,4,5,1] => {{1,2,6},{3,7},{4},{5}} => 9
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [2,7,1,3,4,5,6] => {{1,2,7},{3},{4},{5},{6}} => 6
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [3,1,4,5,6,7,2] => {{1,3,4,5,6,7},{2}} => 6
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [3,1,4,5,7,2,6] => {{1,3,4,5,7},{2},{6}} => 6
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [3,1,4,6,2,7,5] => {{1,3,4,6,7},{2},{5}} => 6
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => [3,1,4,6,7,5,2] => {{1,3,4,6},{2},{5,7}} => 7
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [3,1,4,7,2,5,6] => {{1,3,4,7},{2},{5},{6}} => 6
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [3,1,5,2,6,7,4] => {{1,3,5,6,7},{2},{4}} => 6
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [3,1,5,2,7,4,6] => {{1,3,5,7},{2},{4},{6}} => 6
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => [3,1,5,6,4,7,2] => {{1,3,5},{2},{4,6,7}} => 7
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [3,1,5,6,7,4,2] => {{1,3,5,7},{2},{4,6}} => 8
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4] => [3,1,5,7,4,2,6] => {{1,3,5},{2},{4,7},{6}} => 7
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [3,1,6,2,4,7,5] => {{1,3,6,7},{2},{4},{5}} => 6
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => [3,1,6,2,7,5,4] => {{1,3,6},{2},{4},{5,7}} => 7
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [3,1,6,7,4,5,2] => {{1,3,6},{2},{4,7},{5}} => 8
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [3,1,7,2,4,5,6] => {{1,3,7},{2},{4},{5},{6}} => 6
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => [3,4,2,5,6,7,1] => {{1,3},{2,4,5,6,7}} => 7
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => [3,4,2,5,7,1,6] => {{1,3},{2,4,5,7},{6}} => 7
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => [3,4,2,6,1,7,5] => {{1,3},{2,4,6,7},{5}} => 7
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => [3,4,2,6,7,5,1] => {{1,3},{2,4,6},{5,7}} => 8
[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4] => [3,4,2,7,1,5,6] => {{1,3},{2,4,7},{5},{6}} => 7
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => [3,4,5,2,6,7,1] => {{1,3,5,6,7},{2,4}} => 8
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => [3,4,5,2,7,1,6] => {{1,3,5,7},{2,4},{6}} => 8
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => [3,4,5,6,1,7,2] => {{1,3,5},{2,4,6,7}} => 9
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => [3,4,5,6,7,2,1] => {{1,3,5,7},{2,4,6}} => 10
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => [3,4,5,7,1,2,6] => {{1,3,5},{2,4,7},{6}} => 9
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => [3,4,6,2,1,7,5] => {{1,3,6,7},{2,4},{5}} => 8
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => [3,4,6,2,7,5,1] => {{1,3,6},{2,4},{5,7}} => 9
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [3,4,6,7,1,5,2] => {{1,3,6},{2,4,7},{5}} => 10
[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3] => [3,4,7,2,1,5,6] => {{1,3,7},{2,4},{5},{6}} => 8
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => [3,5,2,1,6,7,4] => {{1,3},{2,5,6,7},{4}} => 7
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => [3,5,2,1,7,4,6] => {{1,3},{2,5,7},{4},{6}} => 7
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => [3,5,2,6,4,7,1] => {{1,3},{2,5},{4,6,7}} => 8
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => [3,5,2,6,7,4,1] => {{1,3},{2,5,7},{4,6}} => 9
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => [3,5,2,7,4,1,6] => {{1,3},{2,5},{4,7},{6}} => 8
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [3,5,6,2,4,7,1] => {{1,3,6,7},{2,5},{4}} => 9
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => [3,5,6,2,7,4,1] => {{1,3,6},{2,5,7},{4}} => 10
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [3,5,6,7,4,1,2] => {{1,3,6},{2,5},{4,7}} => 11
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => [3,5,7,2,4,1,6] => {{1,3,7},{2,5},{4},{6}} => 9
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [3,6,2,1,4,7,5] => {{1,3},{2,6,7},{4},{5}} => 7
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [3,6,2,1,7,5,4] => {{1,3},{2,6},{4},{5,7}} => 8
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => [3,6,2,7,4,5,1] => {{1,3},{2,6},{4,7},{5}} => 9
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [3,6,7,2,4,5,1] => {{1,3,7},{2,6},{4},{5}} => 10
[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [3,7,2,1,4,5,6] => {{1,3},{2,7},{4},{5},{6}} => 7
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [4,1,2,5,6,7,3] => {{1,4,5,6,7},{2},{3}} => 6
[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [4,1,2,5,7,3,6] => {{1,4,5,7},{2},{3},{6}} => 6
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [4,1,2,6,3,7,5] => {{1,4,6,7},{2},{3},{5}} => 6
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => [4,1,2,6,7,5,3] => {{1,4,6},{2},{3},{5,7}} => 7
[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [4,1,2,7,3,5,6] => {{1,4,7},{2},{3},{5},{6}} => 6
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => [4,1,5,3,6,7,2] => {{1,4},{2},{3,5,6,7}} => 7
[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5] => [4,1,5,3,7,2,6] => {{1,4},{2},{3,5,7},{6}} => 7
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => [4,1,5,6,3,7,2] => {{1,4,6,7},{2},{3,5}} => 8
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => [4,1,5,6,7,2,3] => {{1,4,6},{2},{3,5,7}} => 9
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => [4,1,5,7,3,2,6] => {{1,4,7},{2},{3,5},{6}} => 8
[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6] => [4,1,6,3,2,7,5] => {{1,4},{2},{3,6,7},{5}} => 7
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => [4,1,6,3,7,5,2] => {{1,4},{2},{3,6},{5,7}} => 8
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => [4,1,6,7,3,5,2] => {{1,4,7},{2},{3,6},{5}} => 9
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3] => [4,1,7,3,2,5,6] => {{1,4},{2},{3,7},{5},{6}} => 7
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => [4,5,2,3,6,7,1] => {{1,4},{2,5,6,7},{3}} => 8
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => [4,5,2,3,7,1,6] => {{1,4},{2,5,7},{3},{6}} => 8
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => [4,5,2,6,3,7,1] => {{1,4,6,7},{2,5},{3}} => 9
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => [4,5,2,6,7,1,3] => {{1,4,6},{2,5,7},{3}} => 10
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [4,5,2,7,3,1,6] => {{1,4,7},{2,5},{3},{6}} => 9
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => [4,5,6,3,2,7,1] => {{1,4},{2,5},{3,6,7}} => 10
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [4,5,6,3,7,1,2] => {{1,4},{2,5,7},{3,6}} => 11
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => [4,5,6,7,3,1,2] => {{1,4,7},{2,5},{3,6}} => 12
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => [4,5,7,3,2,1,6] => {{1,4},{2,5},{3,7},{6}} => 10
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => [4,6,2,3,1,7,5] => {{1,4},{2,6,7},{3},{5}} => 8
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => [4,6,2,3,7,5,1] => {{1,4},{2,6},{3},{5,7}} => 9
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => [4,6,2,7,3,5,1] => {{1,4,7},{2,6},{3},{5}} => 10
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => [4,6,7,3,2,5,1] => {{1,4},{2,6},{3,7},{5}} => 11
[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2] => [4,7,2,3,1,5,6] => {{1,4},{2,7},{3},{5},{6}} => 8
[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => [5,1,2,3,6,7,4] => {{1,5,6,7},{2},{3},{4}} => 6
[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [5,1,2,3,7,4,6] => {{1,5,7},{2},{3},{4},{6}} => 6
[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6] => [5,1,2,6,4,7,3] => {{1,5},{2},{3},{4,6,7}} => 7
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => [5,1,2,6,7,4,3] => {{1,5,7},{2},{3},{4,6}} => 8
[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4] => [5,1,2,7,4,3,6] => {{1,5},{2},{3},{4,7},{6}} => 7
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => [5,1,6,3,4,7,2] => {{1,5},{2},{3,6,7},{4}} => 8
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => [5,1,6,3,7,4,2] => {{1,5,7},{2},{3,6},{4}} => 9
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => [5,1,6,7,4,3,2] => {{1,5},{2},{3,6},{4,7}} => 10
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3] => [5,1,7,3,4,2,6] => {{1,5},{2},{3,7},{4},{6}} => 8
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [5,6,2,3,4,7,1] => {{1,5},{2,6,7},{3},{4}} => 9
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => [5,6,2,3,7,4,1] => {{1,5,7},{2,6},{3},{4}} => 10
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => [5,6,2,7,4,3,1] => {{1,5},{2,6},{3},{4,7}} => 11
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => [5,6,7,3,4,2,1] => {{1,5},{2,6},{3,7},{4}} => 12
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => [5,7,2,3,4,1,6] => {{1,5},{2,7},{3},{4},{6}} => 9
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [6,1,2,3,4,7,5] => {{1,6,7},{2},{3},{4},{5}} => 6
[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5] => [6,1,2,3,7,5,4] => {{1,6},{2},{3},{4},{5,7}} => 7
[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4] => [6,1,2,7,4,5,3] => {{1,6},{2},{3},{4,7},{5}} => 8
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => [6,1,7,3,4,5,2] => {{1,6},{2},{3,7},{4},{5}} => 9
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => [6,7,2,3,4,5,1] => {{1,6},{2,7},{3},{4},{5}} => 10
[1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => {{1,7},{2},{3},{4},{5},{6}} => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,1,2,3,4,5,6,7] => [2,3,4,5,6,7,8,1] => {{1,2,3,4,5,6,7,8}} => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [2,3,4,5,6,8,1,7] => {{1,2,3,4,5,6,8},{7}} => 7
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [6,1,2,3,4,8,5,7] => [2,3,4,5,7,1,8,6] => {{1,2,3,4,5,7,8},{6}} => 7
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => [2,3,5,1,6,7,8,4] => {{1,2,3,5,6,7,8},{4}} => 7
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [2,4,1,5,6,7,8,3] => {{1,2,4,5,6,7,8},{3}} => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => [3,1,4,5,6,7,8,2] => {{1,3,4,5,6,7,8},{2}} => 7
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,3,1,2,4,5,6,7] => [3,4,2,5,6,7,8,1] => {{1,3},{2,4,5,6,7,8}} => 8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,4,1,2,3,5,6,7] => [3,4,5,2,6,7,8,1] => {{1,3,5,6,7,8},{2,4}} => 9
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,3,8,1,4,5,6,7] => [4,1,2,5,6,7,8,3] => {{1,4,5,6,7,8},{2},{3}} => 7
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Description
The dimension of a set partition.
This is the sum of the lengths of the arcs of a set partition. Equivalently, one obtains that this is the sum of the maximal entries of the blocks minus the sum of the minimal entries of the blocks.
A slightly shifted definition of the dimension is St000572The dimension exponent of a set partition..
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
weak exceedance partition
Description
The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
Map
inverse
Description
Sends a permutation to its inverse.