Identifier
Values
[1,0] => [2,1] => [1,2] => {{1},{2}} => 2
[1,0,1,0] => [3,1,2] => [3,1,2] => {{1,2,3}} => 1
[1,1,0,0] => [2,3,1] => [1,2,3] => {{1},{2},{3}} => 3
[1,0,1,0,1,0] => [4,1,2,3] => [3,4,1,2] => {{1,3},{2,4}} => 1
[1,0,1,1,0,0] => [3,1,4,2] => [4,1,3,2] => {{1,2,4},{3}} => 2
[1,1,0,0,1,0] => [2,4,1,3] => [1,4,2,3] => {{1},{2,3,4}} => 2
[1,1,0,1,0,0] => [4,3,1,2] => [4,2,1,3] => {{1,3,4},{2}} => 2
[1,1,1,0,0,0] => [2,3,4,1] => [1,2,3,4] => {{1},{2},{3},{4}} => 4
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [3,4,5,1,2] => {{1,2,3,4,5}} => 1
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [3,5,1,4,2] => {{1,3},{2,5},{4}} => 2
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [4,1,5,3,2] => {{1,2,3,4,5}} => 1
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [4,5,3,1,2] => {{1,4},{2,5},{3}} => 2
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [5,1,3,4,2] => {{1,2,5},{3},{4}} => 3
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [1,4,5,2,3] => {{1},{2,4},{3,5}} => 2
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [1,5,2,4,3] => {{1},{2,3,5},{4}} => 3
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [4,2,5,1,3] => {{1,4},{2},{3,5}} => 2
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [4,5,2,1,3] => {{1,4},{2,3,5}} => 1
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [5,2,1,4,3] => {{1,3,5},{2},{4}} => 3
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [1,2,5,3,4] => {{1},{2},{3,4,5}} => 3
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [1,5,3,2,4] => {{1},{2,4,5},{3}} => 3
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [5,2,3,1,4] => {{1,4,5},{2},{3}} => 3
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}} => 5
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [3,4,5,6,1,2] => {{1,3,5},{2,4,6}} => 1
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [3,4,6,1,5,2] => {{1,2,3,4,6},{5}} => 2
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [3,5,1,6,4,2] => {{1,3},{2,4,5,6}} => 1
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [3,5,6,4,1,2] => {{1,2,3,5,6},{4}} => 2
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [3,6,1,4,5,2] => {{1,3},{2,6},{4},{5}} => 3
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [4,1,5,6,3,2] => {{1,2,4,6},{3,5}} => 1
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [4,1,6,3,5,2] => {{1,2,3,4,6},{5}} => 2
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [4,5,3,6,1,2] => {{1,2,4,5,6},{3}} => 2
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [4,5,6,3,1,2] => {{1,2,3,4,5,6}} => 1
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [4,6,3,1,5,2] => {{1,4},{2,6},{3},{5}} => 3
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [5,1,3,6,4,2] => {{1,2,4,5,6},{3}} => 2
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [5,1,6,4,3,2] => {{1,2,3,5,6},{4}} => 2
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [5,6,3,4,1,2] => {{1,5},{2,6},{3},{4}} => 3
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [6,1,3,4,5,2] => {{1,2,6},{3},{4},{5}} => 4
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [1,4,5,6,2,3] => {{1},{2,3,4,5,6}} => 2
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [1,4,6,2,5,3] => {{1},{2,4},{3,6},{5}} => 3
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [1,5,2,6,4,3] => {{1},{2,3,4,5,6}} => 2
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [1,5,6,4,2,3] => {{1},{2,5},{3,6},{4}} => 3
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [1,6,2,4,5,3] => {{1},{2,3,6},{4},{5}} => 4
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [4,2,5,6,1,3] => {{1,3,4,5,6},{2}} => 2
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [4,2,6,1,5,3] => {{1,4},{2},{3,6},{5}} => 3
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [4,5,2,6,1,3] => {{1,2,3,4,5,6}} => 1
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [4,5,6,1,2,3] => {{1,4},{2,5},{3,6}} => 1
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [4,6,2,1,5,3] => {{1,4},{2,3,6},{5}} => 2
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [5,2,1,6,4,3] => {{1,3,4,5,6},{2}} => 2
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [5,2,6,4,1,3] => {{1,5},{2},{3,6},{4}} => 3
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [5,6,2,4,1,3] => {{1,5},{2,3,6},{4}} => 2
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [6,2,1,4,5,3] => {{1,3,6},{2},{4},{5}} => 4
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [1,2,5,6,3,4] => {{1},{2},{3,5},{4,6}} => 3
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [1,2,6,3,5,4] => {{1},{2},{3,4,6},{5}} => 4
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [1,5,3,6,2,4] => {{1},{2,5},{3},{4,6}} => 3
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [1,5,6,3,2,4] => {{1},{2,5},{3,4,6}} => 2
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [1,6,3,2,5,4] => {{1},{2,4,6},{3},{5}} => 4
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [5,2,3,6,1,4] => {{1,5},{2},{3},{4,6}} => 3
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [5,2,6,3,1,4] => {{1,5},{2},{3,4,6}} => 2
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [5,6,3,2,1,4] => {{1,5},{2,4,6},{3}} => 2
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [6,2,3,1,5,4] => {{1,4,6},{2},{3},{5}} => 4
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [1,2,3,6,4,5] => {{1},{2},{3},{4,5,6}} => 4
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [1,2,6,4,3,5] => {{1},{2},{3,5,6},{4}} => 4
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [1,6,3,4,2,5] => {{1},{2,5,6},{3},{4}} => 4
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [6,2,3,4,1,5] => {{1,5,6},{2},{3},{4}} => 4
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}} => 6
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [3,4,5,6,7,1,2] => {{1,2,3,4,5,6,7}} => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [3,4,5,7,1,6,2] => {{1,3,5},{2,4,7},{6}} => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [3,4,6,1,7,5,2] => {{1,2,3,4,5,6,7}} => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => [3,4,6,7,5,1,2] => {{1,3,6},{2,4,7},{5}} => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [3,4,7,1,5,6,2] => {{1,2,3,4,7},{5},{6}} => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [3,5,1,6,7,4,2] => {{1,3},{2,5,7},{4,6}} => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [3,5,1,7,4,6,2] => {{1,3},{2,4,5,7},{6}} => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => [3,5,6,4,7,1,2] => {{1,3,6},{2,5,7},{4}} => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => [3,5,6,7,4,1,2] => {{1,3,6},{2,4,5,7}} => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => [3,5,7,4,1,6,2] => {{1,2,3,5,7},{4},{6}} => 3
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [3,6,1,4,7,5,2] => {{1,3},{2,5,6,7},{4}} => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => [3,6,1,7,5,4,2] => {{1,3},{2,4,6,7},{5}} => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => [3,6,7,4,5,1,2] => {{1,2,3,6,7},{4},{5}} => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [3,7,1,4,5,6,2] => {{1,3},{2,7},{4},{5},{6}} => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [4,1,5,6,7,3,2] => {{1,2,3,4,5,6,7}} => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [4,1,5,7,3,6,2] => {{1,2,4,7},{3,5},{6}} => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [4,1,6,3,7,5,2] => {{1,2,3,4,5,6,7}} => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => [4,1,6,7,5,3,2] => {{1,2,4,7},{3,6},{5}} => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [4,1,7,3,5,6,2] => {{1,2,3,4,7},{5},{6}} => 3
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => [4,5,3,6,7,1,2] => {{1,4,6},{2,5,7},{3}} => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => [4,5,3,7,1,6,2] => {{1,2,4,5,7},{3},{6}} => 3
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => [4,5,6,3,7,1,2] => {{1,3,4,6},{2,5,7}} => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [4,5,6,7,1,3,2] => {{1,2,4,5,7},{3,6}} => 1
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => [4,5,7,3,1,6,2] => {{1,2,3,4,5,7},{6}} => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => [4,6,3,1,7,5,2] => {{1,4},{2,5,6,7},{3}} => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => [4,6,3,7,5,1,2] => {{1,2,4,6,7},{3},{5}} => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => [4,6,7,3,5,1,2] => {{1,2,3,4,6,7},{5}} => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => [4,7,3,1,5,6,2] => {{1,4},{2,7},{3},{5},{6}} => 4
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [5,1,3,6,7,4,2] => {{1,2,5,7},{3},{4,6}} => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [5,1,3,7,4,6,2] => {{1,2,4,5,7},{3},{6}} => 3
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => [5,1,6,4,7,3,2] => {{1,2,5,7},{3,6},{4}} => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [5,1,6,7,4,3,2] => {{1,2,4,5,7},{3,6}} => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => [5,1,7,4,3,6,2] => {{1,2,3,5,7},{4},{6}} => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => [5,6,3,4,7,1,2] => {{1,2,5,6,7},{3},{4}} => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [5,6,3,7,4,1,2] => {{1,2,4,5,6,7},{3}} => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => [5,6,7,4,3,1,2] => {{1,2,3,5,6,7},{4}} => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => [5,7,3,4,1,6,2] => {{1,5},{2,7},{3},{4},{6}} => 4
>>> Load all 249 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [6,1,3,4,7,5,2] => {{1,2,5,6,7},{3},{4}} => 3
[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [6,1,3,7,5,4,2] => {{1,2,4,6,7},{3},{5}} => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [6,1,7,4,5,3,2] => {{1,2,3,6,7},{4},{5}} => 3
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => [6,7,3,4,5,1,2] => {{1,6},{2,7},{3},{4},{5}} => 4
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [7,1,3,4,5,6,2] => {{1,2,7},{3},{4},{5},{6}} => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [1,4,5,6,7,2,3] => {{1},{2,4,6},{3,5,7}} => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [1,4,5,7,2,6,3] => {{1},{2,3,4,5,7},{6}} => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [1,4,6,2,7,5,3] => {{1},{2,4},{3,5,6,7}} => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => [1,4,6,7,5,2,3] => {{1},{2,3,4,6,7},{5}} => 3
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [1,4,7,2,5,6,3] => {{1},{2,4},{3,7},{5},{6}} => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [1,5,2,6,7,4,3] => {{1},{2,3,5,7},{4,6}} => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [1,5,2,7,4,6,3] => {{1},{2,3,4,5,7},{6}} => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => [1,5,6,4,7,2,3] => {{1},{2,3,5,6,7},{4}} => 3
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [1,5,6,7,4,2,3] => {{1},{2,3,4,5,6,7}} => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4] => [1,5,7,4,2,6,3] => {{1},{2,5},{3,7},{4},{6}} => 4
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [1,6,2,4,7,5,3] => {{1},{2,3,5,6,7},{4}} => 3
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => [1,6,2,7,5,4,3] => {{1},{2,3,4,6,7},{5}} => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [1,6,7,4,5,2,3] => {{1},{2,6},{3,7},{4},{5}} => 4
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [1,7,2,4,5,6,3] => {{1},{2,3,7},{4},{5},{6}} => 5
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => [4,2,5,6,7,1,3] => {{1,4,6},{2},{3,5,7}} => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => [4,2,5,7,1,6,3] => {{1,3,4,5,7},{2},{6}} => 3
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => [4,2,6,1,7,5,3] => {{1,4},{2},{3,5,6,7}} => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => [4,2,6,7,5,1,3] => {{1,3,4,6,7},{2},{5}} => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4] => [4,2,7,1,5,6,3] => {{1,4},{2},{3,7},{5},{6}} => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => [4,5,2,6,7,1,3] => {{1,4,6},{2,3,5,7}} => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => [4,5,2,7,1,6,3] => {{1,2,3,4,5,7},{6}} => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => [4,5,6,1,7,2,3] => {{1,4},{2,3,5,6,7}} => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => [4,5,6,7,2,1,3] => {{1,3,4,6,7},{2,5}} => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => [4,5,7,1,2,6,3] => {{1,4},{2,5},{3,7},{6}} => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => [4,6,2,1,7,5,3] => {{1,4},{2,3,5,6,7}} => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => [4,6,2,7,5,1,3] => {{1,2,3,4,6,7},{5}} => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [4,6,7,1,5,2,3] => {{1,4},{2,6},{3,7},{5}} => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3] => [4,7,2,1,5,6,3] => {{1,4},{2,3,7},{5},{6}} => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => [5,2,1,6,7,4,3] => {{1,3,5,7},{2},{4,6}} => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => [5,2,1,7,4,6,3] => {{1,3,4,5,7},{2},{6}} => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => [5,2,6,4,7,1,3] => {{1,3,5,6,7},{2},{4}} => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => [5,2,6,7,4,1,3] => {{1,3,4,5,6,7},{2}} => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => [5,2,7,4,1,6,3] => {{1,5},{2},{3,7},{4},{6}} => 4
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [5,6,2,4,7,1,3] => {{1,2,3,5,6,7},{4}} => 2
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => [5,6,2,7,4,1,3] => {{1,2,3,4,5,6,7}} => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [5,6,7,4,1,2,3] => {{1,5},{2,6},{3,7},{4}} => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => [5,7,2,4,1,6,3] => {{1,5},{2,3,7},{4},{6}} => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [6,2,1,4,7,5,3] => {{1,3,5,6,7},{2},{4}} => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [6,2,1,7,5,4,3] => {{1,3,4,6,7},{2},{5}} => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => [6,2,7,4,5,1,3] => {{1,6},{2},{3,7},{4},{5}} => 4
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [6,7,2,4,5,1,3] => {{1,6},{2,3,7},{4},{5}} => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [7,2,1,4,5,6,3] => {{1,3,7},{2},{4},{5},{6}} => 5
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [1,2,5,6,7,3,4] => {{1},{2},{3,4,5,6,7}} => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [1,2,5,7,3,6,4] => {{1},{2},{3,5},{4,7},{6}} => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [1,2,6,3,7,5,4] => {{1},{2},{3,4,5,6,7}} => 3
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => [1,2,6,7,5,3,4] => {{1},{2},{3,6},{4,7},{5}} => 4
[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [1,2,7,3,5,6,4] => {{1},{2},{3,4,7},{5},{6}} => 5
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => [1,5,3,6,7,2,4] => {{1},{2,4,5,6,7},{3}} => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5] => [1,5,3,7,2,6,4] => {{1},{2,5},{3},{4,7},{6}} => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => [1,5,6,3,7,2,4] => {{1},{2,3,4,5,6,7}} => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => [1,5,6,7,2,3,4] => {{1},{2,5},{3,6},{4,7}} => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => [1,5,7,3,2,6,4] => {{1},{2,5},{3,4,7},{6}} => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6] => [1,6,3,2,7,5,4] => {{1},{2,4,5,6,7},{3}} => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => [1,6,3,7,5,2,4] => {{1},{2,6},{3},{4,7},{5}} => 4
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => [1,6,7,3,5,2,4] => {{1},{2,6},{3,4,7},{5}} => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3] => [1,7,3,2,5,6,4] => {{1},{2,4,7},{3},{5},{6}} => 5
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => [5,2,3,6,7,1,4] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => [5,2,3,7,1,6,4] => {{1,5},{2},{3},{4,7},{6}} => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => [5,2,6,3,7,1,4] => {{1,3,4,5,6,7},{2}} => 2
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => [5,2,6,7,1,3,4] => {{1,5},{2},{3,6},{4,7}} => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [5,2,7,3,1,6,4] => {{1,5},{2},{3,4,7},{6}} => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => [5,6,3,2,7,1,4] => {{1,2,4,5,6,7},{3}} => 2
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [5,6,3,7,1,2,4] => {{1,5},{2,6},{3},{4,7}} => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => [5,6,7,3,1,2,4] => {{1,5},{2,6},{3,4,7}} => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => [5,7,3,2,1,6,4] => {{1,5},{2,4,7},{3},{6}} => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => [6,2,3,1,7,5,4] => {{1,4,5,6,7},{2},{3}} => 3
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => [6,2,3,7,5,1,4] => {{1,6},{2},{3},{4,7},{5}} => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => [6,2,7,3,5,1,4] => {{1,6},{2},{3,4,7},{5}} => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => [6,7,3,2,5,1,4] => {{1,6},{2,4,7},{3},{5}} => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2] => [7,2,3,1,5,6,4] => {{1,4,7},{2},{3},{5},{6}} => 5
[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => [1,2,3,6,7,4,5] => {{1},{2},{3},{4,6},{5,7}} => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [1,2,3,7,4,6,5] => {{1},{2},{3},{4,5,7},{6}} => 5
[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6] => [1,2,6,4,7,3,5] => {{1},{2},{3,6},{4},{5,7}} => 4
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => [1,2,6,7,4,3,5] => {{1},{2},{3,6},{4,5,7}} => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4] => [1,2,7,4,3,6,5] => {{1},{2},{3,5,7},{4},{6}} => 5
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => [1,6,3,4,7,2,5] => {{1},{2,6},{3},{4},{5,7}} => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => [1,6,3,7,4,2,5] => {{1},{2,6},{3},{4,5,7}} => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => [1,6,7,4,3,2,5] => {{1},{2,6},{3,5,7},{4}} => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3] => [1,7,3,4,2,6,5] => {{1},{2,5,7},{3},{4},{6}} => 5
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [6,2,3,4,7,1,5] => {{1,6},{2},{3},{4},{5,7}} => 4
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => [6,2,3,7,4,1,5] => {{1,6},{2},{3},{4,5,7}} => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => [6,2,7,4,3,1,5] => {{1,6},{2},{3,5,7},{4}} => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => [6,7,3,4,2,1,5] => {{1,6},{2,5,7},{3},{4}} => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => [7,2,3,4,1,6,5] => {{1,5,7},{2},{3},{4},{6}} => 5
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [1,2,3,4,7,5,6] => {{1},{2},{3},{4},{5,6,7}} => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5] => [1,2,3,7,5,4,6] => {{1},{2},{3},{4,6,7},{5}} => 5
[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4] => [1,2,7,4,5,3,6] => {{1},{2},{3,6,7},{4},{5}} => 5
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => [1,7,3,4,5,2,6] => {{1},{2,6,7},{3},{4},{5}} => 5
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => [7,2,3,4,5,1,6] => {{1,6,7},{2},{3},{4},{5}} => 5
[1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => {{1},{2},{3},{4},{5},{6},{7}} => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,1,2,3,4,5,8,6] => [3,4,5,6,8,1,7,2] => {{1,2,3,4,5,6,8},{7}} => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [8,1,2,3,4,7,5,6] => [3,4,5,7,8,6,1,2] => {{1,2,3,4,5,7,8},{6}} => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [5,1,2,3,8,4,6,7] => [3,4,6,1,7,8,5,2] => {{1,2,3,4,6,8},{5,7}} => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [5,1,2,3,7,4,8,6] => [3,4,6,1,8,5,7,2] => {{1,2,3,4,5,6,8},{7}} => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,1,2,3,6,4,5,7] => [3,4,6,7,5,8,1,2] => {{1,2,3,4,6,7,8},{5}} => 2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [8,1,2,3,7,4,5,6] => [3,4,6,7,8,5,1,2] => {{1,2,3,4,5,6,7,8}} => 1
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => [3,4,7,1,5,8,6,2] => {{1,2,3,4,6,7,8},{5}} => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [5,1,2,3,8,7,4,6] => [3,4,7,1,8,6,5,2] => {{1,2,3,4,5,7,8},{6}} => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [4,1,2,8,3,5,6,7] => [3,5,1,6,7,8,4,2] => {{1,3},{2,4,5,6,7,8}} => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [3,5,1,7,4,8,6,2] => {{1,3},{2,4,5,6,7,8}} => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,1,2,5,3,4,6,7] => [3,5,6,4,7,8,1,2] => {{1,2,3,5,6,7,8},{4}} => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [3,1,7,2,4,5,8,6] => [4,1,5,6,8,3,7,2] => {{1,2,3,4,5,6,8},{7}} => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,6,2,4,8,5,7] => [4,1,5,7,3,8,6,2] => {{1,2,4,6,7,8},{3,5}} => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [3,1,8,2,4,7,5,6] => [4,1,5,7,8,6,3,2] => {{1,2,3,4,5,7,8},{6}} => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [3,1,5,2,7,4,8,6] => [4,1,6,3,8,5,7,2] => {{1,2,3,4,5,6,8},{7}} => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [3,1,8,2,7,4,5,6] => [4,1,6,7,8,5,3,2] => {{1,2,3,4,5,6,7,8}} => 1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,2,6,8,4,7] => [4,1,7,3,5,8,6,2] => {{1,2,3,4,6,7,8},{5}} => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,1,4,2,3,5,6,7] => [4,5,3,6,7,8,1,2] => {{1,2,4,5,6,7,8},{3}} => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,1,5,2,3,4,6,7] => [4,5,6,3,7,8,1,2] => {{1,2,3,4,5,6,7,8}} => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [6,1,8,2,3,4,5,7] => [4,5,6,7,1,8,3,2] => {{1,2,3,4,5,6,7,8}} => 1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [6,1,5,2,3,8,4,7] => [4,5,7,3,1,8,6,2] => {{1,2,3,4,5,6,7,8}} => 1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [3,1,6,5,2,8,4,7] => [5,1,7,4,3,8,6,2] => {{1,2,3,5,6,7,8},{4}} => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [7,1,8,6,2,3,4,5] => [5,6,7,8,4,1,3,2] => {{1,2,4,5,6,8},{3,7}} => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,8,1,3,4,5,6,7] => [1,4,5,6,7,8,2,3] => {{1},{2,3,4,5,6,7,8}} => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [2,4,1,8,3,5,6,7] => [1,5,2,6,7,8,4,3] => {{1},{2,3,4,5,6,7,8}} => 2
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,8,5,7] => [1,5,2,7,4,8,6,3] => {{1},{2,3,4,5,6,7,8}} => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [2,7,1,6,3,4,8,5] => [1,5,6,8,4,2,7,3] => {{1},{2,3,4,5,6,8},{7}} => 3
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [2,8,1,6,3,7,4,5] => [1,5,7,8,4,6,2,3] => {{1},{2,3,4,5,7,8},{6}} => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,3,1,2,4,5,6,7] => [4,2,5,6,7,8,1,3] => {{1,3,4,5,6,7,8},{2}} => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [6,3,1,2,4,8,5,7] => [4,2,5,7,1,8,6,3] => {{1,3,4,5,6,7,8},{2}} => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,4,1,2,3,5,6,7] => [4,5,2,6,7,8,1,3] => {{1,2,3,4,5,6,7,8}} => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [5,8,1,2,7,3,4,6] => [4,6,7,1,8,5,2,3] => {{1,4},{2,3,5,6,7,8}} => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [4,3,1,8,2,5,6,7] => [5,2,1,6,7,8,4,3] => {{1,3,4,5,6,7,8},{2}} => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,4,1,8,2,3,5,6] => [5,6,2,7,8,1,4,3] => {{1,2,3,5,6,8},{4,7}} => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [7,4,1,6,2,3,8,5] => [5,6,2,8,4,1,7,3] => {{1,2,3,4,5,6,8},{7}} => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [8,7,1,6,2,3,4,5] => [5,6,7,8,4,2,1,3] => {{1,3,4,5,7,8},{2,6}} => 1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [8,4,1,6,2,7,3,5] => [5,7,2,8,4,6,1,3] => {{1,2,3,4,5,7,8},{6}} => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [8,3,1,5,7,2,4,6] => [6,2,7,4,8,5,1,3] => {{1,3,5,6,7,8},{2},{4}} => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [8,4,1,5,7,2,3,6] => [6,7,2,4,8,5,1,3] => {{1,2,3,5,6,7,8},{4}} => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [8,4,1,7,6,2,3,5] => [6,7,2,8,5,4,1,3] => {{1,2,3,4,6,7,8},{5}} => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [2,3,8,1,7,4,5,6] => [1,2,6,7,8,5,3,4] => {{1},{2},{3,4,5,6,7,8}} => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [2,7,5,1,3,4,8,6] => [1,5,6,3,8,2,7,4] => {{1},{2,3,4,5,6,8},{7}} => 3
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [2,8,5,1,3,7,4,6] => [1,5,7,3,8,6,2,4] => {{1},{2,3,4,5,7,8},{6}} => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [2,8,4,1,7,3,5,6] => [1,6,3,7,8,5,2,4] => {{1},{2,4,5,6,7,8},{3}} => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [2,8,5,1,7,3,4,6] => [1,6,7,3,8,5,2,4] => {{1},{2,3,4,5,6,7,8}} => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [6,8,5,1,2,3,4,7] => [5,6,7,3,1,8,2,4] => {{1,5},{2,3,4,6,7,8}} => 1
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [8,7,5,1,2,3,4,6] => [5,6,7,3,8,2,1,4] => {{1,3,4,5,7,8},{2,6}} => 1
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [8,3,4,1,7,2,5,6] => [6,2,3,7,8,5,1,4] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [8,3,5,1,7,2,4,6] => [6,2,7,3,8,5,1,4] => {{1,3,4,5,6,7,8},{2}} => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [8,5,4,1,7,2,3,6] => [6,7,3,2,8,5,1,4] => {{1,2,4,5,6,7,8},{3}} => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [2,8,6,5,1,3,4,7] => [1,6,7,4,3,8,2,5] => {{1},{2,3,5,6,7,8},{4}} => 3
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,3,4,6,1,2,5,7] => [6,2,3,7,4,8,1,5] => {{1,4,5,6,7,8},{2},{3}} => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,3,6,5,1,2,4,7] => [6,2,7,4,3,8,1,5] => {{1,3,5,6,7,8},{2},{4}} => 3
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Description
The number of topologically connected components of a set partition.
For example, the set partition $\{\{1,5\},\{2,3\},\{4,6\}\}$ has the two connected components $\{1,4,5,6\}$ and $\{2,3\}$.
The number of set partitions with only one block is oeis:A099947.
Map
Inverse Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.