Identifier
Values
[1,0] => [2,1] => {{1,2}} => {{1,2}} => 2
[1,0,1,0] => [3,1,2] => {{1,2,3}} => {{1,3},{2}} => 2
[1,1,0,0] => [2,3,1] => {{1,2,3}} => {{1,3},{2}} => 2
[1,0,1,0,1,0] => [4,1,2,3] => {{1,2,3,4}} => {{1,4},{2},{3}} => 2
[1,0,1,1,0,0] => [3,1,4,2] => {{1,2,3,4}} => {{1,4},{2},{3}} => 2
[1,1,0,0,1,0] => [2,4,1,3] => {{1,2,3,4}} => {{1,4},{2},{3}} => 2
[1,1,0,1,0,0] => [4,3,1,2] => {{1,2,3,4}} => {{1,4},{2},{3}} => 2
[1,1,1,0,0,0] => [2,3,4,1] => {{1,2,3,4}} => {{1,4},{2},{3}} => 2
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => {{1,2,3,4,5}} => {{1,5},{2},{3},{4}} => 2
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => {{1,2,3,4,5}} => {{1,5},{2},{3},{4}} => 2
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => {{1,2,3,4,5}} => {{1,5},{2},{3},{4}} => 2
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => {{1,2,3,4,5}} => {{1,5},{2},{3},{4}} => 2
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => {{1,2,3,4,5}} => {{1,5},{2},{3},{4}} => 2
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => {{1,2,3,4,5}} => {{1,5},{2},{3},{4}} => 2
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => {{1,2,3,4,5}} => {{1,5},{2},{3},{4}} => 2
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => {{1,2,3,4,5}} => {{1,5},{2},{3},{4}} => 2
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => {{1,3,5},{2,4}} => {{1,5},{2,4},{3}} => 3
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => {{1,2,3,4,5}} => {{1,5},{2},{3},{4}} => 2
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => {{1,2,3,4,5}} => {{1,5},{2},{3},{4}} => 2
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => {{1,2,3,4,5}} => {{1,5},{2},{3},{4}} => 2
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => {{1,2,3,4,5}} => {{1,5},{2},{3},{4}} => 2
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => {{1,2,3,4,5}} => {{1,5},{2},{3},{4}} => 2
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => {{1,2,4,6},{3,5}} => {{1,6},{2},{3,5},{4}} => 2
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => {{1,3,5,6},{2,4}} => {{1,5,6},{2,4},{3}} => 3
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => {{1,3,5},{2,4,6}} => {{1,5},{2,4,6},{3}} => 3
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => {{1,3,5,6},{2,4}} => {{1,5,6},{2,4},{3}} => 3
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => {{1,3,6},{2,4,5}} => {{1,6},{2,4,5},{3}} => 3
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => {{1,2,4,6},{3,5}} => {{1,6},{2},{3,5},{4}} => 2
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => {{1,4,6},{2,3,5}} => {{1,6},{2,3,5},{4}} => 4
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => {{1,3,4,6},{2,5}} => {{1,6},{2,5},{3},{4}} => 3
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => {{1,2,3,4,5,6}} => {{1,6},{2},{3},{4},{5}} => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => {{1,2,3,5,7},{4,6}} => {{1,7},{2},{3},{4,6},{5}} => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => {{1,2,4,6,7},{3,5}} => {{1,6,7},{2},{3,5},{4}} => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => {{1,2,4,6},{3,5,7}} => {{1,6},{2},{3,5,7},{4}} => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => {{1,2,4,6,7},{3,5}} => {{1,6,7},{2},{3,5},{4}} => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => {{1,2,4,7},{3,5,6}} => {{1,7},{2},{3,5,6},{4}} => 2
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => {{1,2,3,5,7},{4,6}} => {{1,7},{2},{3},{4,6},{5}} => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => {{1,2,5,7},{3,4,6}} => {{1,7},{2},{3,4,6},{5}} => 2
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => {{1,2,4,5,7},{3,6}} => {{1,7},{2},{3,6},{4},{5}} => 2
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
>>> Load all 197 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => {{1,2,3,5,7},{4,6}} => {{1,7},{2},{3},{4,6},{5}} => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => {{1,3,5,6,7},{2,4}} => {{1,5,6,7},{2,4},{3}} => 3
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => {{1,3,5,6,7},{2,4}} => {{1,5,6,7},{2,4},{3}} => 3
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => {{1,3,5},{2,4,6,7}} => {{1,5},{2,4,6,7},{3}} => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => {{1,3,5,7},{2,4,6}} => {{1,7},{2,4,6},{3},{5}} => 3
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => {{1,3,5},{2,4,6,7}} => {{1,5},{2,4,6,7},{3}} => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => {{1,3,5,6,7},{2,4}} => {{1,5,6,7},{2,4},{3}} => 3
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => {{1,3,5,6,7},{2,4}} => {{1,5,6,7},{2,4},{3}} => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => {{1,3,5,6},{2,4,7}} => {{1,6},{2,4,7},{3},{5}} => 3
[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3] => {{1,3,5,6,7},{2,4}} => {{1,5,6,7},{2,4},{3}} => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => {{1,2,3,5,7},{4,6}} => {{1,7},{2},{3},{4,6},{5}} => 2
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => {{1,3,6,7},{2,4,5}} => {{1,6,7},{2,4,5},{3}} => 3
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => {{1,3,6},{2,4,5,7}} => {{1,6},{2,4,5,7},{3}} => 3
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => {{1,3,6,7},{2,4,5}} => {{1,6,7},{2,4,5},{3}} => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => {{1,3,7},{2,4,5,6}} => {{1,7},{2,4,5,6},{3}} => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => {{1,2,4,6,7},{3,5}} => {{1,6,7},{2},{3,5},{4}} => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => {{1,2,4,6},{3,5,7}} => {{1,6},{2},{3,5,7},{4}} => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => {{1,2,4,6,7},{3,5}} => {{1,6,7},{2},{3,5},{4}} => 2
[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => {{1,2,4,7},{3,5,6}} => {{1,7},{2},{3,5,6},{4}} => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => {{1,4,6,7},{2,3,5}} => {{1,6,7},{2,3,5},{4}} => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => {{1,4,6},{2,3,5,7}} => {{1,6},{2,3,5,7},{4}} => 4
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => {{1,4,6,7},{2,3,5}} => {{1,6,7},{2,3,5},{4}} => 4
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => {{1,3,4,6,7},{2,5}} => {{1,6,7},{2,5},{3},{4}} => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => {{1,3,4,6},{2,5,7}} => {{1,6},{2,5,7},{3},{4}} => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => {{1,3,4,6,7},{2,5}} => {{1,6,7},{2,5},{3},{4}} => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => {{1,4,7},{2,3,5,6}} => {{1,7},{2,3,5,6},{4}} => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => {{1,3,4,7},{2,5,6}} => {{1,7},{2,5,6},{3},{4}} => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => {{1,2,3,5,7},{4,6}} => {{1,7},{2},{3},{4,6},{5}} => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => {{1,2,5,7},{3,4,6}} => {{1,7},{2},{3,4,6},{5}} => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => {{1,2,4,5,7},{3,6}} => {{1,7},{2},{3,6},{4},{5}} => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => {{1,5,7},{2,3,4,6}} => {{1,7},{2,3,4,6},{5}} => 5
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => {{1,4,5,7},{2,3,6}} => {{1,7},{2,3,6},{4},{5}} => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => {{1,3,4,5,7},{2,6}} => {{1,7},{2,6},{3},{4},{5}} => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => {{1,2,3,4,5,6,7}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[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}} => {{1,7},{2},{3},{4},{5},{6}} => 2
[] => [1] => {{1}} => {{1}} => 1
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Description
The smallest closer of a set partition.
A closer (or right hand endpoint) of a set partition is a number that is maximal in its block. For this statistic, singletons are considered as closers.
In other words, this is the smallest among the maximal elements of the blocks.
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
Callan switch
Description
Switch the first closer and the minimum of the smallest closer and the second element of the block containing 1 in a set partition.
More precisely, this involution implements a joint symmetry between St000971The smallest closer of a set partition. and St001784The minimum of the smallest closer and the second element of the block containing 1 in a set partition..
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.