Identifier
Values
{{1}} => [1] => [1,0] => [] => 0
{{1,2}} => [2] => [1,1,0,0] => [] => 0
{{1},{2}} => [1,1] => [1,0,1,0] => [1] => 1
{{1,2,3}} => [3] => [1,1,1,0,0,0] => [] => 0
{{1,2},{3}} => [2,1] => [1,1,0,0,1,0] => [2] => 2
{{1,3},{2}} => [2,1] => [1,1,0,0,1,0] => [2] => 2
{{1},{2,3}} => [1,2] => [1,0,1,1,0,0] => [1,1] => 2
{{1},{2},{3}} => [1,1,1] => [1,0,1,0,1,0] => [2,1] => 3
{{1,2,3,4}} => [4] => [1,1,1,1,0,0,0,0] => [] => 0
{{1,2,3},{4}} => [3,1] => [1,1,1,0,0,0,1,0] => [3] => 3
{{1,2,4},{3}} => [3,1] => [1,1,1,0,0,0,1,0] => [3] => 3
{{1,2},{3,4}} => [2,2] => [1,1,0,0,1,1,0,0] => [2,2] => 4
{{1,2},{3},{4}} => [2,1,1] => [1,1,0,0,1,0,1,0] => [3,2] => 5
{{1,3,4},{2}} => [3,1] => [1,1,1,0,0,0,1,0] => [3] => 3
{{1,3},{2,4}} => [2,2] => [1,1,0,0,1,1,0,0] => [2,2] => 4
{{1,3},{2},{4}} => [2,1,1] => [1,1,0,0,1,0,1,0] => [3,2] => 5
{{1,4},{2,3}} => [2,2] => [1,1,0,0,1,1,0,0] => [2,2] => 4
{{1},{2,3,4}} => [1,3] => [1,0,1,1,1,0,0,0] => [1,1,1] => 3
{{1},{2,3},{4}} => [1,2,1] => [1,0,1,1,0,0,1,0] => [3,1,1] => 5
{{1,4},{2},{3}} => [2,1,1] => [1,1,0,0,1,0,1,0] => [3,2] => 5
{{1},{2,4},{3}} => [1,2,1] => [1,0,1,1,0,0,1,0] => [3,1,1] => 5
{{1},{2},{3,4}} => [1,1,2] => [1,0,1,0,1,1,0,0] => [2,2,1] => 5
{{1},{2},{3},{4}} => [1,1,1,1] => [1,0,1,0,1,0,1,0] => [3,2,1] => 6
{{1,2,3,4,5}} => [5] => [1,1,1,1,1,0,0,0,0,0] => [] => 0
{{1,2,3,4},{5}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [4] => 4
{{1,2,3,5},{4}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [4] => 4
{{1,2,3},{4,5}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 6
{{1,2,3},{4},{5}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 7
{{1,2,4,5},{3}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [4] => 4
{{1,2,4},{3,5}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 6
{{1,2,4},{3},{5}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 7
{{1,2,5},{3,4}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 6
{{1,2},{3,4,5}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 6
{{1,2},{3,4},{5}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 8
{{1,2,5},{3},{4}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 7
{{1,2},{3,5},{4}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 8
{{1,2},{3},{4,5}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 8
{{1,2},{3},{4},{5}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 9
{{1,3,4,5},{2}} => [4,1] => [1,1,1,1,0,0,0,0,1,0] => [4] => 4
{{1,3,4},{2,5}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 6
{{1,3,4},{2},{5}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 7
{{1,3,5},{2,4}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 6
{{1,3},{2,4,5}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 6
{{1,3},{2,4},{5}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 8
{{1,3,5},{2},{4}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 7
{{1,3},{2,5},{4}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 8
{{1,3},{2},{4,5}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 8
{{1,3},{2},{4},{5}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 9
{{1,4,5},{2,3}} => [3,2] => [1,1,1,0,0,0,1,1,0,0] => [3,3] => 6
{{1,4},{2,3,5}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 6
{{1,4},{2,3},{5}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 8
{{1,5},{2,3,4}} => [2,3] => [1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 6
{{1},{2,3,4,5}} => [1,4] => [1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 4
{{1},{2,3,4},{5}} => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 7
{{1,5},{2,3},{4}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 8
{{1},{2,3,5},{4}} => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 7
{{1},{2,3},{4,5}} => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 8
{{1},{2,3},{4},{5}} => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 9
{{1,4,5},{2},{3}} => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => [4,3] => 7
{{1,4},{2,5},{3}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 8
{{1,4},{2},{3,5}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 8
{{1,4},{2},{3},{5}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 9
{{1,5},{2,4},{3}} => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 8
{{1},{2,4,5},{3}} => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 7
{{1},{2,4},{3,5}} => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 8
{{1},{2,4},{3},{5}} => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 9
{{1,5},{2},{3,4}} => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 8
{{1},{2,5},{3,4}} => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 8
{{1},{2},{3,4,5}} => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 7
{{1},{2},{3,4},{5}} => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 9
{{1,5},{2},{3},{4}} => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 9
{{1},{2,5},{3},{4}} => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 9
{{1},{2},{3,5},{4}} => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 9
{{1},{2},{3},{4,5}} => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 9
{{1},{2},{3},{4},{5}} => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 10
{{1,2,3,4,5,6}} => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => [] => 0
{{1,2,3,4,5},{6}} => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 5
{{1,2,3,4,6},{5}} => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 5
{{1,2,3,4},{5,6}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 8
{{1,2,3,4},{5},{6}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 9
{{1,2,3,5,6},{4}} => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 5
{{1,2,3,5},{4,6}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 8
{{1,2,3,5},{4},{6}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 9
{{1,2,3,6},{4,5}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 8
{{1,2,3},{4,5,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 9
{{1,2,3,6},{4},{5}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 9
{{1,2,4,5,6},{3}} => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 5
{{1,2,4,5},{3,6}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 8
{{1,2,4,5},{3},{6}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 9
{{1,2,4,6},{3,5}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 8
{{1,2,4},{3,5,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 9
{{1,2,4,6},{3},{5}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 9
{{1,2,5,6},{3,4}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 8
{{1,2,5},{3,4,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 9
{{1,2,6},{3,4,5}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 9
{{1,2},{3,4,5,6}} => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 8
{{1,2,5,6},{3},{4}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 9
{{1,3,4,5,6},{2}} => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 5
{{1,3,4,5},{2,6}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 8
{{1,3,4,5},{2},{6}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 9
{{1,3,4,6},{2,5}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 8
>>> Load all 186 entries. <<<
{{1,3,4},{2,5,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 9
{{1,3,4,6},{2},{5}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 9
{{1,3,5,6},{2,4}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 8
{{1,3,5},{2,4,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 9
{{1,3,6},{2,4,5}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 9
{{1,3},{2,4,5,6}} => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 8
{{1,3,5,6},{2},{4}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 9
{{1,4,5,6},{2,3}} => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 8
{{1,4,5},{2,3,6}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 9
{{1,4,6},{2,3,5}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 9
{{1,4},{2,3,5,6}} => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 8
{{1,5,6},{2,3,4}} => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 9
{{1,5},{2,3,4,6}} => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 8
{{1,6},{2,3,4,5}} => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 8
{{1},{2,3,4,5,6}} => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 5
{{1},{2,3,4,5},{6}} => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 9
{{1},{2,3,4,6},{5}} => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 9
{{1},{2,3,5,6},{4}} => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 9
{{1,4,5,6},{2},{3}} => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 9
{{1},{2,4,5,6},{3}} => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 9
{{1},{2},{3,4,5,6}} => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 9
{{1,2,3,4,5,6,7}} => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [] => 0
{{1,2,3,4,5,6},{7}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 6
{{1,2,3,4,5,7},{6}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 6
{{1,2,3,4,5},{6,7}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 10
{{1,2,3,4,6,7},{5}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 6
{{1,2,3,4,6},{5,7}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 10
{{1,2,3,4,7},{5,6}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 10
{{1,2,3,5,6,7},{4}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 6
{{1,2,3,5,6},{4,7}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 10
{{1,2,3,5,7},{4,6}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 10
{{1,2,3,6,7},{4,5}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 10
{{1,2,4,5,6,7},{3}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 6
{{1,2,4,5,6},{3,7}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 10
{{1,2,4,5,7},{3,6}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 10
{{1,2,4,6,7},{3,5}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 10
{{1,2,5,6,7},{3,4}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 10
{{1,2},{3,4,5,6,7}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 10
{{1,3,4,5,6,7},{2}} => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 6
{{1,3,4,5,6},{2,7}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 10
{{1,3,4,5,7},{2,6}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 10
{{1,3,4,6,7},{2,5}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 10
{{1,3,5,6,7},{2,4}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 10
{{1,3},{2,4,5,6,7}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 10
{{1,4,5,6,7},{2,3}} => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 10
{{1,4},{2,3,5,6,7}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 10
{{1,5},{2,3,4,6,7}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 10
{{1,6},{2,3,4,5,7}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 10
{{1,7},{2,3,4,5,6}} => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 10
{{1},{2,3,4,5,6,7}} => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 6
{{1},{2,3,4,5,6,7,8}} => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 7
{{1,3,4,5,6,7,8},{2}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 7
{{1,2,4,5,6,7,8},{3}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 7
{{1,2,3,5,6,7,8},{4}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 7
{{1,2,3,4,6,7,8},{5}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 7
{{1,2,3,4,5,7,8},{6}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 7
{{1,2,3,4,5,6,7},{8}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 7
{{1,2,3,4,5,6,8},{7}} => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 7
{{1,2,3,4,5,6,7,8}} => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [] => 0
{{1,2,3,4,5,6,7,8},{9}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 8
{{1},{2,3,4,5,6,7,8,9}} => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 8
{{1,2,3,4,5,6,7,8,9},{10}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 9
{{1},{2,3,4,5,6,7,8,9,10}} => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 9
{{1,2,3,4,5,6,7,8,9,10},{11}} => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 10
{{1},{2,3,4,5,6,7,8,9,10,11}} => [1,10] => [1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => 10
{{1,2,3,4,5,6,7,8,9}} => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [] => 0
{{1,2,3,4,5,6,7,8,9,10}} => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [] => 0
{{1,3,4,5,6,7,8,9},{2}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 8
{{1,3,4,5,6,7,8,9,10},{2}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 9
{{1,2,3,4,5,6,7,9},{8}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 8
{{1,2,3,4,5,6,7,8,10},{9}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 9
{{1,2,3,4,5,6,7,8,9,11},{10}} => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 10
{{1,2,3,5,6,7,8,9,10},{4}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 9
{{1,2,3,4,6,7,8,9,10},{5}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 9
{{1,3,4,5,6,7,8,9,10,11},{2}} => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 10
{{1,2,3,4,5,6,8,9},{7}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 8
{{1,2,3,4,5,7,8,9},{6}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 8
{{1,2,3,4,6,7,8,9},{5}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 8
{{1,2,3,5,6,7,8,9},{4}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 8
{{1,2,4,5,6,7,8,9},{3}} => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 8
{{1,2,3,4,5,6,7,9,10},{8}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 9
{{1,2,3,4,5,6,8,9,10},{7}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 9
{{1,2,3,4,5,7,8,9,10},{6}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 9
{{1,2,4,5,6,7,8,9,10},{3}} => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 9
{{1,2,3,4,5,6,7,8,10,11},{9}} => [10,1] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 10
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Description
The size of a partition.
This statistic is the constant statistic of the level sets.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
Map
to composition
Description
The integer composition of block sizes of a set partition.
For a set partition of $\{1,2,\dots,n\}$, this is the integer composition of $n$ obtained by sorting the blocks by their minimal element and then taking the block sizes.