Identifier
Values
{{1}} => [1] => [1] => [1,0] => 0
{{1,2}} => [2] => [1,1] => [1,1,0,0] => 1
{{1},{2}} => [1,1] => [2] => [1,0,1,0] => 0
{{1,2,3}} => [3] => [3] => [1,0,1,0,1,0] => 0
{{1,2},{3}} => [2,1] => [1,1,1] => [1,1,0,1,0,0] => 0
{{1,3},{2}} => [2,1] => [1,1,1] => [1,1,0,1,0,0] => 0
{{1},{2,3}} => [2,1] => [1,1,1] => [1,1,0,1,0,0] => 0
{{1},{2},{3}} => [1,1,1] => [2,1] => [1,0,1,1,0,0] => 0
{{1,2,3,4}} => [4] => [2,2] => [1,1,1,0,0,0] => 3
{{1,2,3},{4}} => [3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 0
{{1,2,4},{3}} => [3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 0
{{1,2},{3,4}} => [2,2] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 0
{{1,2},{3},{4}} => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 0
{{1,3,4},{2}} => [3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 0
{{1,3},{2,4}} => [2,2] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 0
{{1,3},{2},{4}} => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 0
{{1,4},{2,3}} => [2,2] => [1,1,1,1] => [1,1,0,1,0,1,0,0] => 0
{{1},{2,3,4}} => [3,1] => [3,1] => [1,0,1,0,1,1,0,0] => 0
{{1},{2,3},{4}} => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 0
{{1,4},{2},{3}} => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 0
{{1},{2,4},{3}} => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 0
{{1},{2},{3,4}} => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 0
{{1},{2},{3},{4}} => [1,1,1,1] => [4] => [1,0,1,0,1,0,1,0] => 0
{{1,2,3,4,5}} => [5] => [5] => [1,0,1,0,1,0,1,0,1,0] => 0
{{1,2,3,4},{5}} => [4,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
{{1,2,3,5},{4}} => [4,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
{{1,2,3},{4,5}} => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
{{1,2,3},{4},{5}} => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
{{1,2,4,5},{3}} => [4,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
{{1,2,4},{3,5}} => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
{{1,2,4},{3},{5}} => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
{{1,2,5},{3,4}} => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
{{1,2},{3,4,5}} => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
{{1,2},{3,4},{5}} => [2,2,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
{{1,2,5},{3},{4}} => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
{{1,2},{3,5},{4}} => [2,2,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
{{1,2},{3},{4,5}} => [2,2,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
{{1,2},{3},{4},{5}} => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 0
{{1,3,4,5},{2}} => [4,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
{{1,3,4},{2,5}} => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
{{1,3,4},{2},{5}} => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
{{1,3,5},{2,4}} => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
{{1,3},{2,4,5}} => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
{{1,3},{2,4},{5}} => [2,2,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
{{1,3,5},{2},{4}} => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
{{1,3},{2,5},{4}} => [2,2,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
{{1,3},{2},{4,5}} => [2,2,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
{{1,3},{2},{4},{5}} => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 0
{{1,4,5},{2,3}} => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
{{1,4},{2,3,5}} => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
{{1,4},{2,3},{5}} => [2,2,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
{{1,5},{2,3,4}} => [3,2] => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => 0
{{1},{2,3,4,5}} => [4,1] => [2,2,1] => [1,1,1,0,0,1,0,0] => 0
{{1},{2,3,4},{5}} => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
{{1,5},{2,3},{4}} => [2,2,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
{{1},{2,3,5},{4}} => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
{{1},{2,3},{4,5}} => [2,2,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
{{1},{2,3},{4},{5}} => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 0
{{1,4,5},{2},{3}} => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
{{1,4},{2,5},{3}} => [2,2,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
{{1,4},{2},{3,5}} => [2,2,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
{{1,4},{2},{3},{5}} => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 0
{{1,5},{2,4},{3}} => [2,2,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
{{1},{2,4,5},{3}} => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
{{1},{2,4},{3,5}} => [2,2,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
{{1},{2,4},{3},{5}} => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 0
{{1,5},{2},{3,4}} => [2,2,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
{{1},{2,5},{3,4}} => [2,2,1] => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => 0
{{1},{2},{3,4,5}} => [3,1,1] => [3,2] => [1,0,1,1,1,0,0,0] => 0
{{1},{2},{3,4},{5}} => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 0
{{1,5},{2},{3},{4}} => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 0
{{1},{2,5},{3},{4}} => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 0
{{1},{2},{3,5},{4}} => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 0
{{1},{2},{3},{4,5}} => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => 0
{{1},{2},{3},{4},{5}} => [1,1,1,1,1] => [4,1] => [1,0,1,0,1,0,1,1,0,0] => 0
{{1,2,3,4,5,6}} => [6] => [3,3] => [1,1,1,0,1,0,0,0] => 0
{{1,2,3,4},{5,6}} => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
{{1,2,3,4},{5},{6}} => [4,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
{{1,2,3,5},{4,6}} => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
{{1,2,3,5},{4},{6}} => [4,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
{{1,2,3,6},{4,5}} => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
{{1,2,3,6},{4},{5}} => [4,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
{{1,2,3},{4},{5},{6}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1,2,4,5},{3,6}} => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
{{1,2,4,5},{3},{6}} => [4,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
{{1,2,4,6},{3,5}} => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
{{1,2,4,6},{3},{5}} => [4,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
{{1,2,4},{3},{5},{6}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1,2,5,6},{3,4}} => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
{{1,2},{3,4,5,6}} => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
{{1,2,5,6},{3},{4}} => [4,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
{{1,2,5},{3},{4},{6}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1,2,6},{3},{4},{5}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1,3,4,5},{2,6}} => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
{{1,3,4,5},{2},{6}} => [4,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
{{1,3,4,6},{2,5}} => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
{{1,3,4,6},{2},{5}} => [4,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
{{1,3,4},{2},{5},{6}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1,3,5,6},{2,4}} => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
{{1,3},{2,4,5,6}} => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
{{1,3,5,6},{2},{4}} => [4,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
>>> Load all 282 entries. <<<
{{1,3,5},{2},{4},{6}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1,3,6},{2},{4},{5}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1,4,5,6},{2,3}} => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
{{1,4},{2,3,5,6}} => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
{{1,5},{2,3,4,6}} => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
{{1,6},{2,3,4,5}} => [4,2] => [2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => 0
{{1},{2,3,4,5},{6}} => [4,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
{{1},{2,3,4,6},{5}} => [4,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
{{1},{2,3,4},{5},{6}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1},{2,3,5,6},{4}} => [4,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
{{1},{2,3,5},{4},{6}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1},{2,3,6},{4},{5}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1,4,5,6},{2},{3}} => [4,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
{{1,4,5},{2},{3},{6}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1,4,6},{2},{3},{5}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1},{2,4,5,6},{3}} => [4,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
{{1},{2,4,5},{3},{6}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1},{2,4,6},{3},{5}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1},{2},{3,4,5,6}} => [4,1,1] => [2,2,2] => [1,1,1,1,0,0,0,0] => 6
{{1},{2},{3,4,5},{6}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1},{2},{3,4,6},{5}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1,5,6},{2},{3},{4}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1},{2,5,6},{3},{4}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1},{2},{3,5,6},{4}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1},{2},{3},{4,5,6}} => [3,1,1,1] => [3,2,1] => [1,0,1,1,1,0,0,1,0,0] => 2
{{1},{2},{3},{4},{5},{6}} => [1,1,1,1,1,1] => [4,2] => [1,0,1,0,1,1,1,0,0,0] => 0
{{1,2,3,4,5,6},{7}} => [6,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
{{1,2,3,4,5,7},{6}} => [6,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
{{1,2,3,4,6,7},{5}} => [6,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
{{1,2,3,4},{5,6,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,2,3,4},{5},{6},{7}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,2,3,5,6,7},{4}} => [6,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
{{1,2,3,5},{4,6,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,2,3,5},{4},{6},{7}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,2,3,6},{4,5,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,2,3,7},{4,5,6}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,2,3},{4,5,6,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,2,3,6},{4},{5},{7}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,2,3},{4},{5},{6},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1,2,4,5,6,7},{3}} => [6,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
{{1,2,4,5},{3,6,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,2,4,5},{3},{6},{7}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,2,4,6},{3,5,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,2,4,7},{3,5,6}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,2,4},{3,5,6,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,2,4,6},{3},{5},{7}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,2,4},{3},{5},{6},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1,2,5,6},{3,4,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,2,5,7},{3,4,6}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,2,5},{3,4,6,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,2,6,7},{3,4,5}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,2,6},{3,4,5,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,2,7},{3,4,5,6}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,2,5,6},{3},{4},{7}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,2,5},{3},{4},{6},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1,3,4,5,6,7},{2}} => [6,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
{{1,3,4,5},{2,6,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,3,4,5},{2},{6},{7}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,3,4,6},{2,5,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,3,4,7},{2,5,6}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,3,4},{2,5,6,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,3,4,6},{2},{5},{7}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,3,4},{2},{5},{6},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1,3,5,6},{2,4,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,3,5,7},{2,4,6}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,3,5},{2,4,6,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,3,6,7},{2,4,5}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,3,6},{2,4,5,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,3,7},{2,4,5,6}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,3,5,6},{2},{4},{7}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,3,5},{2},{4},{6},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1,4,5,6},{2,3,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,4,5,7},{2,3,6}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,4,5},{2,3,6,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,4,6,7},{2,3,5}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,4,6},{2,3,5,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,4,7},{2,3,5,6}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,5,6,7},{2,3,4}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,5,6},{2,3,4,7}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,5,7},{2,3,4,6}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1,6,7},{2,3,4,5}} => [4,3] => [3,2,2] => [1,0,1,1,1,1,0,0,0,0] => 0
{{1},{2,3,4,5,6,7}} => [6,1] => [3,3,1] => [1,1,1,0,1,0,0,1,0,0] => 0
{{1},{2,3,4,5},{6},{7}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1},{2,3,4,6},{5},{7}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1},{2,3,4,7},{5},{6}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1},{2,3,4},{5},{6},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2,3,5,6},{4},{7}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1},{2,3,5,7},{4},{6}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1},{2,3,5},{4},{6},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2,3,6,7},{4},{5}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1},{2,3,6},{4},{5},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2,3,7},{4},{5},{6}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1,4,5,6},{2},{3},{7}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,4,5},{2},{3},{6},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2,4,5,6},{3},{7}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1},{2,4,5,7},{3},{6}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1},{2,4,5},{3},{6},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2,4,6,7},{3},{5}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1},{2,4,6},{3},{5},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2,4,7},{3},{5},{6}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2},{3,4,5,6},{7}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1},{2},{3,4,5,7},{6}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1},{2},{3,4,5},{6},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2},{3,4,6,7},{5}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1},{2},{3,4,6},{5},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2},{3,4,7},{5},{6}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2,5,6,7},{3},{4}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1},{2,5,6},{3},{4},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2,5,7},{3},{4},{6}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2},{3,5,6,7},{4}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1},{2},{3,5,6},{4},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2},{3,5,7},{4},{6}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2},{3},{4,5,6,7}} => [4,1,1,1] => [2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => 0
{{1},{2},{3},{4,5,6},{7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2},{3},{4,5,7},{6}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2,6,7},{3},{4},{5}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2},{3,6,7},{4},{5}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2},{3},{4,6,7},{5}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2},{3},{4},{5,6,7}} => [3,1,1,1,1] => [4,3] => [1,0,1,1,1,0,1,0,0,0] => 0
{{1},{2},{3,4,5,6,7,8}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1},{2,4,5,6,7,8},{3}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1},{2,3,4,6,7,8},{5}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1},{2,3,4,5,7,8},{6}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1},{2,3,4,5,6,8},{7}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1,3,4,5,6,7},{2},{8}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1,3,4,5,6,8},{2},{7}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1,2,4,6,7,8},{3},{5}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1,2,4,5,7,8},{3},{6}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1,2,4,5,6,8},{3},{7}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1,2,3,4},{5,6,7,8}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,2,3,6,7,8},{4},{5}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1,2,3,5,7,8},{4},{6}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1,2,3,5,6,7},{4},{8}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1,6,7,8},{2,3,4,5}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,2,3,4,7,8},{5},{6}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1,2,3,4,6,7},{5},{8}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1,2,3,4,6,8},{5},{7}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1,2,3,4,5,6},{7},{8}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1,2,7,8},{3,4,5,6}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,2,3,4,5,7},{6},{8}} => [6,1,1] => [3,3,2] => [1,1,1,0,1,1,0,0,0,0] => 0
{{1,2,3,8},{4,5,6,7}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,2,3,4,5,6,7,8}} => [8] => [4,4] => [1,1,1,0,1,0,1,0,0,0] => 0
{{1,3,5,7},{2,4,6,8}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,2,5,7},{3,4,6,8}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,3,4,7},{2,5,6,8}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,2,3,7},{4,5,6,8}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,3,5,6},{2,4,7,8}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,2,5,6},{3,4,7,8}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,2,4,6},{3,5,7,8}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,2,3,6},{4,5,7,8}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,4,5,8},{2,3,6,7}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,3,6,7},{2,4,5,8}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,2,3,4,5,6},{7,8,9}} => [6,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 10
{{1,4,5,7},{2,3,6,8}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,5,7,8},{2,3,4,6}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,3,6,8},{2,4,5,7}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,2,6,8},{3,4,5,7}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,2,3},{4,5,6,7,8,9}} => [6,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 10
{{1,2,5,8},{3,4,6,7}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,4,6,8},{2,3,5,7}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,4,7,8},{2,3,5,6}} => [4,4] => [2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => 0
{{1,2,9},{3,4,5,6,7,8}} => [6,3] => [3,3,3] => [1,1,1,1,1,0,0,0,0,0] => 10
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Description
The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path.
Map
shape
Description
Sends a set partition to the integer partition obtained by the sizes of the blocks.
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
Glaisher-Franklin
Description
The Glaisher-Franklin bijection on integer partitions.
This map sends the set of even part sizes, each divided by two, to the set of repeated part sizes, see [1, 3.3.1].