Identifier
Values
{{1}} => [1] => [1,0] => [1,0] => 0
{{1,2}} => [2] => [1,0,1,0] => [1,1,0,0] => 0
{{1},{2}} => [1,1] => [1,1,0,0] => [1,0,1,0] => 1
{{1,2,3}} => [3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => 0
{{1,2},{3}} => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
{{1,3},{2}} => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
{{1},{2,3}} => [2,1] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => 1
{{1},{2},{3}} => [1,1,1] => [1,1,0,1,0,0] => [1,1,0,1,0,0] => 2
{{1,2,3,4}} => [4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => 0
{{1,2,3},{4}} => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
{{1,2,4},{3}} => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
{{1,2},{3},{4}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 2
{{1,3,4},{2}} => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
{{1,3},{2},{4}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 2
{{1},{2,3,4}} => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
{{1},{2,3},{4}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 2
{{1,4},{2},{3}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 2
{{1},{2,4},{3}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 2
{{1},{2},{3,4}} => [2,1,1] => [1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,0] => 2
{{1},{2},{3},{4}} => [1,1,1,1] => [1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 3
{{1,2,3,4,5}} => [5] => [1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,0] => 0
{{1,2,3,4},{5}} => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
{{1,2,3,5},{4}} => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
{{1,2,3},{4},{5}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,2,4,5},{3}} => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
{{1,2,4},{3},{5}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,2,5},{3},{4}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,2},{3},{4},{5}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,3,4,5},{2}} => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
{{1,3,4},{2},{5}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,3,5},{2},{4}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,3},{2},{4},{5}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1},{2,3,4,5}} => [4,1] => [1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,0,1,0] => 1
{{1},{2,3,4},{5}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1},{2,3,5},{4}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1},{2,3},{4},{5}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,4,5},{2},{3}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,4},{2},{3},{5}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1},{2,4,5},{3}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1},{2,4},{3},{5}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1},{2},{3,4,5}} => [3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1},{2},{3,4},{5}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,5},{2},{3},{4}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1},{2,5},{3},{4}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1},{2},{3,5},{4}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1},{2},{3},{4,5}} => [2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1},{2},{3},{4},{5}} => [1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,2,3,4,5,6}} => [6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
{{1,2,3,4,5},{6}} => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
{{1,2,3,4,6},{5}} => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
{{1,2,3,4},{5},{6}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,2,3,5,6},{4}} => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
{{1,2,3,5},{4},{6}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,2,3,6},{4},{5}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,2,3},{4},{5},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,4,5,6},{3}} => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
{{1,2,4,5},{3},{6}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,2,4,6},{3},{5}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,2,4},{3},{5},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,5,6},{3},{4}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,2,5},{3},{4},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,6},{3},{4},{5}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2},{3},{4},{5},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
{{1,3,4,5,6},{2}} => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
{{1,3,4,5},{2},{6}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,3,4,6},{2},{5}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,3,4},{2},{5},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,3,5,6},{2},{4}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,3,5},{2},{4},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,3,6},{2},{4},{5}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,3},{2},{4},{5},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
{{1},{2,3,4,5,6}} => [5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
{{1},{2,3,4,5},{6}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1},{2,3,4,6},{5}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1},{2,3,4},{5},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1},{2,3,5,6},{4}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1},{2,3,5},{4},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1},{2,3,6},{4},{5}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1},{2,3},{4},{5},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
{{1,4,5,6},{2},{3}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,4,5},{2},{3},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,4,6},{2},{3},{5}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,4},{2},{3},{5},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
{{1},{2,4,5,6},{3}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1},{2,4,5},{3},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1},{2,4,6},{3},{5}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1},{2,4},{3},{5},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
{{1},{2},{3,4,5,6}} => [4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1},{2},{3,4,5},{6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1},{2},{3,4,6},{5}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1},{2},{3,4},{5},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
{{1,5,6},{2},{3},{4}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
{{1},{2,5,6},{3},{4}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1},{2,5},{3},{4},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
{{1},{2},{3,5,6},{4}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1},{2},{3,5},{4},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
{{1},{2},{3},{4,5,6}} => [3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1},{2},{3},{4,5},{6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
{{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
{{1},{2,6},{3},{4},{5}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
>>> Load all 226 entries. <<<
{{1},{2},{3,6},{4},{5}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
{{1},{2},{3},{4,6},{5}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
{{1},{2},{3},{4},{5,6}} => [2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
{{1},{2},{3},{4},{5},{6}} => [1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
{{1,2,3,4,5,6,7}} => [7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
{{1,2,3,4,5,6},{7}} => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
{{1,2,3,4,5,7},{6}} => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
{{1,2,3,4,5},{6},{7}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,3,4,6,7},{5}} => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
{{1,2,3,4,6},{5},{7}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,3,4,7},{5},{6}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,3,4},{5},{6},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,2,3,5,6,7},{4}} => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
{{1,2,3,5,6},{4},{7}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,3,5,7},{4},{6}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,3,5},{4},{6},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,2,3,6,7},{4},{5}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,3,6},{4},{5},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,2,3},{4},{5},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,2,4,5,6,7},{3}} => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
{{1,2,4,5,6},{3},{7}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,4,5,7},{3},{6}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,4,5},{3},{6},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,2,4,6,7},{3},{5}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,4,6},{3},{5},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,2,4},{3},{5},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,2,5,6,7},{3},{4}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,5,6},{3},{4},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,2,5},{3},{4},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1,3,4,5,6,7},{2}} => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
{{1,3,4,5,6},{2},{7}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,3,4,5,7},{2},{6}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,3,4,5},{2},{6},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,3,4,6,7},{2},{5}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,3,4,6},{2},{5},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,3,4},{2},{5},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,3,5,6,7},{2},{4}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,3,5,6},{2},{4},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,3,5},{2},{4},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,3},{2},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1},{2,3,4,5,6,7}} => [6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
{{1},{2,3,4,5,6},{7}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1},{2,3,4,5,7},{6}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1},{2,3,4,5},{6},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1},{2,3,4,6,7},{5}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1},{2,3,4,6},{5},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1},{2,3,4,7},{5},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1},{2,3,4},{5},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2,3,5,6,7},{4}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1},{2,3,5,6},{4},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1},{2,3,5,7},{4},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1},{2,3,5},{4},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2,3,6,7},{4},{5}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1},{2,3,6},{4},{5},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2,3,7},{4},{5},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2,3},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1,4,5,6,7},{2},{3}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,4,5,6},{2},{3},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,4,5},{2},{3},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1},{2,4,5,6,7},{3}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1},{2,4,5,6},{3},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1},{2,4,5,7},{3},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1},{2,4,5},{3},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2,4,6,7},{3},{5}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1},{2,4,6},{3},{5},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2,4,7},{3},{5},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2,4},{3},{5},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1},{2},{3,4,5,6,7}} => [5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1},{2},{3,4,5,6},{7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1},{2},{3,4,5,7},{6}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1},{2},{3,4,5},{6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2},{3,4,6,7},{5}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1},{2},{3,4,6},{5},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2},{3,4,7},{5},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2},{3,4},{5},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1},{2,5,6,7},{3},{4}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1},{2,5,6},{3},{4},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2,5,7},{3},{4},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2,5},{3},{4},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1},{2},{3,5,6,7},{4}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1},{2},{3,5,6},{4},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2},{3,5,7},{4},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2},{3,5},{4},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1},{2},{3},{4,5,6,7}} => [4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1},{2},{3},{4,5,6},{7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2},{3},{4,5,7},{6}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2},{3},{4,5},{6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1},{2,6,7},{3},{4},{5}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2,6},{3},{4},{5},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1},{2},{3,6,7},{4},{5}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2},{3,6},{4},{5},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1},{2},{3},{4,6,7},{5}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2},{3},{4,6},{5},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1},{2},{3},{4},{5,6,7}} => [3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1},{2},{3},{4},{5,6},{7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1},{2,7},{3},{4},{5},{6}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1},{2},{3,7},{4},{5},{6}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1},{2},{3},{4,7},{5},{6}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1},{2},{3},{4},{5,7},{6}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1},{2},{3},{4},{5},{6,7}} => [2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 5
{{1},{2},{3},{4},{5},{6},{7}} => [1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 6
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Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Map
Lalanne-Kreweras involution
Description
The Lalanne-Kreweras involution on Dyck paths.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
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
shape
Description
Sends a set partition to the integer partition obtained by the sizes of the blocks.