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
{{1,2,3,4}} => [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}} => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 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}} => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 2
{{1,4},{2,3}} => [2,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => 2
{{1},{2,3,4}} => [3,1] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => 1
{{1,2,3,4,5}} => [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}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 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}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
{{1,2,5},{3,4}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
{{1,2},{3,4,5}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
{{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}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
{{1,3,5},{2,4}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
{{1,3},{2,4,5}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
{{1,4,5},{2,3}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
{{1,4},{2,3,5}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
{{1,5},{2,3,4}} => [3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => 2
{{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
{{1,2,3,4,5,6}} => [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}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 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}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,2,3,6},{4,5}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,2,3},{4,5,6}} => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 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}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,2,4,6},{3,5}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,2,4},{3,5,6}} => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 3
{{1,2,5,6},{3,4}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,2,5},{3,4,6}} => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 3
{{1,2,6},{3,4,5}} => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 3
{{1,2},{3,4,5,6}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{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}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,3,4,6},{2,5}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,3,4},{2,5,6}} => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 3
{{1,3,5,6},{2,4}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,3,5},{2,4,6}} => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 3
{{1,3,6},{2,4,5}} => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 3
{{1,3},{2,4,5,6}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,4,5,6},{2,3}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,4,5},{2,3,6}} => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 3
{{1,4,6},{2,3,5}} => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 3
{{1,4},{2,3,5,6}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,5,6},{2,3,4}} => [3,3] => [1,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0] => 3
{{1,5},{2,3,4,6}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{1,6},{2,3,4,5}} => [4,2] => [1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,0,0] => 2
{{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
{{1,2,3,4,5,6,7}} => [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}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 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}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,2,3,4,7},{5,6}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,2,3,4},{5,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 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}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,2,3,5,7},{4,6}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,2,3,5},{4,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,2,3,6,7},{4,5}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,2,3,6},{4,5,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,2,3,7},{4,5,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,2,3},{4,5,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{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}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,2,4,5,7},{3,6}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,2,4,5},{3,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,2,4,6,7},{3,5}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,2,4,6},{3,5,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,2,4,7},{3,5,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,2,4},{3,5,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,2,5,6,7},{3,4}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,2,5,6},{3,4,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,2,5,7},{3,4,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,2,5},{3,4,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,2,6,7},{3,4,5}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,2,6},{3,4,5,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,2,7},{3,4,5,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,2},{3,4,5,6,7}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{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}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,3,4,5,7},{2,6}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,3,4,5},{2,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,3,4,6,7},{2,5}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,3,4,6},{2,5,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
>>> Load all 210 entries. <<<
{{1,3,4,7},{2,5,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,3,4},{2,5,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,3,5,6,7},{2,4}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,3,5,6},{2,4,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,3,5,7},{2,4,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,3,5},{2,4,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,3,6,7},{2,4,5}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,3,6},{2,4,5,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,3,7},{2,4,5,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,3},{2,4,5,6,7}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,4,5,6,7},{2,3}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,4,5,6},{2,3,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,4,5,7},{2,3,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,4,5},{2,3,6,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,4,6,7},{2,3,5}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,4,6},{2,3,5,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,4,7},{2,3,5,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,4},{2,3,5,6,7}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,5,6,7},{2,3,4}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,5,6},{2,3,4,7}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,5,7},{2,3,4,6}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,5},{2,3,4,6,7}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,6,7},{2,3,4,5}} => [4,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,0,0,0] => 3
{{1,6},{2,3,4,5,7}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{1,7},{2,3,4,5,6}} => [5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
{{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},{3,4,5,6,7,8}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,3},{4,5,6,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,4,5,6,7,8},{2,3}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,3,4},{5,6,7,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,5,6,7,8},{2,3,4}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,3,4,5},{6,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,6,7,8},{2,3,4,5}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,2,6,7,8},{3,4,5}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,3,6,7,8},{4,5}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,3,4,5,6},{7,8}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,7,8},{3,4,5,6}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,2,3,7,8},{4,5,6}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,8},{2,3,4,5,6,7}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,8},{3,4,5,6,7}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,3,8},{4,5,6,7}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,2,3,4,8},{5,6,7}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,3,4,5,8},{6,7}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,3,5,6,7,8},{2,4}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,3,4,6,7,8},{2,5}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,4,6,7,8},{3,5}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,4,5,7,8},{3,6}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,3,5,7,8},{4,6}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,4,5,6,8},{3,7}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,3,5,6,8},{4,7}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,3,4,6,8},{5,7}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,4,5,6,7},{3,8}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,3,5,7,8},{2,4,6}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,5,7,8},{3,4,6}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,3,4,7,8},{2,5,6}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,4,7,8},{3,5,6}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,5,6,8},{3,4,7}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,3,4,6,8},{2,5,7}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,4,6,8},{3,5,7}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,3,6,8},{4,5,7}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,3,5,8},{4,6,7}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,3,6,7},{4,5,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,3,4,5,7},{2,6,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,3,4,7},{5,6,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,4,5,6},{3,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,3,5,6},{4,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,3,4,6},{5,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,3,5,7},{2,4,6,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,2,5,7},{3,4,6,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,3,4,7},{2,5,6,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,2,3,7},{4,5,6,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,3,5,6},{2,4,7,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,2,5,6},{3,4,7,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,2,4,6},{3,5,7,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,2,3,6},{4,5,7,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,3},{2,4,5,6,7,8}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,4},{2,3,5,6,7,8}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,5},{2,3,4,6,7,8}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,4,5,8},{2,3,6,7}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,2,3,4,5},{6,7,8,9,10}} => [5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
{{1,5,6},{2,3,4,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,3,6,7},{2,4,5,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,2,3,4,5,6},{7,8,9}} => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,2,3,4,5},{6,7,8,9}} => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
{{1,2,3,4,5,6},{7,8,9,10}} => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,4,5,7},{2,3,6,8}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,2,3,4},{5,6,7,8,9,10}} => [6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 4
{{1,4,6},{2,3,5,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,6},{3,4,5,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,5,7,8},{2,3,4,6}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,3,6,8},{2,4,5,7}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,2,6,8},{3,4,5,7}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,6},{2,3,4,5,7,8}} => [6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 2
{{1,2,4},{3,5,6,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,5,8},{2,3,4,6,7}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,3,4},{2,5,6,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,5},{3,4,6,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,3},{4,5,6,7,8,9}} => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,2,3,4},{5,6,7,8,9}} => [5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
{{1,4,6,7,8},{2,3,5}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,3,6,7,8},{2,4,5}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,4,5,7,8},{2,3,6}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,2,5,8},{3,4,6,7}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,6,7},{2,3,4,5,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,4,6,8},{2,3,5,7}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,4,7,8},{2,3,5,6}} => [4,4] => [1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => 4
{{1,2,9},{3,4,5,6,7,8}} => [6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 3
{{1,2,7},{3,4,5,6,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
{{1,4,5},{2,3,6,7,8}} => [5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
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
Delest-Viennot-inverse
Description
Return the Dyck path obtained by applying the inverse of Delest-Viennot's bijection to the corresponding parallelogram polyomino.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\beta^{(-1)}\circ\gamma)(D)$.