Identifier
- St000250: Set partitions ⟶ ℤ
Values
{{1,2}} => 3
{{1},{2}} => 2
{{1,2,3}} => 4
{{1,2},{3}} => 3
{{1,3},{2}} => 3
{{1},{2,3}} => 3
{{1},{2},{3}} => 3
{{1,2,3,4}} => 5
{{1,2,3},{4}} => 4
{{1,2,4},{3}} => 4
{{1,2},{3,4}} => 4
{{1,2},{3},{4}} => 4
{{1,3,4},{2}} => 4
{{1,3},{2,4}} => 2
{{1,3},{2},{4}} => 3
{{1,4},{2,3}} => 4
{{1},{2,3,4}} => 4
{{1},{2,3},{4}} => 4
{{1,4},{2},{3}} => 4
{{1},{2,4},{3}} => 3
{{1},{2},{3,4}} => 4
{{1},{2},{3},{4}} => 4
{{1,2,3,4,5}} => 6
{{1,2,3,4},{5}} => 5
{{1,2,3,5},{4}} => 5
{{1,2,3},{4,5}} => 5
{{1,2,3},{4},{5}} => 5
{{1,2,4,5},{3}} => 5
{{1,2,4},{3,5}} => 3
{{1,2,4},{3},{5}} => 4
{{1,2,5},{3,4}} => 5
{{1,2},{3,4,5}} => 5
{{1,2},{3,4},{5}} => 5
{{1,2,5},{3},{4}} => 5
{{1,2},{3,5},{4}} => 4
{{1,2},{3},{4,5}} => 5
{{1,2},{3},{4},{5}} => 5
{{1,3,4,5},{2}} => 5
{{1,3,4},{2,5}} => 3
{{1,3,4},{2},{5}} => 4
{{1,3,5},{2,4}} => 3
{{1,3},{2,4,5}} => 3
{{1,3},{2,4},{5}} => 3
{{1,3,5},{2},{4}} => 4
{{1,3},{2,5},{4}} => 3
{{1,3},{2},{4,5}} => 4
{{1,3},{2},{4},{5}} => 4
{{1,4,5},{2,3}} => 5
{{1,4},{2,3,5}} => 3
{{1,4},{2,3},{5}} => 4
{{1,5},{2,3,4}} => 5
{{1},{2,3,4,5}} => 5
{{1},{2,3,4},{5}} => 5
{{1,5},{2,3},{4}} => 5
{{1},{2,3,5},{4}} => 4
{{1},{2,3},{4,5}} => 5
{{1},{2,3},{4},{5}} => 5
{{1,4,5},{2},{3}} => 5
{{1,4},{2,5},{3}} => 3
{{1,4},{2},{3,5}} => 3
{{1,4},{2},{3},{5}} => 4
{{1,5},{2,4},{3}} => 4
{{1},{2,4,5},{3}} => 4
{{1},{2,4},{3,5}} => 3
{{1},{2,4},{3},{5}} => 4
{{1,5},{2},{3,4}} => 5
{{1},{2,5},{3,4}} => 4
{{1},{2},{3,4,5}} => 5
{{1},{2},{3,4},{5}} => 5
{{1,5},{2},{3},{4}} => 5
{{1},{2,5},{3},{4}} => 4
{{1},{2},{3,5},{4}} => 4
{{1},{2},{3},{4,5}} => 5
{{1},{2},{3},{4},{5}} => 5
{{1,2,3,4,5,6}} => 7
{{1,2,3,4,5},{6}} => 6
{{1,2,3,4,6},{5}} => 6
{{1,2,3,4},{5,6}} => 6
{{1,2,3,4},{5},{6}} => 6
{{1,2,3,5,6},{4}} => 6
{{1,2,3,5},{4,6}} => 4
{{1,2,3,5},{4},{6}} => 5
{{1,2,3,6},{4,5}} => 6
{{1,2,3},{4,5,6}} => 6
{{1,2,3},{4,5},{6}} => 6
{{1,2,3,6},{4},{5}} => 6
{{1,2,3},{4,6},{5}} => 5
{{1,2,3},{4},{5,6}} => 6
{{1,2,3},{4},{5},{6}} => 6
{{1,2,4,5,6},{3}} => 6
{{1,2,4,5},{3,6}} => 4
{{1,2,4,5},{3},{6}} => 5
{{1,2,4,6},{3,5}} => 4
{{1,2,4},{3,5,6}} => 4
{{1,2,4},{3,5},{6}} => 4
{{1,2,4,6},{3},{5}} => 5
{{1,2,4},{3,6},{5}} => 4
{{1,2,4},{3},{5,6}} => 5
{{1,2,4},{3},{5},{6}} => 5
{{1,2,5,6},{3,4}} => 6
{{1,2,5},{3,4,6}} => 4
>>> Load all 1200 entries. <<<{{1,2,5},{3,4},{6}} => 5
{{1,2,6},{3,4,5}} => 6
{{1,2},{3,4,5,6}} => 6
{{1,2},{3,4,5},{6}} => 6
{{1,2,6},{3,4},{5}} => 6
{{1,2},{3,4,6},{5}} => 5
{{1,2},{3,4},{5,6}} => 6
{{1,2},{3,4},{5},{6}} => 6
{{1,2,5,6},{3},{4}} => 6
{{1,2,5},{3,6},{4}} => 4
{{1,2,5},{3},{4,6}} => 4
{{1,2,5},{3},{4},{6}} => 5
{{1,2,6},{3,5},{4}} => 5
{{1,2},{3,5,6},{4}} => 5
{{1,2},{3,5},{4,6}} => 4
{{1,2},{3,5},{4},{6}} => 5
{{1,2,6},{3},{4,5}} => 6
{{1,2},{3,6},{4,5}} => 5
{{1,2},{3},{4,5,6}} => 6
{{1,2},{3},{4,5},{6}} => 6
{{1,2,6},{3},{4},{5}} => 6
{{1,2},{3,6},{4},{5}} => 5
{{1,2},{3},{4,6},{5}} => 5
{{1,2},{3},{4},{5,6}} => 6
{{1,2},{3},{4},{5},{6}} => 6
{{1,3,4,5,6},{2}} => 6
{{1,3,4,5},{2,6}} => 4
{{1,3,4,5},{2},{6}} => 5
{{1,3,4,6},{2,5}} => 4
{{1,3,4},{2,5,6}} => 4
{{1,3,4},{2,5},{6}} => 4
{{1,3,4,6},{2},{5}} => 5
{{1,3,4},{2,6},{5}} => 4
{{1,3,4},{2},{5,6}} => 5
{{1,3,4},{2},{5},{6}} => 5
{{1,3,5,6},{2,4}} => 4
{{1,3,5},{2,4,6}} => 2
{{1,3,5},{2,4},{6}} => 3
{{1,3,6},{2,4,5}} => 4
{{1,3},{2,4,5,6}} => 4
{{1,3},{2,4,5},{6}} => 4
{{1,3,6},{2,4},{5}} => 4
{{1,3},{2,4,6},{5}} => 3
{{1,3},{2,4},{5,6}} => 4
{{1,3},{2,4},{5},{6}} => 4
{{1,3,5,6},{2},{4}} => 5
{{1,3,5},{2,6},{4}} => 3
{{1,3,5},{2},{4,6}} => 3
{{1,3,5},{2},{4},{6}} => 4
{{1,3,6},{2,5},{4}} => 4
{{1,3},{2,5,6},{4}} => 4
{{1,3},{2,5},{4,6}} => 3
{{1,3},{2,5},{4},{6}} => 4
{{1,3,6},{2},{4,5}} => 5
{{1,3},{2,6},{4,5}} => 4
{{1,3},{2},{4,5,6}} => 5
{{1,3},{2},{4,5},{6}} => 5
{{1,3,6},{2},{4},{5}} => 5
{{1,3},{2,6},{4},{5}} => 4
{{1,3},{2},{4,6},{5}} => 4
{{1,3},{2},{4},{5,6}} => 5
{{1,3},{2},{4},{5},{6}} => 5
{{1,4,5,6},{2,3}} => 6
{{1,4,5},{2,3,6}} => 4
{{1,4,5},{2,3},{6}} => 5
{{1,4,6},{2,3,5}} => 4
{{1,4},{2,3,5,6}} => 4
{{1,4},{2,3,5},{6}} => 4
{{1,4,6},{2,3},{5}} => 5
{{1,4},{2,3,6},{5}} => 4
{{1,4},{2,3},{5,6}} => 5
{{1,4},{2,3},{5},{6}} => 5
{{1,5,6},{2,3,4}} => 6
{{1,5},{2,3,4,6}} => 4
{{1,5},{2,3,4},{6}} => 5
{{1,6},{2,3,4,5}} => 6
{{1},{2,3,4,5,6}} => 6
{{1},{2,3,4,5},{6}} => 6
{{1,6},{2,3,4},{5}} => 6
{{1},{2,3,4,6},{5}} => 5
{{1},{2,3,4},{5,6}} => 6
{{1},{2,3,4},{5},{6}} => 6
{{1,5,6},{2,3},{4}} => 6
{{1,5},{2,3,6},{4}} => 4
{{1,5},{2,3},{4,6}} => 4
{{1,5},{2,3},{4},{6}} => 5
{{1,6},{2,3,5},{4}} => 5
{{1},{2,3,5,6},{4}} => 5
{{1},{2,3,5},{4,6}} => 4
{{1},{2,3,5},{4},{6}} => 5
{{1,6},{2,3},{4,5}} => 6
{{1},{2,3,6},{4,5}} => 5
{{1},{2,3},{4,5,6}} => 6
{{1},{2,3},{4,5},{6}} => 6
{{1,6},{2,3},{4},{5}} => 6
{{1},{2,3,6},{4},{5}} => 5
{{1},{2,3},{4,6},{5}} => 5
{{1},{2,3},{4},{5,6}} => 6
{{1},{2,3},{4},{5},{6}} => 6
{{1,4,5,6},{2},{3}} => 6
{{1,4,5},{2,6},{3}} => 4
{{1,4,5},{2},{3,6}} => 4
{{1,4,5},{2},{3},{6}} => 5
{{1,4,6},{2,5},{3}} => 4
{{1,4},{2,5,6},{3}} => 4
{{1,4},{2,5},{3,6}} => 3
{{1,4},{2,5},{3},{6}} => 4
{{1,4,6},{2},{3,5}} => 4
{{1,4},{2,6},{3,5}} => 3
{{1,4},{2},{3,5,6}} => 4
{{1,4},{2},{3,5},{6}} => 4
{{1,4,6},{2},{3},{5}} => 5
{{1,4},{2,6},{3},{5}} => 4
{{1,4},{2},{3,6},{5}} => 4
{{1,4},{2},{3},{5,6}} => 5
{{1,4},{2},{3},{5},{6}} => 5
{{1,5,6},{2,4},{3}} => 5
{{1,5},{2,4,6},{3}} => 3
{{1,5},{2,4},{3,6}} => 3
{{1,5},{2,4},{3},{6}} => 4
{{1,6},{2,4,5},{3}} => 5
{{1},{2,4,5,6},{3}} => 5
{{1},{2,4,5},{3,6}} => 4
{{1},{2,4,5},{3},{6}} => 5
{{1,6},{2,4},{3,5}} => 4
{{1},{2,4,6},{3,5}} => 3
{{1},{2,4},{3,5,6}} => 4
{{1},{2,4},{3,5},{6}} => 4
{{1,6},{2,4},{3},{5}} => 5
{{1},{2,4,6},{3},{5}} => 4
{{1},{2,4},{3,6},{5}} => 4
{{1},{2,4},{3},{5,6}} => 5
{{1},{2,4},{3},{5},{6}} => 5
{{1,5,6},{2},{3,4}} => 6
{{1,5},{2,6},{3,4}} => 4
{{1,5},{2},{3,4,6}} => 4
{{1,5},{2},{3,4},{6}} => 5
{{1,6},{2,5},{3,4}} => 5
{{1},{2,5,6},{3,4}} => 5
{{1},{2,5},{3,4,6}} => 4
{{1},{2,5},{3,4},{6}} => 5
{{1,6},{2},{3,4,5}} => 6
{{1},{2,6},{3,4,5}} => 5
{{1},{2},{3,4,5,6}} => 6
{{1},{2},{3,4,5},{6}} => 6
{{1,6},{2},{3,4},{5}} => 6
{{1},{2,6},{3,4},{5}} => 5
{{1},{2},{3,4,6},{5}} => 5
{{1},{2},{3,4},{5,6}} => 6
{{1},{2},{3,4},{5},{6}} => 6
{{1,5,6},{2},{3},{4}} => 6
{{1,5},{2,6},{3},{4}} => 4
{{1,5},{2},{3,6},{4}} => 4
{{1,5},{2},{3},{4,6}} => 4
{{1,5},{2},{3},{4},{6}} => 5
{{1,6},{2,5},{3},{4}} => 5
{{1},{2,5,6},{3},{4}} => 5
{{1},{2,5},{3,6},{4}} => 4
{{1},{2,5},{3},{4,6}} => 4
{{1},{2,5},{3},{4},{6}} => 5
{{1,6},{2},{3,5},{4}} => 5
{{1},{2,6},{3,5},{4}} => 4
{{1},{2},{3,5,6},{4}} => 5
{{1},{2},{3,5},{4,6}} => 4
{{1},{2},{3,5},{4},{6}} => 5
{{1,6},{2},{3},{4,5}} => 6
{{1},{2,6},{3},{4,5}} => 5
{{1},{2},{3,6},{4,5}} => 5
{{1},{2},{3},{4,5,6}} => 6
{{1},{2},{3},{4,5},{6}} => 6
{{1,6},{2},{3},{4},{5}} => 6
{{1},{2,6},{3},{4},{5}} => 5
{{1},{2},{3,6},{4},{5}} => 5
{{1},{2},{3},{4,6},{5}} => 5
{{1},{2},{3},{4},{5,6}} => 6
{{1},{2},{3},{4},{5},{6}} => 6
{{1,2,3,4,5,6,7}} => 8
{{1,2,3,4,5,6},{7}} => 7
{{1,2,3,4,5,7},{6}} => 7
{{1,2,3,4,5},{6,7}} => 7
{{1,2,3,4,5},{6},{7}} => 7
{{1,2,3,4,6,7},{5}} => 7
{{1,2,3,4,6},{5,7}} => 5
{{1,2,3,4,6},{5},{7}} => 6
{{1,2,3,4,7},{5,6}} => 7
{{1,2,3,4},{5,6,7}} => 7
{{1,2,3,4},{5,6},{7}} => 7
{{1,2,3,4,7},{5},{6}} => 7
{{1,2,3,4},{5,7},{6}} => 6
{{1,2,3,4},{5},{6,7}} => 7
{{1,2,3,4},{5},{6},{7}} => 7
{{1,2,3,5,6,7},{4}} => 7
{{1,2,3,5,6},{4,7}} => 5
{{1,2,3,5,6},{4},{7}} => 6
{{1,2,3,5,7},{4,6}} => 5
{{1,2,3,5},{4,6,7}} => 5
{{1,2,3,5},{4,6},{7}} => 5
{{1,2,3,5,7},{4},{6}} => 6
{{1,2,3,5},{4,7},{6}} => 5
{{1,2,3,5},{4},{6,7}} => 6
{{1,2,3,5},{4},{6},{7}} => 6
{{1,2,3,6,7},{4,5}} => 7
{{1,2,3,6},{4,5,7}} => 5
{{1,2,3,6},{4,5},{7}} => 6
{{1,2,3,7},{4,5,6}} => 7
{{1,2,3},{4,5,6,7}} => 7
{{1,2,3},{4,5,6},{7}} => 7
{{1,2,3,7},{4,5},{6}} => 7
{{1,2,3},{4,5,7},{6}} => 6
{{1,2,3},{4,5},{6,7}} => 7
{{1,2,3},{4,5},{6},{7}} => 7
{{1,2,3,6,7},{4},{5}} => 7
{{1,2,3,6},{4,7},{5}} => 5
{{1,2,3,6},{4},{5,7}} => 5
{{1,2,3,6},{4},{5},{7}} => 6
{{1,2,3,7},{4,6},{5}} => 6
{{1,2,3},{4,6,7},{5}} => 6
{{1,2,3},{4,6},{5,7}} => 5
{{1,2,3},{4,6},{5},{7}} => 6
{{1,2,3,7},{4},{5,6}} => 7
{{1,2,3},{4,7},{5,6}} => 6
{{1,2,3},{4},{5,6,7}} => 7
{{1,2,3},{4},{5,6},{7}} => 7
{{1,2,3,7},{4},{5},{6}} => 7
{{1,2,3},{4,7},{5},{6}} => 6
{{1,2,3},{4},{5,7},{6}} => 6
{{1,2,3},{4},{5},{6,7}} => 7
{{1,2,3},{4},{5},{6},{7}} => 7
{{1,2,4,5,6,7},{3}} => 7
{{1,2,4,5,6},{3,7}} => 5
{{1,2,4,5,6},{3},{7}} => 6
{{1,2,4,5,7},{3,6}} => 5
{{1,2,4,5},{3,6,7}} => 5
{{1,2,4,5},{3,6},{7}} => 5
{{1,2,4,5,7},{3},{6}} => 6
{{1,2,4,5},{3,7},{6}} => 5
{{1,2,4,5},{3},{6,7}} => 6
{{1,2,4,5},{3},{6},{7}} => 6
{{1,2,4,6,7},{3,5}} => 5
{{1,2,4,6},{3,5,7}} => 3
{{1,2,4,6},{3,5},{7}} => 4
{{1,2,4,7},{3,5,6}} => 5
{{1,2,4},{3,5,6,7}} => 5
{{1,2,4},{3,5,6},{7}} => 5
{{1,2,4,7},{3,5},{6}} => 5
{{1,2,4},{3,5,7},{6}} => 4
{{1,2,4},{3,5},{6,7}} => 5
{{1,2,4},{3,5},{6},{7}} => 5
{{1,2,4,6,7},{3},{5}} => 6
{{1,2,4,6},{3,7},{5}} => 4
{{1,2,4,6},{3},{5,7}} => 4
{{1,2,4,6},{3},{5},{7}} => 5
{{1,2,4,7},{3,6},{5}} => 5
{{1,2,4},{3,6,7},{5}} => 5
{{1,2,4},{3,6},{5,7}} => 4
{{1,2,4},{3,6},{5},{7}} => 5
{{1,2,4,7},{3},{5,6}} => 6
{{1,2,4},{3,7},{5,6}} => 5
{{1,2,4},{3},{5,6,7}} => 6
{{1,2,4},{3},{5,6},{7}} => 6
{{1,2,4,7},{3},{5},{6}} => 6
{{1,2,4},{3,7},{5},{6}} => 5
{{1,2,4},{3},{5,7},{6}} => 5
{{1,2,4},{3},{5},{6,7}} => 6
{{1,2,4},{3},{5},{6},{7}} => 6
{{1,2,5,6,7},{3,4}} => 7
{{1,2,5,6},{3,4,7}} => 5
{{1,2,5,6},{3,4},{7}} => 6
{{1,2,5,7},{3,4,6}} => 5
{{1,2,5},{3,4,6,7}} => 5
{{1,2,5},{3,4,6},{7}} => 5
{{1,2,5,7},{3,4},{6}} => 6
{{1,2,5},{3,4,7},{6}} => 5
{{1,2,5},{3,4},{6,7}} => 6
{{1,2,5},{3,4},{6},{7}} => 6
{{1,2,6,7},{3,4,5}} => 7
{{1,2,6},{3,4,5,7}} => 5
{{1,2,6},{3,4,5},{7}} => 6
{{1,2,7},{3,4,5,6}} => 7
{{1,2},{3,4,5,6,7}} => 7
{{1,2},{3,4,5,6},{7}} => 7
{{1,2,7},{3,4,5},{6}} => 7
{{1,2},{3,4,5,7},{6}} => 6
{{1,2},{3,4,5},{6,7}} => 7
{{1,2},{3,4,5},{6},{7}} => 7
{{1,2,6,7},{3,4},{5}} => 7
{{1,2,6},{3,4,7},{5}} => 5
{{1,2,6},{3,4},{5,7}} => 5
{{1,2,6},{3,4},{5},{7}} => 6
{{1,2,7},{3,4,6},{5}} => 6
{{1,2},{3,4,6,7},{5}} => 6
{{1,2},{3,4,6},{5,7}} => 5
{{1,2},{3,4,6},{5},{7}} => 6
{{1,2,7},{3,4},{5,6}} => 7
{{1,2},{3,4,7},{5,6}} => 6
{{1,2},{3,4},{5,6,7}} => 7
{{1,2},{3,4},{5,6},{7}} => 7
{{1,2,7},{3,4},{5},{6}} => 7
{{1,2},{3,4,7},{5},{6}} => 6
{{1,2},{3,4},{5,7},{6}} => 6
{{1,2},{3,4},{5},{6,7}} => 7
{{1,2},{3,4},{5},{6},{7}} => 7
{{1,2,5,6,7},{3},{4}} => 7
{{1,2,5,6},{3,7},{4}} => 5
{{1,2,5,6},{3},{4,7}} => 5
{{1,2,5,6},{3},{4},{7}} => 6
{{1,2,5,7},{3,6},{4}} => 5
{{1,2,5},{3,6,7},{4}} => 5
{{1,2,5},{3,6},{4,7}} => 4
{{1,2,5},{3,6},{4},{7}} => 5
{{1,2,5,7},{3},{4,6}} => 5
{{1,2,5},{3,7},{4,6}} => 4
{{1,2,5},{3},{4,6,7}} => 5
{{1,2,5},{3},{4,6},{7}} => 5
{{1,2,5,7},{3},{4},{6}} => 6
{{1,2,5},{3,7},{4},{6}} => 5
{{1,2,5},{3},{4,7},{6}} => 5
{{1,2,5},{3},{4},{6,7}} => 6
{{1,2,5},{3},{4},{6},{7}} => 6
{{1,2,6,7},{3,5},{4}} => 6
{{1,2,6},{3,5,7},{4}} => 4
{{1,2,6},{3,5},{4,7}} => 4
{{1,2,6},{3,5},{4},{7}} => 5
{{1,2,7},{3,5,6},{4}} => 6
{{1,2},{3,5,6,7},{4}} => 6
{{1,2},{3,5,6},{4,7}} => 5
{{1,2},{3,5,6},{4},{7}} => 6
{{1,2,7},{3,5},{4,6}} => 5
{{1,2},{3,5,7},{4,6}} => 4
{{1,2},{3,5},{4,6,7}} => 5
{{1,2},{3,5},{4,6},{7}} => 5
{{1,2,7},{3,5},{4},{6}} => 6
{{1,2},{3,5,7},{4},{6}} => 5
{{1,2},{3,5},{4,7},{6}} => 5
{{1,2},{3,5},{4},{6,7}} => 6
{{1,2},{3,5},{4},{6},{7}} => 6
{{1,2,6,7},{3},{4,5}} => 7
{{1,2,6},{3,7},{4,5}} => 5
{{1,2,6},{3},{4,5,7}} => 5
{{1,2,6},{3},{4,5},{7}} => 6
{{1,2,7},{3,6},{4,5}} => 6
{{1,2},{3,6,7},{4,5}} => 6
{{1,2},{3,6},{4,5,7}} => 5
{{1,2},{3,6},{4,5},{7}} => 6
{{1,2,7},{3},{4,5,6}} => 7
{{1,2},{3,7},{4,5,6}} => 6
{{1,2},{3},{4,5,6,7}} => 7
{{1,2},{3},{4,5,6},{7}} => 7
{{1,2,7},{3},{4,5},{6}} => 7
{{1,2},{3,7},{4,5},{6}} => 6
{{1,2},{3},{4,5,7},{6}} => 6
{{1,2},{3},{4,5},{6,7}} => 7
{{1,2},{3},{4,5},{6},{7}} => 7
{{1,2,6,7},{3},{4},{5}} => 7
{{1,2,6},{3,7},{4},{5}} => 5
{{1,2,6},{3},{4,7},{5}} => 5
{{1,2,6},{3},{4},{5,7}} => 5
{{1,2,6},{3},{4},{5},{7}} => 6
{{1,2,7},{3,6},{4},{5}} => 6
{{1,2},{3,6,7},{4},{5}} => 6
{{1,2},{3,6},{4,7},{5}} => 5
{{1,2},{3,6},{4},{5,7}} => 5
{{1,2},{3,6},{4},{5},{7}} => 6
{{1,2,7},{3},{4,6},{5}} => 6
{{1,2},{3,7},{4,6},{5}} => 5
{{1,2},{3},{4,6,7},{5}} => 6
{{1,2},{3},{4,6},{5,7}} => 5
{{1,2},{3},{4,6},{5},{7}} => 6
{{1,2,7},{3},{4},{5,6}} => 7
{{1,2},{3,7},{4},{5,6}} => 6
{{1,2},{3},{4,7},{5,6}} => 6
{{1,2},{3},{4},{5,6,7}} => 7
{{1,2},{3},{4},{5,6},{7}} => 7
{{1,2,7},{3},{4},{5},{6}} => 7
{{1,2},{3,7},{4},{5},{6}} => 6
{{1,2},{3},{4,7},{5},{6}} => 6
{{1,2},{3},{4},{5,7},{6}} => 6
{{1,2},{3},{4},{5},{6,7}} => 7
{{1,2},{3},{4},{5},{6},{7}} => 7
{{1,3,4,5,6,7},{2}} => 7
{{1,3,4,5,6},{2,7}} => 5
{{1,3,4,5,6},{2},{7}} => 6
{{1,3,4,5,7},{2,6}} => 5
{{1,3,4,5},{2,6,7}} => 5
{{1,3,4,5},{2,6},{7}} => 5
{{1,3,4,5,7},{2},{6}} => 6
{{1,3,4,5},{2,7},{6}} => 5
{{1,3,4,5},{2},{6,7}} => 6
{{1,3,4,5},{2},{6},{7}} => 6
{{1,3,4,6,7},{2,5}} => 5
{{1,3,4,6},{2,5,7}} => 3
{{1,3,4,6},{2,5},{7}} => 4
{{1,3,4,7},{2,5,6}} => 5
{{1,3,4},{2,5,6,7}} => 5
{{1,3,4},{2,5,6},{7}} => 5
{{1,3,4,7},{2,5},{6}} => 5
{{1,3,4},{2,5,7},{6}} => 4
{{1,3,4},{2,5},{6,7}} => 5
{{1,3,4},{2,5},{6},{7}} => 5
{{1,3,4,6,7},{2},{5}} => 6
{{1,3,4,6},{2,7},{5}} => 4
{{1,3,4,6},{2},{5,7}} => 4
{{1,3,4,6},{2},{5},{7}} => 5
{{1,3,4,7},{2,6},{5}} => 5
{{1,3,4},{2,6,7},{5}} => 5
{{1,3,4},{2,6},{5,7}} => 4
{{1,3,4},{2,6},{5},{7}} => 5
{{1,3,4,7},{2},{5,6}} => 6
{{1,3,4},{2,7},{5,6}} => 5
{{1,3,4},{2},{5,6,7}} => 6
{{1,3,4},{2},{5,6},{7}} => 6
{{1,3,4,7},{2},{5},{6}} => 6
{{1,3,4},{2,7},{5},{6}} => 5
{{1,3,4},{2},{5,7},{6}} => 5
{{1,3,4},{2},{5},{6,7}} => 6
{{1,3,4},{2},{5},{6},{7}} => 6
{{1,3,5,6,7},{2,4}} => 5
{{1,3,5,6},{2,4,7}} => 3
{{1,3,5,6},{2,4},{7}} => 4
{{1,3,5,7},{2,4,6}} => 3
{{1,3,5},{2,4,6,7}} => 3
{{1,3,5},{2,4,6},{7}} => 3
{{1,3,5,7},{2,4},{6}} => 4
{{1,3,5},{2,4,7},{6}} => 3
{{1,3,5},{2,4},{6,7}} => 4
{{1,3,5},{2,4},{6},{7}} => 4
{{1,3,6,7},{2,4,5}} => 5
{{1,3,6},{2,4,5,7}} => 3
{{1,3,6},{2,4,5},{7}} => 4
{{1,3,7},{2,4,5,6}} => 5
{{1,3},{2,4,5,6,7}} => 5
{{1,3},{2,4,5,6},{7}} => 5
{{1,3,7},{2,4,5},{6}} => 5
{{1,3},{2,4,5,7},{6}} => 4
{{1,3},{2,4,5},{6,7}} => 5
{{1,3},{2,4,5},{6},{7}} => 5
{{1,3,6,7},{2,4},{5}} => 5
{{1,3,6},{2,4,7},{5}} => 3
{{1,3,6},{2,4},{5,7}} => 3
{{1,3,6},{2,4},{5},{7}} => 4
{{1,3,7},{2,4,6},{5}} => 4
{{1,3},{2,4,6,7},{5}} => 4
{{1,3},{2,4,6},{5,7}} => 3
{{1,3},{2,4,6},{5},{7}} => 4
{{1,3,7},{2,4},{5,6}} => 5
{{1,3},{2,4,7},{5,6}} => 4
{{1,3},{2,4},{5,6,7}} => 5
{{1,3},{2,4},{5,6},{7}} => 5
{{1,3,7},{2,4},{5},{6}} => 5
{{1,3},{2,4,7},{5},{6}} => 4
{{1,3},{2,4},{5,7},{6}} => 4
{{1,3},{2,4},{5},{6,7}} => 5
{{1,3},{2,4},{5},{6},{7}} => 5
{{1,3,5,6,7},{2},{4}} => 6
{{1,3,5,6},{2,7},{4}} => 4
{{1,3,5,6},{2},{4,7}} => 4
{{1,3,5,6},{2},{4},{7}} => 5
{{1,3,5,7},{2,6},{4}} => 4
{{1,3,5},{2,6,7},{4}} => 4
{{1,3,5},{2,6},{4,7}} => 3
{{1,3,5},{2,6},{4},{7}} => 4
{{1,3,5,7},{2},{4,6}} => 4
{{1,3,5},{2,7},{4,6}} => 3
{{1,3,5},{2},{4,6,7}} => 4
{{1,3,5},{2},{4,6},{7}} => 4
{{1,3,5,7},{2},{4},{6}} => 5
{{1,3,5},{2,7},{4},{6}} => 4
{{1,3,5},{2},{4,7},{6}} => 4
{{1,3,5},{2},{4},{6,7}} => 5
{{1,3,5},{2},{4},{6},{7}} => 5
{{1,3,6,7},{2,5},{4}} => 5
{{1,3,6},{2,5,7},{4}} => 3
{{1,3,6},{2,5},{4,7}} => 3
{{1,3,6},{2,5},{4},{7}} => 4
{{1,3,7},{2,5,6},{4}} => 5
{{1,3},{2,5,6,7},{4}} => 5
{{1,3},{2,5,6},{4,7}} => 4
{{1,3},{2,5,6},{4},{7}} => 5
{{1,3,7},{2,5},{4,6}} => 4
{{1,3},{2,5,7},{4,6}} => 3
{{1,3},{2,5},{4,6,7}} => 4
{{1,3},{2,5},{4,6},{7}} => 4
{{1,3,7},{2,5},{4},{6}} => 5
{{1,3},{2,5,7},{4},{6}} => 4
{{1,3},{2,5},{4,7},{6}} => 4
{{1,3},{2,5},{4},{6,7}} => 5
{{1,3},{2,5},{4},{6},{7}} => 5
{{1,3,6,7},{2},{4,5}} => 6
{{1,3,6},{2,7},{4,5}} => 4
{{1,3,6},{2},{4,5,7}} => 4
{{1,3,6},{2},{4,5},{7}} => 5
{{1,3,7},{2,6},{4,5}} => 5
{{1,3},{2,6,7},{4,5}} => 5
{{1,3},{2,6},{4,5,7}} => 4
{{1,3},{2,6},{4,5},{7}} => 5
{{1,3,7},{2},{4,5,6}} => 6
{{1,3},{2,7},{4,5,6}} => 5
{{1,3},{2},{4,5,6,7}} => 6
{{1,3},{2},{4,5,6},{7}} => 6
{{1,3,7},{2},{4,5},{6}} => 6
{{1,3},{2,7},{4,5},{6}} => 5
{{1,3},{2},{4,5,7},{6}} => 5
{{1,3},{2},{4,5},{6,7}} => 6
{{1,3},{2},{4,5},{6},{7}} => 6
{{1,3,6,7},{2},{4},{5}} => 6
{{1,3,6},{2,7},{4},{5}} => 4
{{1,3,6},{2},{4,7},{5}} => 4
{{1,3,6},{2},{4},{5,7}} => 4
{{1,3,6},{2},{4},{5},{7}} => 5
{{1,3,7},{2,6},{4},{5}} => 5
{{1,3},{2,6,7},{4},{5}} => 5
{{1,3},{2,6},{4,7},{5}} => 4
{{1,3},{2,6},{4},{5,7}} => 4
{{1,3},{2,6},{4},{5},{7}} => 5
{{1,3,7},{2},{4,6},{5}} => 5
{{1,3},{2,7},{4,6},{5}} => 4
{{1,3},{2},{4,6,7},{5}} => 5
{{1,3},{2},{4,6},{5,7}} => 4
{{1,3},{2},{4,6},{5},{7}} => 5
{{1,3,7},{2},{4},{5,6}} => 6
{{1,3},{2,7},{4},{5,6}} => 5
{{1,3},{2},{4,7},{5,6}} => 5
{{1,3},{2},{4},{5,6,7}} => 6
{{1,3},{2},{4},{5,6},{7}} => 6
{{1,3,7},{2},{4},{5},{6}} => 6
{{1,3},{2,7},{4},{5},{6}} => 5
{{1,3},{2},{4,7},{5},{6}} => 5
{{1,3},{2},{4},{5,7},{6}} => 5
{{1,3},{2},{4},{5},{6,7}} => 6
{{1,3},{2},{4},{5},{6},{7}} => 6
{{1,4,5,6,7},{2,3}} => 7
{{1,4,5,6},{2,3,7}} => 5
{{1,4,5,6},{2,3},{7}} => 6
{{1,4,5,7},{2,3,6}} => 5
{{1,4,5},{2,3,6,7}} => 5
{{1,4,5},{2,3,6},{7}} => 5
{{1,4,5,7},{2,3},{6}} => 6
{{1,4,5},{2,3,7},{6}} => 5
{{1,4,5},{2,3},{6,7}} => 6
{{1,4,5},{2,3},{6},{7}} => 6
{{1,4,6,7},{2,3,5}} => 5
{{1,4,6},{2,3,5,7}} => 3
{{1,4,6},{2,3,5},{7}} => 4
{{1,4,7},{2,3,5,6}} => 5
{{1,4},{2,3,5,6,7}} => 5
{{1,4},{2,3,5,6},{7}} => 5
{{1,4,7},{2,3,5},{6}} => 5
{{1,4},{2,3,5,7},{6}} => 4
{{1,4},{2,3,5},{6,7}} => 5
{{1,4},{2,3,5},{6},{7}} => 5
{{1,4,6,7},{2,3},{5}} => 6
{{1,4,6},{2,3,7},{5}} => 4
{{1,4,6},{2,3},{5,7}} => 4
{{1,4,6},{2,3},{5},{7}} => 5
{{1,4,7},{2,3,6},{5}} => 5
{{1,4},{2,3,6,7},{5}} => 5
{{1,4},{2,3,6},{5,7}} => 4
{{1,4},{2,3,6},{5},{7}} => 5
{{1,4,7},{2,3},{5,6}} => 6
{{1,4},{2,3,7},{5,6}} => 5
{{1,4},{2,3},{5,6,7}} => 6
{{1,4},{2,3},{5,6},{7}} => 6
{{1,4,7},{2,3},{5},{6}} => 6
{{1,4},{2,3,7},{5},{6}} => 5
{{1,4},{2,3},{5,7},{6}} => 5
{{1,4},{2,3},{5},{6,7}} => 6
{{1,4},{2,3},{5},{6},{7}} => 6
{{1,5,6,7},{2,3,4}} => 7
{{1,5,6},{2,3,4,7}} => 5
{{1,5,6},{2,3,4},{7}} => 6
{{1,5,7},{2,3,4,6}} => 5
{{1,5},{2,3,4,6,7}} => 5
{{1,5},{2,3,4,6},{7}} => 5
{{1,5,7},{2,3,4},{6}} => 6
{{1,5},{2,3,4,7},{6}} => 5
{{1,5},{2,3,4},{6,7}} => 6
{{1,5},{2,3,4},{6},{7}} => 6
{{1,6,7},{2,3,4,5}} => 7
{{1,6},{2,3,4,5,7}} => 5
{{1,6},{2,3,4,5},{7}} => 6
{{1,7},{2,3,4,5,6}} => 7
{{1},{2,3,4,5,6,7}} => 7
{{1},{2,3,4,5,6},{7}} => 7
{{1,7},{2,3,4,5},{6}} => 7
{{1},{2,3,4,5,7},{6}} => 6
{{1},{2,3,4,5},{6,7}} => 7
{{1},{2,3,4,5},{6},{7}} => 7
{{1,6,7},{2,3,4},{5}} => 7
{{1,6},{2,3,4,7},{5}} => 5
{{1,6},{2,3,4},{5,7}} => 5
{{1,6},{2,3,4},{5},{7}} => 6
{{1,7},{2,3,4,6},{5}} => 6
{{1},{2,3,4,6,7},{5}} => 6
{{1},{2,3,4,6},{5,7}} => 5
{{1},{2,3,4,6},{5},{7}} => 6
{{1,7},{2,3,4},{5,6}} => 7
{{1},{2,3,4,7},{5,6}} => 6
{{1},{2,3,4},{5,6,7}} => 7
{{1},{2,3,4},{5,6},{7}} => 7
{{1,7},{2,3,4},{5},{6}} => 7
{{1},{2,3,4,7},{5},{6}} => 6
{{1},{2,3,4},{5,7},{6}} => 6
{{1},{2,3,4},{5},{6,7}} => 7
{{1},{2,3,4},{5},{6},{7}} => 7
{{1,5,6,7},{2,3},{4}} => 7
{{1,5,6},{2,3,7},{4}} => 5
{{1,5,6},{2,3},{4,7}} => 5
{{1,5,6},{2,3},{4},{7}} => 6
{{1,5,7},{2,3,6},{4}} => 5
{{1,5},{2,3,6,7},{4}} => 5
{{1,5},{2,3,6},{4,7}} => 4
{{1,5},{2,3,6},{4},{7}} => 5
{{1,5,7},{2,3},{4,6}} => 5
{{1,5},{2,3,7},{4,6}} => 4
{{1,5},{2,3},{4,6,7}} => 5
{{1,5},{2,3},{4,6},{7}} => 5
{{1,5,7},{2,3},{4},{6}} => 6
{{1,5},{2,3,7},{4},{6}} => 5
{{1,5},{2,3},{4,7},{6}} => 5
{{1,5},{2,3},{4},{6,7}} => 6
{{1,5},{2,3},{4},{6},{7}} => 6
{{1,6,7},{2,3,5},{4}} => 6
{{1,6},{2,3,5,7},{4}} => 4
{{1,6},{2,3,5},{4,7}} => 4
{{1,6},{2,3,5},{4},{7}} => 5
{{1,7},{2,3,5,6},{4}} => 6
{{1},{2,3,5,6,7},{4}} => 6
{{1},{2,3,5,6},{4,7}} => 5
{{1},{2,3,5,6},{4},{7}} => 6
{{1,7},{2,3,5},{4,6}} => 5
{{1},{2,3,5,7},{4,6}} => 4
{{1},{2,3,5},{4,6,7}} => 5
{{1},{2,3,5},{4,6},{7}} => 5
{{1,7},{2,3,5},{4},{6}} => 6
{{1},{2,3,5,7},{4},{6}} => 5
{{1},{2,3,5},{4,7},{6}} => 5
{{1},{2,3,5},{4},{6,7}} => 6
{{1},{2,3,5},{4},{6},{7}} => 6
{{1,6,7},{2,3},{4,5}} => 7
{{1,6},{2,3,7},{4,5}} => 5
{{1,6},{2,3},{4,5,7}} => 5
{{1,6},{2,3},{4,5},{7}} => 6
{{1,7},{2,3,6},{4,5}} => 6
{{1},{2,3,6,7},{4,5}} => 6
{{1},{2,3,6},{4,5,7}} => 5
{{1},{2,3,6},{4,5},{7}} => 6
{{1,7},{2,3},{4,5,6}} => 7
{{1},{2,3,7},{4,5,6}} => 6
{{1},{2,3},{4,5,6,7}} => 7
{{1},{2,3},{4,5,6},{7}} => 7
{{1,7},{2,3},{4,5},{6}} => 7
{{1},{2,3,7},{4,5},{6}} => 6
{{1},{2,3},{4,5,7},{6}} => 6
{{1},{2,3},{4,5},{6,7}} => 7
{{1},{2,3},{4,5},{6},{7}} => 7
{{1,6,7},{2,3},{4},{5}} => 7
{{1,6},{2,3,7},{4},{5}} => 5
{{1,6},{2,3},{4,7},{5}} => 5
{{1,6},{2,3},{4},{5,7}} => 5
{{1,6},{2,3},{4},{5},{7}} => 6
{{1,7},{2,3,6},{4},{5}} => 6
{{1},{2,3,6,7},{4},{5}} => 6
{{1},{2,3,6},{4,7},{5}} => 5
{{1},{2,3,6},{4},{5,7}} => 5
{{1},{2,3,6},{4},{5},{7}} => 6
{{1,7},{2,3},{4,6},{5}} => 6
{{1},{2,3,7},{4,6},{5}} => 5
{{1},{2,3},{4,6,7},{5}} => 6
{{1},{2,3},{4,6},{5,7}} => 5
{{1},{2,3},{4,6},{5},{7}} => 6
{{1,7},{2,3},{4},{5,6}} => 7
{{1},{2,3,7},{4},{5,6}} => 6
{{1},{2,3},{4,7},{5,6}} => 6
{{1},{2,3},{4},{5,6,7}} => 7
{{1},{2,3},{4},{5,6},{7}} => 7
{{1,7},{2,3},{4},{5},{6}} => 7
{{1},{2,3,7},{4},{5},{6}} => 6
{{1},{2,3},{4,7},{5},{6}} => 6
{{1},{2,3},{4},{5,7},{6}} => 6
{{1},{2,3},{4},{5},{6,7}} => 7
{{1},{2,3},{4},{5},{6},{7}} => 7
{{1,4,5,6,7},{2},{3}} => 7
{{1,4,5,6},{2,7},{3}} => 5
{{1,4,5,6},{2},{3,7}} => 5
{{1,4,5,6},{2},{3},{7}} => 6
{{1,4,5,7},{2,6},{3}} => 5
{{1,4,5},{2,6,7},{3}} => 5
{{1,4,5},{2,6},{3,7}} => 4
{{1,4,5},{2,6},{3},{7}} => 5
{{1,4,5,7},{2},{3,6}} => 5
{{1,4,5},{2,7},{3,6}} => 4
{{1,4,5},{2},{3,6,7}} => 5
{{1,4,5},{2},{3,6},{7}} => 5
{{1,4,5,7},{2},{3},{6}} => 6
{{1,4,5},{2,7},{3},{6}} => 5
{{1,4,5},{2},{3,7},{6}} => 5
{{1,4,5},{2},{3},{6,7}} => 6
{{1,4,5},{2},{3},{6},{7}} => 6
{{1,4,6,7},{2,5},{3}} => 5
{{1,4,6},{2,5,7},{3}} => 3
{{1,4,6},{2,5},{3,7}} => 3
{{1,4,6},{2,5},{3},{7}} => 4
{{1,4,7},{2,5,6},{3}} => 5
{{1,4},{2,5,6,7},{3}} => 5
{{1,4},{2,5,6},{3,7}} => 4
{{1,4},{2,5,6},{3},{7}} => 5
{{1,4,7},{2,5},{3,6}} => 4
{{1,4},{2,5,7},{3,6}} => 3
{{1,4},{2,5},{3,6,7}} => 4
{{1,4},{2,5},{3,6},{7}} => 4
{{1,4,7},{2,5},{3},{6}} => 5
{{1,4},{2,5,7},{3},{6}} => 4
{{1,4},{2,5},{3,7},{6}} => 4
{{1,4},{2,5},{3},{6,7}} => 5
{{1,4},{2,5},{3},{6},{7}} => 5
{{1,4,6,7},{2},{3,5}} => 5
{{1,4,6},{2,7},{3,5}} => 3
{{1,4,6},{2},{3,5,7}} => 3
{{1,4,6},{2},{3,5},{7}} => 4
{{1,4,7},{2,6},{3,5}} => 4
{{1,4},{2,6,7},{3,5}} => 4
{{1,4},{2,6},{3,5,7}} => 3
{{1,4},{2,6},{3,5},{7}} => 4
{{1,4,7},{2},{3,5,6}} => 5
{{1,4},{2,7},{3,5,6}} => 4
{{1,4},{2},{3,5,6,7}} => 5
{{1,4},{2},{3,5,6},{7}} => 5
{{1,4,7},{2},{3,5},{6}} => 5
{{1,4},{2,7},{3,5},{6}} => 4
{{1,4},{2},{3,5,7},{6}} => 4
{{1,4},{2},{3,5},{6,7}} => 5
{{1,4},{2},{3,5},{6},{7}} => 5
{{1,4,6,7},{2},{3},{5}} => 6
{{1,4,6},{2,7},{3},{5}} => 4
{{1,4,6},{2},{3,7},{5}} => 4
{{1,4,6},{2},{3},{5,7}} => 4
{{1,4,6},{2},{3},{5},{7}} => 5
{{1,4,7},{2,6},{3},{5}} => 5
{{1,4},{2,6,7},{3},{5}} => 5
{{1,4},{2,6},{3,7},{5}} => 4
{{1,4},{2,6},{3},{5,7}} => 4
{{1,4},{2,6},{3},{5},{7}} => 5
{{1,4,7},{2},{3,6},{5}} => 5
{{1,4},{2,7},{3,6},{5}} => 4
{{1,4},{2},{3,6,7},{5}} => 5
{{1,4},{2},{3,6},{5,7}} => 4
{{1,4},{2},{3,6},{5},{7}} => 5
{{1,4,7},{2},{3},{5,6}} => 6
{{1,4},{2,7},{3},{5,6}} => 5
{{1,4},{2},{3,7},{5,6}} => 5
{{1,4},{2},{3},{5,6,7}} => 6
{{1,4},{2},{3},{5,6},{7}} => 6
{{1,4,7},{2},{3},{5},{6}} => 6
{{1,4},{2,7},{3},{5},{6}} => 5
{{1,4},{2},{3,7},{5},{6}} => 5
{{1,4},{2},{3},{5,7},{6}} => 5
{{1,4},{2},{3},{5},{6,7}} => 6
{{1,4},{2},{3},{5},{6},{7}} => 6
{{1,5,6,7},{2,4},{3}} => 6
{{1,5,6},{2,4,7},{3}} => 4
{{1,5,6},{2,4},{3,7}} => 4
{{1,5,6},{2,4},{3},{7}} => 5
{{1,5,7},{2,4,6},{3}} => 4
{{1,5},{2,4,6,7},{3}} => 4
{{1,5},{2,4,6},{3,7}} => 3
{{1,5},{2,4,6},{3},{7}} => 4
{{1,5,7},{2,4},{3,6}} => 4
{{1,5},{2,4,7},{3,6}} => 3
{{1,5},{2,4},{3,6,7}} => 4
{{1,5},{2,4},{3,6},{7}} => 4
{{1,5,7},{2,4},{3},{6}} => 5
{{1,5},{2,4,7},{3},{6}} => 4
{{1,5},{2,4},{3,7},{6}} => 4
{{1,5},{2,4},{3},{6,7}} => 5
{{1,5},{2,4},{3},{6},{7}} => 5
{{1,6,7},{2,4,5},{3}} => 6
{{1,6},{2,4,5,7},{3}} => 4
{{1,6},{2,4,5},{3,7}} => 4
{{1,6},{2,4,5},{3},{7}} => 5
{{1,7},{2,4,5,6},{3}} => 6
{{1},{2,4,5,6,7},{3}} => 6
{{1},{2,4,5,6},{3,7}} => 5
{{1},{2,4,5,6},{3},{7}} => 6
{{1,7},{2,4,5},{3,6}} => 5
{{1},{2,4,5,7},{3,6}} => 4
{{1},{2,4,5},{3,6,7}} => 5
{{1},{2,4,5},{3,6},{7}} => 5
{{1,7},{2,4,5},{3},{6}} => 6
{{1},{2,4,5,7},{3},{6}} => 5
{{1},{2,4,5},{3,7},{6}} => 5
{{1},{2,4,5},{3},{6,7}} => 6
{{1},{2,4,5},{3},{6},{7}} => 6
{{1,6,7},{2,4},{3,5}} => 5
{{1,6},{2,4,7},{3,5}} => 3
{{1,6},{2,4},{3,5,7}} => 3
{{1,6},{2,4},{3,5},{7}} => 4
{{1,7},{2,4,6},{3,5}} => 4
{{1},{2,4,6,7},{3,5}} => 4
{{1},{2,4,6},{3,5,7}} => 3
{{1},{2,4,6},{3,5},{7}} => 4
{{1,7},{2,4},{3,5,6}} => 5
{{1},{2,4,7},{3,5,6}} => 4
{{1},{2,4},{3,5,6,7}} => 5
{{1},{2,4},{3,5,6},{7}} => 5
{{1,7},{2,4},{3,5},{6}} => 5
{{1},{2,4,7},{3,5},{6}} => 4
{{1},{2,4},{3,5,7},{6}} => 4
{{1},{2,4},{3,5},{6,7}} => 5
{{1},{2,4},{3,5},{6},{7}} => 5
{{1,6,7},{2,4},{3},{5}} => 6
{{1,6},{2,4,7},{3},{5}} => 4
{{1,6},{2,4},{3,7},{5}} => 4
{{1,6},{2,4},{3},{5,7}} => 4
{{1,6},{2,4},{3},{5},{7}} => 5
{{1,7},{2,4,6},{3},{5}} => 5
{{1},{2,4,6,7},{3},{5}} => 5
{{1},{2,4,6},{3,7},{5}} => 4
{{1},{2,4,6},{3},{5,7}} => 4
{{1},{2,4,6},{3},{5},{7}} => 5
{{1,7},{2,4},{3,6},{5}} => 5
{{1},{2,4,7},{3,6},{5}} => 4
{{1},{2,4},{3,6,7},{5}} => 5
{{1},{2,4},{3,6},{5,7}} => 4
{{1},{2,4},{3,6},{5},{7}} => 5
{{1,7},{2,4},{3},{5,6}} => 6
{{1},{2,4,7},{3},{5,6}} => 5
{{1},{2,4},{3,7},{5,6}} => 5
{{1},{2,4},{3},{5,6,7}} => 6
{{1},{2,4},{3},{5,6},{7}} => 6
{{1,7},{2,4},{3},{5},{6}} => 6
{{1},{2,4,7},{3},{5},{6}} => 5
{{1},{2,4},{3,7},{5},{6}} => 5
{{1},{2,4},{3},{5,7},{6}} => 5
{{1},{2,4},{3},{5},{6,7}} => 6
{{1},{2,4},{3},{5},{6},{7}} => 6
{{1,5,6,7},{2},{3,4}} => 7
{{1,5,6},{2,7},{3,4}} => 5
{{1,5,6},{2},{3,4,7}} => 5
{{1,5,6},{2},{3,4},{7}} => 6
{{1,5,7},{2,6},{3,4}} => 5
{{1,5},{2,6,7},{3,4}} => 5
{{1,5},{2,6},{3,4,7}} => 4
{{1,5},{2,6},{3,4},{7}} => 5
{{1,5,7},{2},{3,4,6}} => 5
{{1,5},{2,7},{3,4,6}} => 4
{{1,5},{2},{3,4,6,7}} => 5
{{1,5},{2},{3,4,6},{7}} => 5
{{1,5,7},{2},{3,4},{6}} => 6
{{1,5},{2,7},{3,4},{6}} => 5
{{1,5},{2},{3,4,7},{6}} => 5
{{1,5},{2},{3,4},{6,7}} => 6
{{1,5},{2},{3,4},{6},{7}} => 6
{{1,6,7},{2,5},{3,4}} => 6
{{1,6},{2,5,7},{3,4}} => 4
{{1,6},{2,5},{3,4,7}} => 4
{{1,6},{2,5},{3,4},{7}} => 5
{{1,7},{2,5,6},{3,4}} => 6
{{1},{2,5,6,7},{3,4}} => 6
{{1},{2,5,6},{3,4,7}} => 5
{{1},{2,5,6},{3,4},{7}} => 6
{{1,7},{2,5},{3,4,6}} => 5
{{1},{2,5,7},{3,4,6}} => 4
{{1},{2,5},{3,4,6,7}} => 5
{{1},{2,5},{3,4,6},{7}} => 5
{{1,7},{2,5},{3,4},{6}} => 6
{{1},{2,5,7},{3,4},{6}} => 5
{{1},{2,5},{3,4,7},{6}} => 5
{{1},{2,5},{3,4},{6,7}} => 6
{{1},{2,5},{3,4},{6},{7}} => 6
{{1,6,7},{2},{3,4,5}} => 7
{{1,6},{2,7},{3,4,5}} => 5
{{1,6},{2},{3,4,5,7}} => 5
{{1,6},{2},{3,4,5},{7}} => 6
{{1,7},{2,6},{3,4,5}} => 6
{{1},{2,6,7},{3,4,5}} => 6
{{1},{2,6},{3,4,5,7}} => 5
{{1},{2,6},{3,4,5},{7}} => 6
{{1,7},{2},{3,4,5,6}} => 7
{{1},{2,7},{3,4,5,6}} => 6
{{1},{2},{3,4,5,6,7}} => 7
{{1},{2},{3,4,5,6},{7}} => 7
{{1,7},{2},{3,4,5},{6}} => 7
{{1},{2,7},{3,4,5},{6}} => 6
{{1},{2},{3,4,5,7},{6}} => 6
{{1},{2},{3,4,5},{6,7}} => 7
{{1},{2},{3,4,5},{6},{7}} => 7
{{1,6,7},{2},{3,4},{5}} => 7
{{1,6},{2,7},{3,4},{5}} => 5
{{1,6},{2},{3,4,7},{5}} => 5
{{1,6},{2},{3,4},{5,7}} => 5
{{1,6},{2},{3,4},{5},{7}} => 6
{{1,7},{2,6},{3,4},{5}} => 6
{{1},{2,6,7},{3,4},{5}} => 6
{{1},{2,6},{3,4,7},{5}} => 5
{{1},{2,6},{3,4},{5,7}} => 5
{{1},{2,6},{3,4},{5},{7}} => 6
{{1,7},{2},{3,4,6},{5}} => 6
{{1},{2,7},{3,4,6},{5}} => 5
{{1},{2},{3,4,6,7},{5}} => 6
{{1},{2},{3,4,6},{5,7}} => 5
{{1},{2},{3,4,6},{5},{7}} => 6
{{1,7},{2},{3,4},{5,6}} => 7
{{1},{2,7},{3,4},{5,6}} => 6
{{1},{2},{3,4,7},{5,6}} => 6
{{1},{2},{3,4},{5,6,7}} => 7
{{1},{2},{3,4},{5,6},{7}} => 7
{{1,7},{2},{3,4},{5},{6}} => 7
{{1},{2,7},{3,4},{5},{6}} => 6
{{1},{2},{3,4,7},{5},{6}} => 6
{{1},{2},{3,4},{5,7},{6}} => 6
{{1},{2},{3,4},{5},{6,7}} => 7
{{1},{2},{3,4},{5},{6},{7}} => 7
{{1,5,6,7},{2},{3},{4}} => 7
{{1,5,6},{2,7},{3},{4}} => 5
{{1,5,6},{2},{3,7},{4}} => 5
{{1,5,6},{2},{3},{4,7}} => 5
{{1,5,6},{2},{3},{4},{7}} => 6
{{1,5,7},{2,6},{3},{4}} => 5
{{1,5},{2,6,7},{3},{4}} => 5
{{1,5},{2,6},{3,7},{4}} => 4
{{1,5},{2,6},{3},{4,7}} => 4
{{1,5},{2,6},{3},{4},{7}} => 5
{{1,5,7},{2},{3,6},{4}} => 5
{{1,5},{2,7},{3,6},{4}} => 4
{{1,5},{2},{3,6,7},{4}} => 5
{{1,5},{2},{3,6},{4,7}} => 4
{{1,5},{2},{3,6},{4},{7}} => 5
{{1,5,7},{2},{3},{4,6}} => 5
{{1,5},{2,7},{3},{4,6}} => 4
{{1,5},{2},{3,7},{4,6}} => 4
{{1,5},{2},{3},{4,6,7}} => 5
{{1,5},{2},{3},{4,6},{7}} => 5
{{1,5,7},{2},{3},{4},{6}} => 6
{{1,5},{2,7},{3},{4},{6}} => 5
{{1,5},{2},{3,7},{4},{6}} => 5
{{1,5},{2},{3},{4,7},{6}} => 5
{{1,5},{2},{3},{4},{6,7}} => 6
{{1,5},{2},{3},{4},{6},{7}} => 6
{{1,6,7},{2,5},{3},{4}} => 6
{{1,6},{2,5,7},{3},{4}} => 4
{{1,6},{2,5},{3,7},{4}} => 4
{{1,6},{2,5},{3},{4,7}} => 4
{{1,6},{2,5},{3},{4},{7}} => 5
{{1,7},{2,5,6},{3},{4}} => 6
{{1},{2,5,6,7},{3},{4}} => 6
{{1},{2,5,6},{3,7},{4}} => 5
{{1},{2,5,6},{3},{4,7}} => 5
{{1},{2,5,6},{3},{4},{7}} => 6
{{1,7},{2,5},{3,6},{4}} => 5
{{1},{2,5,7},{3,6},{4}} => 4
{{1},{2,5},{3,6,7},{4}} => 5
{{1},{2,5},{3,6},{4,7}} => 4
{{1},{2,5},{3,6},{4},{7}} => 5
{{1,7},{2,5},{3},{4,6}} => 5
{{1},{2,5,7},{3},{4,6}} => 4
{{1},{2,5},{3,7},{4,6}} => 4
{{1},{2,5},{3},{4,6,7}} => 5
{{1},{2,5},{3},{4,6},{7}} => 5
{{1,7},{2,5},{3},{4},{6}} => 6
{{1},{2,5,7},{3},{4},{6}} => 5
{{1},{2,5},{3,7},{4},{6}} => 5
{{1},{2,5},{3},{4,7},{6}} => 5
{{1},{2,5},{3},{4},{6,7}} => 6
{{1},{2,5},{3},{4},{6},{7}} => 6
{{1,6,7},{2},{3,5},{4}} => 6
{{1,6},{2,7},{3,5},{4}} => 4
{{1,6},{2},{3,5,7},{4}} => 4
{{1,6},{2},{3,5},{4,7}} => 4
{{1,6},{2},{3,5},{4},{7}} => 5
{{1,7},{2,6},{3,5},{4}} => 5
{{1},{2,6,7},{3,5},{4}} => 5
{{1},{2,6},{3,5,7},{4}} => 4
{{1},{2,6},{3,5},{4,7}} => 4
{{1},{2,6},{3,5},{4},{7}} => 5
{{1,7},{2},{3,5,6},{4}} => 6
{{1},{2,7},{3,5,6},{4}} => 5
{{1},{2},{3,5,6,7},{4}} => 6
{{1},{2},{3,5,6},{4,7}} => 5
{{1},{2},{3,5,6},{4},{7}} => 6
{{1,7},{2},{3,5},{4,6}} => 5
{{1},{2,7},{3,5},{4,6}} => 4
{{1},{2},{3,5,7},{4,6}} => 4
{{1},{2},{3,5},{4,6,7}} => 5
{{1},{2},{3,5},{4,6},{7}} => 5
{{1,7},{2},{3,5},{4},{6}} => 6
{{1},{2,7},{3,5},{4},{6}} => 5
{{1},{2},{3,5,7},{4},{6}} => 5
{{1},{2},{3,5},{4,7},{6}} => 5
{{1},{2},{3,5},{4},{6,7}} => 6
{{1},{2},{3,5},{4},{6},{7}} => 6
{{1,6,7},{2},{3},{4,5}} => 7
{{1,6},{2,7},{3},{4,5}} => 5
{{1,6},{2},{3,7},{4,5}} => 5
{{1,6},{2},{3},{4,5,7}} => 5
{{1,6},{2},{3},{4,5},{7}} => 6
{{1,7},{2,6},{3},{4,5}} => 6
{{1},{2,6,7},{3},{4,5}} => 6
{{1},{2,6},{3,7},{4,5}} => 5
{{1},{2,6},{3},{4,5,7}} => 5
{{1},{2,6},{3},{4,5},{7}} => 6
{{1,7},{2},{3,6},{4,5}} => 6
{{1},{2,7},{3,6},{4,5}} => 5
{{1},{2},{3,6,7},{4,5}} => 6
{{1},{2},{3,6},{4,5,7}} => 5
{{1},{2},{3,6},{4,5},{7}} => 6
{{1,7},{2},{3},{4,5,6}} => 7
{{1},{2,7},{3},{4,5,6}} => 6
{{1},{2},{3,7},{4,5,6}} => 6
{{1},{2},{3},{4,5,6,7}} => 7
{{1},{2},{3},{4,5,6},{7}} => 7
{{1,7},{2},{3},{4,5},{6}} => 7
{{1},{2,7},{3},{4,5},{6}} => 6
{{1},{2},{3,7},{4,5},{6}} => 6
{{1},{2},{3},{4,5,7},{6}} => 6
{{1},{2},{3},{4,5},{6,7}} => 7
{{1},{2},{3},{4,5},{6},{7}} => 7
{{1,6,7},{2},{3},{4},{5}} => 7
{{1,6},{2,7},{3},{4},{5}} => 5
{{1,6},{2},{3,7},{4},{5}} => 5
{{1,6},{2},{3},{4,7},{5}} => 5
{{1,6},{2},{3},{4},{5,7}} => 5
{{1,6},{2},{3},{4},{5},{7}} => 6
{{1,7},{2,6},{3},{4},{5}} => 6
{{1},{2,6,7},{3},{4},{5}} => 6
{{1},{2,6},{3,7},{4},{5}} => 5
{{1},{2,6},{3},{4,7},{5}} => 5
{{1},{2,6},{3},{4},{5,7}} => 5
{{1},{2,6},{3},{4},{5},{7}} => 6
{{1,7},{2},{3,6},{4},{5}} => 6
{{1},{2,7},{3,6},{4},{5}} => 5
{{1},{2},{3,6,7},{4},{5}} => 6
{{1},{2},{3,6},{4,7},{5}} => 5
{{1},{2},{3,6},{4},{5,7}} => 5
{{1},{2},{3,6},{4},{5},{7}} => 6
{{1,7},{2},{3},{4,6},{5}} => 6
{{1},{2,7},{3},{4,6},{5}} => 5
{{1},{2},{3,7},{4,6},{5}} => 5
{{1},{2},{3},{4,6,7},{5}} => 6
{{1},{2},{3},{4,6},{5,7}} => 5
{{1},{2},{3},{4,6},{5},{7}} => 6
{{1,7},{2},{3},{4},{5,6}} => 7
{{1},{2,7},{3},{4},{5,6}} => 6
{{1},{2},{3,7},{4},{5,6}} => 6
{{1},{2},{3},{4,7},{5,6}} => 6
{{1},{2},{3},{4},{5,6,7}} => 7
{{1},{2},{3},{4},{5,6},{7}} => 7
{{1,7},{2},{3},{4},{5},{6}} => 7
{{1},{2,7},{3},{4},{5},{6}} => 6
{{1},{2},{3,7},{4},{5},{6}} => 6
{{1},{2},{3},{4,7},{5},{6}} => 6
{{1},{2},{3},{4},{5,7},{6}} => 6
{{1},{2},{3},{4},{5},{6,7}} => 7
{{1},{2},{3},{4},{5},{6},{7}} => 7
{{1},{2},{3,4,5,6,7,8}} => 8
{{1},{2,4,5,6,7,8},{3}} => 7
{{1},{2,3,5,6,7,8},{4}} => 7
{{1},{2,3,4,6,7,8},{5}} => 7
{{1},{2,3,4,5,7,8},{6}} => 7
{{1},{2,3,4,5,6,7},{8}} => 8
{{1},{2,3,4,5,6,8},{7}} => 7
{{1},{2,3,4,5,6,7,8}} => 8
{{1,2},{3,4,5,6,7,8}} => 8
{{1,4,5,6,7,8},{2},{3}} => 8
{{1,3,5,6,7,8},{2},{4}} => 7
{{1,3,4,5,6,7,8},{2}} => 8
{{1,4,5,6,7,8},{2,3}} => 8
{{1,2,4,5,6,7,8},{3}} => 8
{{1,2,5,6,7,8},{3,4}} => 8
{{1,2,3,5,6,7,8},{4}} => 8
{{1,2,3,6,7,8},{4,5}} => 8
{{1,2,3,4,6,7,8},{5}} => 8
{{1,2,3,4,5,6},{7,8}} => 8
{{1,2,3,4,7,8},{5,6}} => 8
{{1,2,3,4,5,7,8},{6}} => 8
{{1,2,3,4,5,6,7},{8}} => 8
{{1,8},{2,3,4,5,6,7}} => 8
{{1,2,3,4,5,8},{6,7}} => 8
{{1,2,3,4,5,6,8},{7}} => 8
{{1,2,3,4,5,6,7,8}} => 9
{{1,3,5,6,7,8},{2,4}} => 6
{{1,3,4,6,7,8},{2,5}} => 6
{{1,2,4,6,7,8},{3,5}} => 6
{{1,3,4,5,7,8},{2,6}} => 6
{{1,2,4,5,7,8},{3,6}} => 6
{{1,2,3,5,7,8},{4,6}} => 6
{{1,3,4,5,6,8},{2,7}} => 6
{{1,2,4,5,6,8},{3,7}} => 6
{{1,2,3,5,6,8},{4,7}} => 6
{{1,2,3,4,6,8},{5,7}} => 6
{{1,3,4,5,6,7},{2,8}} => 6
{{1,2,4,5,6,7},{3,8}} => 6
{{1,2,3,5,6,7},{4,8}} => 6
{{1,2,3,4,6,7},{5,8}} => 6
{{1,2,3,4,5,7},{6,8}} => 6
{{1,3},{2,4,5,6,7,8}} => 6
{{1,4},{2,3,5,6,7,8}} => 6
{{1,5},{2,3,4,6,7,8}} => 6
{{1,6},{2,3,4,5,7,8}} => 6
{{1,7},{2,3,4,5,6,8}} => 6
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 4,1 1,2,11,1 10,15,26,1 1,10,65,69,57,1 28,140,336,252,120,1
$F_{2} = q^{2} + q^{3}$
$F_{3} = 4\ q^{3} + q^{4}$
$F_{4} = q^{2} + 2\ q^{3} + 11\ q^{4} + q^{5}$
$F_{5} = 10\ q^{3} + 15\ q^{4} + 26\ q^{5} + q^{6}$
$F_{6} = q^{2} + 10\ q^{3} + 65\ q^{4} + 69\ q^{5} + 57\ q^{6} + q^{7}$
$F_{7} = 28\ q^{3} + 140\ q^{4} + 336\ q^{5} + 252\ q^{6} + 120\ q^{7} + q^{8}$
Description
References
[1] Birdsong, S., Hetyei, Gábor The Toric h-Vector of a Cubical Complex in Terms of Noncrossing Partition Statistics DOI:10.1007/s00026-014-0243-8
Code
def statistic(S):
n = S.size()
return sum( 1 for B in S for i in B if (i%n)+1 in B ) + len(S)
Created
May 05, 2015 at 11:08 by Christian Stump
Updated
Jun 01, 2015 at 17:51 by Martin Rubey
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