Identifier
Values
{{1},{2}} => [1,1] => ([(0,1)],2) => -1
{{1,2},{3}} => [2,1] => ([(0,2),(1,2)],3) => 0
{{1,3},{2}} => [2,1] => ([(0,2),(1,2)],3) => 0
{{1},{2,3}} => [1,2] => ([(1,2)],3) => 0
{{1},{2},{3}} => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => -1
{{1,2,3},{4}} => [3,1] => ([(0,3),(1,3),(2,3)],4) => 0
{{1,2,4},{3}} => [3,1] => ([(0,3),(1,3),(2,3)],4) => 0
{{1,2},{3,4}} => [2,2] => ([(1,3),(2,3)],4) => 0
{{1,2},{3},{4}} => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
{{1,3,4},{2}} => [3,1] => ([(0,3),(1,3),(2,3)],4) => 0
{{1,3},{2,4}} => [2,2] => ([(1,3),(2,3)],4) => 0
{{1,3},{2},{4}} => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
{{1,4},{2,3}} => [2,2] => ([(1,3),(2,3)],4) => 0
{{1},{2,3,4}} => [1,3] => ([(2,3)],4) => 0
{{1,4},{2},{3}} => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 0
{{1},{2},{3,4}} => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 0
{{1},{2},{3},{4}} => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => -1
{{1,2,3,4},{5}} => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
{{1,2,3,5},{4}} => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
{{1,2,3},{4,5}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
{{1,2,3},{4},{5}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
{{1,2,4,5},{3}} => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
{{1,2,4},{3,5}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
{{1,2,4},{3},{5}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
{{1,2,5},{3,4}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
{{1,2},{3,4,5}} => [2,3] => ([(2,4),(3,4)],5) => 0
{{1,2,5},{3},{4}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
{{1,2},{3},{4,5}} => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
{{1,2},{3},{4},{5}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
{{1,3,4,5},{2}} => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 0
{{1,3,4},{2,5}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
{{1,3,4},{2},{5}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
{{1,3,5},{2,4}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
{{1,3},{2,4,5}} => [2,3] => ([(2,4),(3,4)],5) => 0
{{1,3,5},{2},{4}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
{{1,3},{2},{4,5}} => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
{{1,3},{2},{4},{5}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
{{1,4,5},{2,3}} => [3,2] => ([(1,4),(2,4),(3,4)],5) => 0
{{1,4},{2,3,5}} => [2,3] => ([(2,4),(3,4)],5) => 0
{{1,5},{2,3,4}} => [2,3] => ([(2,4),(3,4)],5) => 0
{{1},{2,3,4,5}} => [1,4] => ([(3,4)],5) => 0
{{1,4,5},{2},{3}} => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
{{1,4},{2},{3,5}} => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
{{1,4},{2},{3},{5}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
{{1,5},{2},{3,4}} => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
{{1},{2},{3,4,5}} => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 0
{{1,5},{2},{3},{4}} => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
{{1},{2},{3},{4,5}} => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 0
{{1},{2},{3},{4},{5}} => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => -1
{{1,2,3,4,5},{6}} => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
{{1,2,3,4,6},{5}} => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
{{1,2,3,4},{5,6}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
{{1,2,3,4},{5},{6}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,2,3,5,6},{4}} => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
{{1,2,3,5},{4,6}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
{{1,2,3,5},{4},{6}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,2,3,6},{4,5}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
{{1,2,3},{4,5,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
{{1,2,3,6},{4},{5}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,2,3},{4},{5,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,2,3},{4},{5},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,2,4,5,6},{3}} => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
{{1,2,4,5},{3,6}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
{{1,2,4,5},{3},{6}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,2,4,6},{3,5}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
{{1,2,4},{3,5,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
{{1,2,4,6},{3},{5}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,2,4},{3},{5,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,2,4},{3},{5},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,2,5,6},{3,4}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
{{1,2,5},{3,4,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
{{1,2,6},{3,4,5}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
{{1,2},{3,4,5,6}} => [2,4] => ([(3,5),(4,5)],6) => 0
{{1,2,5,6},{3},{4}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,2,5},{3},{4,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,2,5},{3},{4},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,2,6},{3},{4,5}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,2},{3},{4,5,6}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,2,6},{3},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,2},{3},{4},{5,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,2},{3},{4},{5},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,3,4,5,6},{2}} => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 0
{{1,3,4,5},{2,6}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
{{1,3,4,5},{2},{6}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,3,4,6},{2,5}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
{{1,3,4},{2,5,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
{{1,3,4,6},{2},{5}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,3,4},{2},{5,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,3,4},{2},{5},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,3,5,6},{2,4}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
{{1,3,5},{2,4,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
{{1,3,6},{2,4,5}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
{{1,3},{2,4,5,6}} => [2,4] => ([(3,5),(4,5)],6) => 0
{{1,3,5,6},{2},{4}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,3,5},{2},{4,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,3,5},{2},{4},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,3,6},{2},{4,5}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,3},{2},{4,5,6}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,3,6},{2},{4},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,3},{2},{4},{5,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,3},{2},{4},{5},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
>>> Load all 321 entries. <<<
{{1,4,5,6},{2,3}} => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 0
{{1,4,5},{2,3,6}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
{{1,4,6},{2,3,5}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
{{1,4},{2,3,5,6}} => [2,4] => ([(3,5),(4,5)],6) => 0
{{1,5,6},{2,3,4}} => [3,3] => ([(2,5),(3,5),(4,5)],6) => 0
{{1,5},{2,3,4,6}} => [2,4] => ([(3,5),(4,5)],6) => 0
{{1,6},{2,3,4,5}} => [2,4] => ([(3,5),(4,5)],6) => 0
{{1},{2,3,4,5,6}} => [1,5] => ([(4,5)],6) => 0
{{1,4,5,6},{2},{3}} => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,4,5},{2},{3,6}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,4,5},{2},{3},{6}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,4,6},{2},{3,5}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,4},{2},{3,5,6}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,4,6},{2},{3},{5}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,4},{2},{3},{5,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,4},{2},{3},{5},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,5,6},{2},{3,4}} => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,5},{2},{3,4,6}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,6},{2},{3,4,5}} => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1},{2},{3,4,5,6}} => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 0
{{1,5,6},{2},{3},{4}} => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,5},{2},{3},{4,6}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,6},{2},{3},{4,5}} => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1},{2},{3},{4,5,6}} => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1},{2},{3},{4},{5,6}} => [1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 0
{{1},{2},{3},{4},{5},{6}} => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => -1
{{1,2,3,4,5,6},{7}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,3,4,5,7},{6}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,3,4,5},{6,7}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,3,4,5},{6},{7}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,3,4,6,7},{5}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,3,4,6},{5,7}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,3,4,6},{5},{7}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,3,4,7},{5,6}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,3,4},{5,6,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,3,4,7},{5},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,3,4},{5},{6,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,3,4},{5},{6},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,3,5,6,7},{4}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,3,5,6},{4,7}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,3,5,6},{4},{7}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,3,5,7},{4,6}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,3,5},{4,6,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,3,5,7},{4},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,3,5},{4},{6,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,3,5},{4},{6},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,3,6,7},{4,5}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,3,6},{4,5,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,3,7},{4,5,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,3},{4,5,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
{{1,2,3,6,7},{4},{5}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,3,6},{4},{5,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,3,6},{4},{5},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,3,7},{4},{5,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,3},{4},{5,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,3},{4},{5},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,3},{4},{5},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,4,5,6,7},{3}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,4,5,6},{3,7}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,4,5,6},{3},{7}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,4,5,7},{3,6}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,4,5},{3,6,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,4,5,7},{3},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,4,5},{3},{6,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,4,5},{3},{6},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,4,6,7},{3,5}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,4,6},{3,5,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,4,7},{3,5,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,4},{3,5,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
{{1,2,4,6,7},{3},{5}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,4,6},{3},{5,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,4,6},{3},{5},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,4,7},{3},{5,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,4},{3},{5,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,4},{3},{5},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,4},{3},{5},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,5,6,7},{3,4}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,5,6},{3,4,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,5,7},{3,4,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,5},{3,4,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
{{1,2,6,7},{3,4,5}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,2,6},{3,4,5,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
{{1,2,7},{3,4,5,6}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
{{1,2},{3,4,5,6,7}} => [2,5] => ([(4,6),(5,6)],7) => 0
{{1,2,5,6,7},{3},{4}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,5,6},{3},{4,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,5,6},{3},{4},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,5,7},{3},{4,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,5},{3},{4,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,5},{3},{4},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,5},{3},{4},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,6,7},{3},{4,5}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,6},{3},{4,5,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,7},{3},{4,5,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2},{3},{4,5,6,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,6},{3},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,7},{3},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2},{3},{4},{5,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2},{3},{4},{5},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,4,5,6,7},{2}} => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,3,4,5,6},{2,7}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,3,4,5,6},{2},{7}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,4,5,7},{2,6}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,3,4,5},{2,6,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,3,4,5,7},{2},{6}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,4,5},{2},{6,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,4,5},{2},{6},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,4,6,7},{2,5}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,3,4,6},{2,5,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,3,4,7},{2,5,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,3,4},{2,5,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
{{1,3,4,6,7},{2},{5}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,4,6},{2},{5,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,4,6},{2},{5},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,4,7},{2},{5,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,4},{2},{5,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,4},{2},{5},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,4},{2},{5},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,5,6,7},{2,4}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,3,5,6},{2,4,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,3,5,7},{2,4,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,3,5},{2,4,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
{{1,3,6,7},{2,4,5}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,3,6},{2,4,5,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
{{1,3,7},{2,4,5,6}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
{{1,3},{2,4,5,6,7}} => [2,5] => ([(4,6),(5,6)],7) => 0
{{1,3,5,6,7},{2},{4}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,5,6},{2},{4,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,5,6},{2},{4},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,5,7},{2},{4,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,5},{2},{4,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,5},{2},{4},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,5},{2},{4},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,6,7},{2},{4,5}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,6},{2},{4,5,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,7},{2},{4,5,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3},{2},{4,5,6,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,6},{2},{4},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,7},{2},{4},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3},{2},{4},{5,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3},{2},{4},{5},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,3},{2},{4},{5},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4,5,6,7},{2,3}} => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,4,5,6},{2,3,7}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,4,5,7},{2,3,6}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,4,5},{2,3,6,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
{{1,4,6,7},{2,3,5}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,4,6},{2,3,5,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
{{1,4,7},{2,3,5,6}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
{{1,4},{2,3,5,6,7}} => [2,5] => ([(4,6),(5,6)],7) => 0
{{1,5,6,7},{2,3,4}} => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 0
{{1,5,6},{2,3,4,7}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
{{1,5,7},{2,3,4,6}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
{{1,5},{2,3,4,6,7}} => [2,5] => ([(4,6),(5,6)],7) => 0
{{1,6,7},{2,3,4,5}} => [3,4] => ([(3,6),(4,6),(5,6)],7) => 0
{{1,6},{2,3,4,5,7}} => [2,5] => ([(4,6),(5,6)],7) => 0
{{1,7},{2,3,4,5,6}} => [2,5] => ([(4,6),(5,6)],7) => 0
{{1},{2,3,4,5,6,7}} => [1,6] => ([(5,6)],7) => 0
{{1,4,5,6,7},{2},{3}} => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4,5,6},{2},{3,7}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4,5,6},{2},{3},{7}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4,5,7},{2},{3,6}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4,5},{2},{3,6,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4,5},{2},{3},{6,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4,5},{2},{3},{6},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4,6,7},{2},{3,5}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4,6},{2},{3,5,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4,7},{2},{3,5,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4},{2},{3,5,6,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4,6},{2},{3},{5,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4,7},{2},{3},{5,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4},{2},{3},{5,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4},{2},{3},{5},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,5,6,7},{2},{3,4}} => [4,1,2] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,5,6},{2},{3,4,7}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,5,7},{2},{3,4,6}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,5},{2},{3,4,6,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,6,7},{2},{3,4,5}} => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,6},{2},{3,4,5,7}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,7},{2},{3,4,5,6}} => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1},{2},{3,4,5,6,7}} => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 0
{{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,5,6},{2},{3},{4,7}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,5,7},{2},{3},{4,6}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,5},{2},{3},{4,6,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,5},{2},{3},{4},{6,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,6,7},{2},{3},{4,5}} => [3,1,1,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,6},{2},{3},{4,5,7}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,7},{2},{3},{4,5,6}} => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1},{2},{3},{4,5,6,7}} => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => ([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1},{2},{3},{4},{5,6,7}} => [1,1,1,1,3] => ([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1},{2},{3},{4},{5},{6,7}} => [1,1,1,1,1,2] => ([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 0
{{1},{2},{3},{4},{5},{6},{7}} => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => -1
search for individual values
searching the database for the individual values of this statistic
Description
The second largest eigenvalue of a graph if it is integral.
This statistic is undefined if the second largest eigenvalue of the graph is not integral.
Chapter 4 of [1] provides lots of context.
Map
to threshold graph
Description
The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
Map
to composition
Description
The integer composition of block sizes of a set partition.
For a set partition of $\{1,2,\dots,n\}$, this is the integer composition of $n$ obtained by sorting the blocks by their minimal element and then taking the block sizes.