Identifier
Values
{{1}} => [1] => [1] => ([],1) => 0
{{1,2}} => [2] => [2] => ([],2) => 0
{{1},{2}} => [1,1] => [1,1] => ([(0,1)],2) => 1
{{1,2,3}} => [3] => [3] => ([],3) => 0
{{1,2},{3}} => [2,1] => [1,2] => ([(1,2)],3) => 1
{{1,3},{2}} => [2,1] => [1,2] => ([(1,2)],3) => 1
{{1},{2},{3}} => [1,1,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 2
{{1,2,3,4}} => [4] => [4] => ([],4) => 0
{{1,2,3},{4}} => [3,1] => [1,3] => ([(2,3)],4) => 1
{{1,2,4},{3}} => [3,1] => [1,3] => ([(2,3)],4) => 1
{{1,2},{3},{4}} => [2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
{{1,3,4},{2}} => [3,1] => [1,3] => ([(2,3)],4) => 1
{{1,3},{2},{4}} => [2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
{{1,4},{2},{3}} => [2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
{{1},{2},{3},{4}} => [1,1,1,1] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
{{1,2,3,4,5}} => [5] => [5] => ([],5) => 0
{{1,2,3,4},{5}} => [4,1] => [1,4] => ([(3,4)],5) => 1
{{1,2,3,5},{4}} => [4,1] => [1,4] => ([(3,4)],5) => 1
{{1,2,3},{4},{5}} => [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
{{1,2,4,5},{3}} => [4,1] => [1,4] => ([(3,4)],5) => 1
{{1,2,4},{3},{5}} => [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
{{1,2,5},{3},{4}} => [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
{{1,2},{3},{4},{5}} => [2,1,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
{{1,3,4,5},{2}} => [4,1] => [1,4] => ([(3,4)],5) => 1
{{1,3,4},{2},{5}} => [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
{{1,3,5},{2},{4}} => [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
{{1,3},{2},{4},{5}} => [2,1,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
{{1},{2,3,4,5}} => [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
{{1},{2,3,4},{5}} => [1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
{{1},{2,3,5},{4}} => [1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
{{1,4,5},{2},{3}} => [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
{{1,4},{2},{3},{5}} => [2,1,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
{{1},{2,4,5},{3}} => [1,3,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
{{1,5},{2},{3},{4}} => [2,1,1,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
{{1},{2},{3},{4},{5}} => [1,1,1,1,1] => [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) => 4
{{1,2,3,4,5,6}} => [6] => [6] => ([],6) => 0
{{1,2,3,4,5},{6}} => [5,1] => [1,5] => ([(4,5)],6) => 1
{{1,2,3,4,6},{5}} => [5,1] => [1,5] => ([(4,5)],6) => 1
{{1,2,3,4},{5},{6}} => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
{{1,2,3,5,6},{4}} => [5,1] => [1,5] => ([(4,5)],6) => 1
{{1,2,3,5},{4},{6}} => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
{{1,2,3,6},{4},{5}} => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
{{1,2,3},{4},{5},{6}} => [3,1,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,2,4,5,6},{3}} => [5,1] => [1,5] => ([(4,5)],6) => 1
{{1,2,4,5},{3},{6}} => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
{{1,2,4,6},{3},{5}} => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
{{1,2,4},{3},{5},{6}} => [3,1,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,2},{3,4,5,6}} => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
{{1,2},{3,4,5},{6}} => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,2},{3,4,6},{5}} => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,2,5,6},{3},{4}} => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
{{1,2,5},{3},{4},{6}} => [3,1,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,2},{3,5,6},{4}} => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,2,6},{3},{4},{5}} => [3,1,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,2},{3},{4},{5},{6}} => [2,1,1,1,1] => [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) => 4
{{1,3,4,5,6},{2}} => [5,1] => [1,5] => ([(4,5)],6) => 1
{{1,3,4,5},{2},{6}} => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
{{1,3,4,6},{2},{5}} => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
{{1,3,4},{2},{5},{6}} => [3,1,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,3},{2,4,5,6}} => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
{{1,3},{2,4,5},{6}} => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,3},{2,4,6},{5}} => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,3,5,6},{2},{4}} => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
{{1,3,5},{2},{4},{6}} => [3,1,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,3},{2,5,6},{4}} => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,3,6},{2},{4},{5}} => [3,1,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,3},{2},{4},{5},{6}} => [2,1,1,1,1] => [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) => 4
{{1,4},{2,3,5,6}} => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
{{1,4},{2,3,5},{6}} => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,4},{2,3,6},{5}} => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,5},{2,3,4,6}} => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
{{1,5},{2,3,4},{6}} => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,6},{2,3,4,5}} => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
{{1,6},{2,3,4},{5}} => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,5},{2,3,6},{4}} => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,6},{2,3,5},{4}} => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,4,5,6},{2},{3}} => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
{{1,4,5},{2},{3},{6}} => [3,1,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,4},{2,5,6},{3}} => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,4,6},{2},{3},{5}} => [3,1,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,4},{2},{3},{5},{6}} => [2,1,1,1,1] => [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) => 4
{{1,5},{2,4,6},{3}} => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,6},{2,4,5},{3}} => [2,3,1] => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,5,6},{2},{3},{4}} => [3,1,1,1] => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
{{1,5},{2},{3},{4},{6}} => [2,1,1,1,1] => [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) => 4
{{1,6},{2},{3},{4},{5}} => [2,1,1,1,1] => [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) => 4
{{1},{2},{3},{4},{5},{6}} => [1,1,1,1,1,1] => [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) => 5
{{1,2,3,4,5,6,7}} => [7] => [7] => ([],7) => 0
{{1,2,3,4,5,6},{7}} => [6,1] => [1,6] => ([(5,6)],7) => 1
{{1,2,3,4,5,7},{6}} => [6,1] => [1,6] => ([(5,6)],7) => 1
{{1,2,3,4,5},{6},{7}} => [5,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
{{1,2,3,4,6,7},{5}} => [6,1] => [1,6] => ([(5,6)],7) => 1
{{1,2,3,4,6},{5},{7}} => [5,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
{{1,2,3,4,7},{5},{6}} => [5,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
{{1,2,3,4},{5},{6},{7}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,3,5,6,7},{4}} => [6,1] => [1,6] => ([(5,6)],7) => 1
{{1,2,3,5,6},{4},{7}} => [5,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
{{1,2,3,5,7},{4},{6}} => [5,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
{{1,2,3,5},{4},{6},{7}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,3},{4,5,6,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
{{1,2,3},{4,5,6},{7}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
>>> Load all 211 entries. <<<
{{1,2,3},{4,5,7},{6}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,3,6,7},{4},{5}} => [5,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
{{1,2,3,6},{4},{5},{7}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,3},{4,6,7},{5}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,3,7},{4},{5},{6}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,3},{4},{5},{6},{7}} => [3,1,1,1,1] => [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) => 4
{{1,2,4,5,6,7},{3}} => [6,1] => [1,6] => ([(5,6)],7) => 1
{{1,2,4,5,6},{3},{7}} => [5,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
{{1,2,4,5,7},{3},{6}} => [5,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
{{1,2,4,5},{3},{6},{7}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,4},{3,5,6,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
{{1,2,4},{3,5,6},{7}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,4},{3,5,7},{6}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,4,6,7},{3},{5}} => [5,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
{{1,2,4,6},{3},{5},{7}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,4},{3,6,7},{5}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,4,7},{3},{5},{6}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,4},{3},{5},{6},{7}} => [3,1,1,1,1] => [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) => 4
{{1,2,5},{3,4,6,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
{{1,2,5},{3,4,6},{7}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,5},{3,4,7},{6}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,6},{3,4,5,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
{{1,2,6},{3,4,5},{7}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,7},{3,4,5,6}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
{{1,2,7},{3,4,5},{6}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,6},{3,4,7},{5}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,7},{3,4,6},{5}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,5,6,7},{3},{4}} => [5,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
{{1,2,5,6},{3},{4},{7}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,5},{3,6,7},{4}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,5,7},{3},{4},{6}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,5},{3},{4},{6},{7}} => [3,1,1,1,1] => [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) => 4
{{1,2,6},{3,5,7},{4}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,7},{3,5,6},{4}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,6,7},{3},{4},{5}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,2,6},{3},{4},{5},{7}} => [3,1,1,1,1] => [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) => 4
{{1,2,7},{3},{4},{5},{6}} => [3,1,1,1,1] => [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) => 4
{{1,2},{3},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [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) => 5
{{1,3,4,5,6,7},{2}} => [6,1] => [1,6] => ([(5,6)],7) => 1
{{1,3,4,5,6},{2},{7}} => [5,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
{{1,3,4,5,7},{2},{6}} => [5,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
{{1,3,4,5},{2},{6},{7}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,4},{2,5,6,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
{{1,3,4},{2,5,6},{7}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,4},{2,5,7},{6}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,4,6,7},{2},{5}} => [5,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
{{1,3,4,6},{2},{5},{7}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,4},{2,6,7},{5}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,4,7},{2},{5},{6}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,4},{2},{5},{6},{7}} => [3,1,1,1,1] => [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) => 4
{{1,3,5},{2,4,6,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
{{1,3,5},{2,4,6},{7}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,5},{2,4,7},{6}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,6},{2,4,5,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
{{1,3,6},{2,4,5},{7}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,7},{2,4,5,6}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
{{1,3,7},{2,4,5},{6}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,6},{2,4,7},{5}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,7},{2,4,6},{5}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,5,6,7},{2},{4}} => [5,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
{{1,3,5,6},{2},{4},{7}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,5},{2,6,7},{4}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,5,7},{2},{4},{6}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,5},{2},{4},{6},{7}} => [3,1,1,1,1] => [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) => 4
{{1,3,6},{2,5,7},{4}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,7},{2,5,6},{4}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,6,7},{2},{4},{5}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,3,6},{2},{4},{5},{7}} => [3,1,1,1,1] => [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) => 4
{{1,3,7},{2},{4},{5},{6}} => [3,1,1,1,1] => [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) => 4
{{1,3},{2},{4},{5},{6},{7}} => [2,1,1,1,1,1] => [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) => 5
{{1,4,5},{2,3,6,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
{{1,4,5},{2,3,6},{7}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,4,5},{2,3,7},{6}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,4,6},{2,3,5,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
{{1,4,6},{2,3,5},{7}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,4,7},{2,3,5,6}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
{{1,4,7},{2,3,5},{6}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,4,6},{2,3,7},{5}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,4,7},{2,3,6},{5}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,5,6},{2,3,4,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
{{1,5,6},{2,3,4},{7}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,5,7},{2,3,4,6}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
{{1,5,7},{2,3,4},{6}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,6,7},{2,3,4,5}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
{{1,6,7},{2,3,4},{5}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,5,6},{2,3,7},{4}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,5,7},{2,3,6},{4}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,6,7},{2,3,5},{4}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,4,5,6,7},{2},{3}} => [5,1,1] => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
{{1,4,5,6},{2},{3},{7}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,4,5},{2,6,7},{3}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,4,5,7},{2},{3},{6}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,4,5},{2},{3},{6},{7}} => [3,1,1,1,1] => [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) => 4
{{1,4,6},{2,5,7},{3}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,4,7},{2,5,6},{3}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,4,6,7},{2},{3},{5}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,4,6},{2},{3},{5},{7}} => [3,1,1,1,1] => [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) => 4
{{1,4,7},{2},{3},{5},{6}} => [3,1,1,1,1] => [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) => 4
{{1,4},{2},{3},{5},{6},{7}} => [2,1,1,1,1,1] => [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) => 5
{{1,5,6},{2,4,7},{3}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,5,7},{2,4,6},{3}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,6,7},{2,4,5},{3}} => [3,3,1] => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,5,6,7},{2},{3},{4}} => [4,1,1,1] => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
{{1,5,6},{2},{3},{4},{7}} => [3,1,1,1,1] => [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) => 4
{{1,5,7},{2},{3},{4},{6}} => [3,1,1,1,1] => [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) => 4
{{1,5},{2},{3},{4},{6},{7}} => [2,1,1,1,1,1] => [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) => 5
{{1,6,7},{2},{3},{4},{5}} => [3,1,1,1,1] => [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) => 4
{{1,6},{2},{3},{4},{5},{7}} => [2,1,1,1,1,1] => [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) => 5
{{1,7},{2},{3},{4},{5},{6}} => [2,1,1,1,1,1] => [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) => 5
{{1},{2},{3},{4},{5},{6},{7}} => [1,1,1,1,1,1,1] => [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) => 6
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searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Description
The largest eigenvalue of a graph if it is integral.
If a graph is $d$-regular, then its largest eigenvalue equals $d$. One can show that the largest eigenvalue always lies between the average degree and the maximal degree.
This statistic is undefined if the largest eigenvalue of the graph is not integral.
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.
Map
rotate front to back
Description
The front to back rotation of the entries of an integer composition.
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.