- FindStat

Identifier

Mp00128: Set partitions —to composition⟶ Integer compositions
Mp00173: Integer compositions —rotate front to back⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001644: Graphs ⟶ ℤ

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}} => [1,2] => [2,1] => ([(0,2),(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}} => [2,2] => [2,2] => ([(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}} => [2,2] => [2,2] => ([(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}} => [2,2] => [2,2] => ([(1,3),(2,3)],4) => 1

{{1},{2,3,4}} => [1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2

{{1},{2,3},{4}} => [1,2,1] => [2,1,1] => ([(0,2),(0,3),(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},{2,4},{3}} => [1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 2

{{1},{2},{3,4}} => [1,1,2] => [1,2,1] => ([(0,3),(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}} => [3,2] => [2,3] => ([(2,4),(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}} => [3,2] => [2,3] => ([(2,4),(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}} => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1

{{1,2},{3,4,5}} => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2

{{1,2},{3,4},{5}} => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(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},{3,5},{4}} => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

{{1,2},{3},{4,5}} => [2,1,2] => [1,2,2] => ([(1,4),(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}} => [3,2] => [2,3] => ([(2,4),(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}} => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1

{{1,3},{2,4,5}} => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2

{{1,3},{2,4},{5}} => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(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},{2,5},{4}} => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

{{1,3},{2},{4,5}} => [2,1,2] => [1,2,2] => ([(1,4),(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

{{1,4,5},{2,3}} => [3,2] => [2,3] => ([(2,4),(3,4)],5) => 1

{{1,4},{2,3,5}} => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2

{{1,4},{2,3},{5}} => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

{{1,5},{2,3,4}} => [2,3] => [3,2] => ([(1,4),(2,4),(3,4)],5) => 2

{{1},{2,3,4,5}} => [1,4] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2

{{1,5},{2,3},{4}} => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

{{1},{2,3},{4,5}} => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

{{1},{2,3},{4},{5}} => [1,2,1,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(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},{2,5},{3}} => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

{{1,4},{2},{3,5}} => [2,1,2] => [1,2,2] => ([(1,4),(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

{{1,5},{2,4},{3}} => [2,2,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

{{1},{2,4},{3,5}} => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

{{1},{2,4},{3},{5}} => [1,2,1,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

{{1,5},{2},{3,4}} => [2,1,2] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5) => 2

{{1},{2,5},{3,4}} => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2

{{1},{2},{3,4,5}} => [1,1,3] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2

{{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},{2,5},{3},{4}} => [1,2,1,1] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3

{{1},{2},{3},{4,5}} => [1,1,1,2] => [1,1,2,1] => ([(0,4),(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}} => [4,2] => [2,4] => ([(3,5),(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}} => [4,2] => [2,4] => ([(3,5),(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}} => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1

{{1,2,3},{4,5,6}} => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

{{1,2,3},{4,5},{6}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(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},{4,6},{5}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,2,3},{4},{5,6}} => [3,1,2] => [1,2,3] => ([(2,5),(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}} => [4,2] => [2,4] => ([(3,5),(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}} => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1

{{1,2,4},{3,5,6}} => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

{{1,2,4},{3,5},{6}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(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},{3,6},{5}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,2,4},{3},{5,6}} => [3,1,2] => [1,2,3] => ([(2,5),(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

{{1,2,5,6},{3,4}} => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1

{{1,2,5},{3,4,6}} => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

{{1,2,5},{3,4},{6}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,2,6},{3,4,5}} => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

{{1,2},{3,4,5,6}} => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

{{1,2,6},{3,4},{5}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

>>> Load all 632 entries. <<<

{{1,2},{3,4},{5,6}} => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,2},{3,4},{5},{6}} => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(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},{3,6},{4}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,2,5},{3},{4,6}} => [3,1,2] => [1,2,3] => ([(2,5),(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

{{1,2,6},{3,5},{4}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,2},{3,5},{4,6}} => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,2},{3,5},{4},{6}} => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1,2,6},{3},{4,5}} => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,2},{3,6},{4,5}} => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,2},{3},{4,5,6}} => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{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},{3,6},{4},{5}} => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1,2},{3},{4},{5,6}} => [2,1,1,2] => [1,1,2,2] => ([(1,5),(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}} => [4,2] => [2,4] => ([(3,5),(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}} => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1

{{1,3,4},{2,5,6}} => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

{{1,3,4},{2,5},{6}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(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},{2,6},{5}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,3,4},{2},{5,6}} => [3,1,2] => [1,2,3] => ([(2,5),(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

{{1,3,5,6},{2,4}} => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1

{{1,3,5},{2,4,6}} => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

{{1,3,5},{2,4},{6}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,3,6},{2,4,5}} => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

{{1,3},{2,4,5,6}} => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

{{1,3,6},{2,4},{5}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,3},{2,4},{5,6}} => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,3},{2,4},{5},{6}} => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(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},{2,6},{4}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,3,5},{2},{4,6}} => [3,1,2] => [1,2,3] => ([(2,5),(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

{{1,3,6},{2,5},{4}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,3},{2,5},{4,6}} => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,3},{2,5},{4},{6}} => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1,3,6},{2},{4,5}} => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,3},{2,6},{4,5}} => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,3},{2},{4,5,6}} => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{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},{2,6},{4},{5}} => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1,3},{2},{4},{5,6}} => [2,1,1,2] => [1,1,2,2] => ([(1,5),(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

{{1,4,5,6},{2,3}} => [4,2] => [2,4] => ([(3,5),(4,5)],6) => 1

{{1,4,5},{2,3,6}} => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

{{1,4,5},{2,3},{6}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,4,6},{2,3,5}} => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

{{1,4},{2,3,5,6}} => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

{{1,4,6},{2,3},{5}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,4},{2,3},{5,6}} => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,4},{2,3},{5},{6}} => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1,5,6},{2,3,4}} => [3,3] => [3,3] => ([(2,5),(3,5),(4,5)],6) => 2

{{1,5},{2,3,4,6}} => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

{{1,6},{2,3,4,5}} => [2,4] => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2

{{1},{2,3,4,5,6}} => [1,5] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2

{{1,5,6},{2,3},{4}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,5},{2,3},{4,6}} => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,5},{2,3},{4},{6}} => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1,6},{2,3},{4,5}} => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1},{2,3},{4,5,6}} => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,6},{2,3},{4},{5}} => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1},{2,3},{4},{5,6}} => [1,2,1,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1},{2,3},{4},{5},{6}} => [1,2,1,1,1] => [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) => 4

{{1,4,5,6},{2},{3}} => [4,1,1] => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2

{{1,4,5},{2,6},{3}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,4,5},{2},{3,6}} => [3,1,2] => [1,2,3] => ([(2,5),(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

{{1,4,6},{2,5},{3}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,4},{2,5},{3,6}} => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,4},{2,5},{3},{6}} => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1,4,6},{2},{3,5}} => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,4},{2,6},{3,5}} => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,4},{2},{3,5,6}} => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{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},{2,6},{3},{5}} => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1,4},{2},{3},{5,6}} => [2,1,1,2] => [1,1,2,2] => ([(1,5),(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

{{1,5,6},{2,4},{3}} => [3,2,1] => [2,1,3] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,5},{2,4},{3,6}} => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,5},{2,4},{3},{6}} => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1,6},{2,4},{3,5}} => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1},{2,4},{3,5,6}} => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,6},{2,4},{3},{5}} => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1},{2,4},{3},{5,6}} => [1,2,1,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1},{2,4},{3},{5},{6}} => [1,2,1,1,1] => [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) => 4

{{1,5,6},{2},{3,4}} => [3,1,2] => [1,2,3] => ([(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,5},{2,6},{3,4}} => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,5},{2},{3,4,6}} => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,6},{2,5},{3,4}} => [2,2,2] => [2,2,2] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1},{2,5},{3,4,6}} => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1,6},{2},{3,4,5}} => [2,1,3] => [1,3,2] => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1},{2,6},{3,4,5}} => [1,2,3] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{1},{2},{3,4,5,6}} => [1,1,4] => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 2

{{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},{2,6},{3},{4}} => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1,5},{2},{3},{4,6}} => [2,1,1,2] => [1,1,2,2] => ([(1,5),(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},{2,5},{3},{4}} => [2,2,1,1] => [2,1,1,2] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1},{2,5},{3},{4,6}} => [1,2,1,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1},{2,5},{3},{4},{6}} => [1,2,1,1,1] => [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) => 4

{{1,6},{2},{3},{4,5}} => [2,1,1,2] => [1,1,2,2] => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1},{2,6},{3},{4,5}} => [1,2,1,2] => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{1},{2},{3},{4,5,6}} => [1,1,1,3] => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3

{{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},{2,6},{3},{4},{5}} => [1,2,1,1,1] => [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) => 4

{{1},{2},{3},{4},{5,6}} => [1,1,1,1,2] => [1,1,1,2,1] => ([(0,5),(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}} => [5,2] => [2,5] => ([(4,6),(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}} => [5,2] => [2,5] => ([(4,6),(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}} => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 1

{{1,2,3,4},{5,6,7}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,2,3,4},{5,6},{7}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(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},{5,7},{6}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,3,4},{5},{6,7}} => [4,1,2] => [1,2,4] => ([(3,6),(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}} => [5,2] => [2,5] => ([(4,6),(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}} => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 1

{{1,2,3,5},{4,6,7}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,2,3,5},{4,6},{7}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(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},{4,7},{6}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,3,5},{4},{6,7}} => [4,1,2] => [1,2,4] => ([(3,6),(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

{{1,2,3,6,7},{4,5}} => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 1

{{1,2,3,6},{4,5,7}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,2,3,6},{4,5},{7}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,3,7},{4,5,6}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,2,3},{4,5,6,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,2,3,7},{4,5},{6}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,3},{4,5},{6,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,3},{4,5},{6},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(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},{4,7},{5}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,3,6},{4},{5,7}} => [4,1,2] => [1,2,4] => ([(3,6),(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

{{1,2,3,7},{4,6},{5}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,3},{4,6},{5,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,3},{4,6},{5},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2,3,7},{4},{5,6}} => [4,1,2] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,3},{4,7},{5,6}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,3},{4},{5,6,7}} => [3,1,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{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},{4,7},{5},{6}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2,3},{4},{5},{6,7}} => [3,1,1,2] => [1,1,2,3] => ([(2,6),(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}} => [5,2] => [2,5] => ([(4,6),(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}} => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 1

{{1,2,4,5},{3,6,7}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,2,4,5},{3,6},{7}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(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},{3,7},{6}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,4,5},{3},{6,7}} => [4,1,2] => [1,2,4] => ([(3,6),(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

{{1,2,4,6,7},{3,5}} => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 1

{{1,2,4,6},{3,5,7}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,2,4,6},{3,5},{7}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,4,7},{3,5,6}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,2,4},{3,5,6,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,2,4,7},{3,5},{6}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,4},{3,5},{6,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,4},{3,5},{6},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(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},{3,7},{5}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,4,6},{3},{5,7}} => [4,1,2] => [1,2,4] => ([(3,6),(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

{{1,2,4,7},{3,6},{5}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,4},{3,6},{5,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,4},{3,6},{5},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2,4,7},{3},{5,6}} => [4,1,2] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,4},{3,7},{5,6}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,4},{3},{5,6,7}} => [3,1,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{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},{3,7},{5},{6}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2,4},{3},{5},{6,7}} => [3,1,1,2] => [1,1,2,3] => ([(2,6),(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

{{1,2,5,6,7},{3,4}} => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 1

{{1,2,5,6},{3,4,7}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,2,5,6},{3,4},{7}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,5,7},{3,4,6}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,2,5},{3,4,6,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,2,5,7},{3,4},{6}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,5},{3,4},{6,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,5},{3,4},{6},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2,6,7},{3,4,5}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,2,6},{3,4,5,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,2,7},{3,4,5,6}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,2},{3,4,5,6,7}} => [2,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,2,6,7},{3,4},{5}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,6},{3,4},{5,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,6},{3,4},{5},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2,7},{3,4},{5,6}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2},{3,4},{5,6,7}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,7},{3,4},{5},{6}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2},{3,4},{5},{6,7}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2},{3,4},{5},{6},{7}} => [2,2,1,1,1] => [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) => 4

{{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},{3,7},{4}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,5,6},{3},{4,7}} => [4,1,2] => [1,2,4] => ([(3,6),(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

{{1,2,5,7},{3,6},{4}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,5},{3,6},{4,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,5},{3,6},{4},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2,5,7},{3},{4,6}} => [4,1,2] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,5},{3,7},{4,6}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,5},{3},{4,6,7}} => [3,1,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{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},{3,7},{4},{6}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2,5},{3},{4},{6,7}} => [3,1,1,2] => [1,1,2,3] => ([(2,6),(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

{{1,2,6,7},{3,5},{4}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,6},{3,5},{4,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,6},{3,5},{4},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2,7},{3,5},{4,6}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2},{3,5},{4,6,7}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,7},{3,5},{4},{6}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2},{3,5},{4},{6,7}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2},{3,5},{4},{6},{7}} => [2,2,1,1,1] => [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) => 4

{{1,2,6,7},{3},{4,5}} => [4,1,2] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,6},{3,7},{4,5}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,6},{3},{4,5,7}} => [3,1,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,7},{3,6},{4,5}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2},{3,6},{4,5,7}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2,7},{3},{4,5,6}} => [3,1,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2},{3,7},{4,5,6}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,2},{3},{4,5,6,7}} => [2,1,4] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{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},{3,7},{4},{5}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2,6},{3},{4},{5,7}} => [3,1,1,2] => [1,1,2,3] => ([(2,6),(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},{3,6},{4},{5}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2},{3,6},{4},{5,7}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2},{3,6},{4},{5},{7}} => [2,2,1,1,1] => [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) => 4

{{1,2,7},{3},{4},{5,6}} => [3,1,1,2] => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2},{3,7},{4},{5,6}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,2},{3},{4},{5,6,7}} => [2,1,1,3] => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{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},{3,7},{4},{5},{6}} => [2,2,1,1,1] => [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) => 4

{{1,2},{3},{4},{5},{6,7}} => [2,1,1,1,2] => [1,1,1,2,2] => ([(1,6),(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}} => [5,2] => [2,5] => ([(4,6),(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}} => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 1

{{1,3,4,5},{2,6,7}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,3,4,5},{2,6},{7}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(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},{2,7},{6}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,4,5},{2},{6,7}} => [4,1,2] => [1,2,4] => ([(3,6),(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

{{1,3,4,6,7},{2,5}} => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 1

{{1,3,4,6},{2,5,7}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,3,4,6},{2,5},{7}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,4,7},{2,5,6}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,3,4},{2,5,6,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,3,4,7},{2,5},{6}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,4},{2,5},{6,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,4},{2,5},{6},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(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},{2,7},{5}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,4,6},{2},{5,7}} => [4,1,2] => [1,2,4] => ([(3,6),(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

{{1,3,4,7},{2,6},{5}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,4},{2,6},{5,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,4},{2,6},{5},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,3,4,7},{2},{5,6}} => [4,1,2] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,4},{2,7},{5,6}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,4},{2},{5,6,7}} => [3,1,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{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},{2,7},{5},{6}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,3,4},{2},{5},{6,7}} => [3,1,1,2] => [1,1,2,3] => ([(2,6),(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

{{1,3,5,6,7},{2,4}} => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 1

{{1,3,5,6},{2,4,7}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,3,5,6},{2,4},{7}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,5,7},{2,4,6}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,3,5},{2,4,6,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,3,5,7},{2,4},{6}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,5},{2,4},{6,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,5},{2,4},{6},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,3,6,7},{2,4,5}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,3,6},{2,4,5,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,3,7},{2,4,5,6}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,3},{2,4,5,6,7}} => [2,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,3,6,7},{2,4},{5}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,6},{2,4},{5,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,6},{2,4},{5},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,3,7},{2,4},{5,6}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3},{2,4},{5,6,7}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,7},{2,4},{5},{6}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,3},{2,4},{5},{6,7}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,3},{2,4},{5},{6},{7}} => [2,2,1,1,1] => [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) => 4

{{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},{2,7},{4}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,5,6},{2},{4,7}} => [4,1,2] => [1,2,4] => ([(3,6),(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

{{1,3,5,7},{2,6},{4}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,5},{2,6},{4,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,5},{2,6},{4},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,3,5,7},{2},{4,6}} => [4,1,2] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,5},{2,7},{4,6}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,5},{2},{4,6,7}} => [3,1,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{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},{2,7},{4},{6}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,3,5},{2},{4},{6,7}} => [3,1,1,2] => [1,1,2,3] => ([(2,6),(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

{{1,3,6,7},{2,5},{4}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,6},{2,5},{4,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,6},{2,5},{4},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,3,7},{2,5},{4,6}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3},{2,5},{4,6,7}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,7},{2,5},{4},{6}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,3},{2,5},{4},{6,7}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,3},{2,5},{4},{6},{7}} => [2,2,1,1,1] => [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) => 4

{{1,3,6,7},{2},{4,5}} => [4,1,2] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,6},{2,7},{4,5}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,6},{2},{4,5,7}} => [3,1,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,7},{2,6},{4,5}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3},{2,6},{4,5,7}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3,7},{2},{4,5,6}} => [3,1,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3},{2,7},{4,5,6}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,3},{2},{4,5,6,7}} => [2,1,4] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{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},{2,7},{4},{5}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,3,6},{2},{4},{5,7}} => [3,1,1,2] => [1,1,2,3] => ([(2,6),(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},{2,6},{4},{5}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,3},{2,6},{4},{5,7}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,3},{2,6},{4},{5},{7}} => [2,2,1,1,1] => [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) => 4

{{1,3,7},{2},{4},{5,6}} => [3,1,1,2] => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,3},{2,7},{4},{5,6}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,3},{2},{4},{5,6,7}} => [2,1,1,3] => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{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},{2,7},{4},{5},{6}} => [2,2,1,1,1] => [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) => 4

{{1,3},{2},{4},{5},{6,7}} => [2,1,1,1,2] => [1,1,1,2,2] => ([(1,6),(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

{{1,4,5,6,7},{2,3}} => [5,2] => [2,5] => ([(4,6),(5,6)],7) => 1

{{1,4,5,6},{2,3,7}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,4,5,6},{2,3},{7}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,5,7},{2,3,6}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,4,5},{2,3,6,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,4,5,7},{2,3},{6}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,5},{2,3},{6,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,5},{2,3},{6},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,4,6,7},{2,3,5}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,4,6},{2,3,5,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,4,7},{2,3,5,6}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,4},{2,3,5,6,7}} => [2,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,4,6,7},{2,3},{5}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,6},{2,3},{5,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,6},{2,3},{5},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,4,7},{2,3},{5,6}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4},{2,3},{5,6,7}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,7},{2,3},{5},{6}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,4},{2,3},{5},{6,7}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,4},{2,3},{5},{6},{7}} => [2,2,1,1,1] => [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) => 4

{{1,5,6,7},{2,3,4}} => [4,3] => [3,4] => ([(3,6),(4,6),(5,6)],7) => 2

{{1,5,6},{2,3,4,7}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,5,7},{2,3,4,6}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,5},{2,3,4,6,7}} => [2,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,6,7},{2,3,4,5}} => [3,4] => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,6},{2,3,4,5,7}} => [2,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,7},{2,3,4,5,6}} => [2,5] => [5,2] => ([(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1},{2,3,4,5,6,7}} => [1,6] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2

{{1,5,6,7},{2,3},{4}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,5,6},{2,3},{4,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,5,6},{2,3},{4},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,5,7},{2,3},{4,6}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,5},{2,3},{4,6,7}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,5,7},{2,3},{4},{6}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,5},{2,3},{4},{6,7}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,5},{2,3},{4},{6},{7}} => [2,2,1,1,1] => [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) => 4

{{1,6,7},{2,3},{4,5}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,6},{2,3},{4,5,7}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,7},{2,3},{4,5,6}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1},{2,3},{4,5,6,7}} => [1,2,4] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,6,7},{2,3},{4},{5}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,6},{2,3},{4},{5,7}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,6},{2,3},{4},{5},{7}} => [2,2,1,1,1] => [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) => 4

{{1,7},{2,3},{4},{5,6}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1},{2,3},{4},{5,6,7}} => [1,2,1,3] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,7},{2,3},{4},{5},{6}} => [2,2,1,1,1] => [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) => 4

{{1},{2,3},{4},{5},{6,7}} => [1,2,1,1,2] => [2,1,1,2,1] => ([(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) => 4

{{1},{2,3},{4},{5},{6},{7}} => [1,2,1,1,1,1] => [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) => 5

{{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},{2,7},{3}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,5,6},{2},{3,7}} => [4,1,2] => [1,2,4] => ([(3,6),(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

{{1,4,5,7},{2,6},{3}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,5},{2,6},{3,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,5},{2,6},{3},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,4,5,7},{2},{3,6}} => [4,1,2] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,5},{2,7},{3,6}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,5},{2},{3,6,7}} => [3,1,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{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},{2,7},{3},{6}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,4,5},{2},{3},{6,7}} => [3,1,1,2] => [1,1,2,3] => ([(2,6),(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

{{1,4,6,7},{2,5},{3}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,6},{2,5},{3,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,6},{2,5},{3},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,4,7},{2,5},{3,6}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4},{2,5},{3,6,7}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,7},{2,5},{3},{6}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,4},{2,5},{3},{6,7}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,4},{2,5},{3},{6},{7}} => [2,2,1,1,1] => [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) => 4

{{1,4,6,7},{2},{3,5}} => [4,1,2] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,6},{2,7},{3,5}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,6},{2},{3,5,7}} => [3,1,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,7},{2,6},{3,5}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4},{2,6},{3,5,7}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4,7},{2},{3,5,6}} => [3,1,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4},{2,7},{3,5,6}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,4},{2},{3,5,6,7}} => [2,1,4] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{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},{2,7},{3},{5}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,4,6},{2},{3},{5,7}} => [3,1,1,2] => [1,1,2,3] => ([(2,6),(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},{2,6},{3},{5}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,4},{2,6},{3},{5,7}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,4},{2,6},{3},{5},{7}} => [2,2,1,1,1] => [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) => 4

{{1,4,7},{2},{3},{5,6}} => [3,1,1,2] => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,4},{2,7},{3},{5,6}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,4},{2},{3},{5,6,7}} => [2,1,1,3] => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{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},{2,7},{3},{5},{6}} => [2,2,1,1,1] => [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) => 4

{{1,4},{2},{3},{5},{6,7}} => [2,1,1,1,2] => [1,1,1,2,2] => ([(1,6),(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

{{1,5,6,7},{2,4},{3}} => [4,2,1] => [2,1,4] => ([(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,5,6},{2,4},{3,7}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,5,6},{2,4},{3},{7}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,5,7},{2,4},{3,6}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,5},{2,4},{3,6,7}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,5,7},{2,4},{3},{6}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,5},{2,4},{3},{6,7}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,5},{2,4},{3},{6},{7}} => [2,2,1,1,1] => [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) => 4

{{1,6,7},{2,4},{3,5}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,6},{2,4},{3,5,7}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,7},{2,4},{3,5,6}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1},{2,4},{3,5,6,7}} => [1,2,4] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,6,7},{2,4},{3},{5}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,6},{2,4},{3},{5,7}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,6},{2,4},{3},{5},{7}} => [2,2,1,1,1] => [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) => 4

{{1,7},{2,4},{3},{5,6}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1},{2,4},{3},{5,6,7}} => [1,2,1,3] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,7},{2,4},{3},{5},{6}} => [2,2,1,1,1] => [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) => 4

{{1},{2,4},{3},{5},{6,7}} => [1,2,1,1,2] => [2,1,1,2,1] => ([(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) => 4

{{1},{2,4},{3},{5},{6},{7}} => [1,2,1,1,1,1] => [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) => 5

{{1,5,6,7},{2},{3,4}} => [4,1,2] => [1,2,4] => ([(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,5,6},{2,7},{3,4}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,5,6},{2},{3,4,7}} => [3,1,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,5,7},{2,6},{3,4}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,5},{2,6},{3,4,7}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,5,7},{2},{3,4,6}} => [3,1,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,5},{2,7},{3,4,6}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,5},{2},{3,4,6,7}} => [2,1,4] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,6,7},{2,5},{3,4}} => [3,2,2] => [2,2,3] => ([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,6},{2,5},{3,4,7}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,7},{2,5},{3,4,6}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1},{2,5},{3,4,6,7}} => [1,2,4] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,6,7},{2},{3,4,5}} => [3,1,3] => [1,3,3] => ([(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,6},{2,7},{3,4,5}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,6},{2},{3,4,5,7}} => [2,1,4] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,7},{2,6},{3,4,5}} => [2,2,3] => [2,3,2] => ([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1},{2,6},{3,4,5,7}} => [1,2,4] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1,7},{2},{3,4,5,6}} => [2,1,4] => [1,4,2] => ([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1},{2,7},{3,4,5,6}} => [1,2,4] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{1},{2},{3,4,5,6,7}} => [1,1,5] => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 2

{{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},{2,7},{3},{4}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,5,6},{2},{3},{4,7}} => [3,1,1,2] => [1,1,2,3] => ([(2,6),(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},{2,6},{3},{4}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,5},{2,6},{3},{4,7}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,5},{2,6},{3},{4},{7}} => [2,2,1,1,1] => [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) => 4

{{1,5,7},{2},{3},{4,6}} => [3,1,1,2] => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,5},{2,7},{3},{4,6}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,5},{2},{3},{4,6,7}} => [2,1,1,3] => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{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},{2,7},{3},{4},{6}} => [2,2,1,1,1] => [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) => 4

{{1,5},{2},{3},{4},{6,7}} => [2,1,1,1,2] => [1,1,1,2,2] => ([(1,6),(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},{2,5},{3},{4}} => [3,2,1,1] => [2,1,1,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,6},{2,5},{3},{4,7}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,6},{2,5},{3},{4},{7}} => [2,2,1,1,1] => [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) => 4

{{1,7},{2,5},{3},{4,6}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1},{2,5},{3},{4,6,7}} => [1,2,1,3] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,7},{2,5},{3},{4},{6}} => [2,2,1,1,1] => [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) => 4

{{1},{2,5},{3},{4},{6,7}} => [1,2,1,1,2] => [2,1,1,2,1] => ([(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) => 4

{{1},{2,5},{3},{4},{6},{7}} => [1,2,1,1,1,1] => [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) => 5

{{1,6,7},{2},{3},{4,5}} => [3,1,1,2] => [1,1,2,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,6},{2,7},{3},{4,5}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,6},{2},{3},{4,5,7}} => [2,1,1,3] => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,7},{2,6},{3},{4,5}} => [2,2,1,2] => [2,1,2,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1},{2,6},{3},{4,5,7}} => [1,2,1,3] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1,7},{2},{3},{4,5,6}} => [2,1,1,3] => [1,1,3,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1},{2,7},{3},{4,5,6}} => [1,2,1,3] => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{1},{2},{3},{4,5,6,7}} => [1,1,1,4] => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3

{{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},{2,7},{3},{4},{5}} => [2,2,1,1,1] => [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) => 4

{{1,6},{2},{3},{4},{5,7}} => [2,1,1,1,2] => [1,1,1,2,2] => ([(1,6),(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},{2,6},{3},{4},{5}} => [2,2,1,1,1] => [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) => 4

{{1},{2,6},{3},{4},{5,7}} => [1,2,1,1,2] => [2,1,1,2,1] => ([(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) => 4

{{1},{2,6},{3},{4},{5},{7}} => [1,2,1,1,1,1] => [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) => 5

{{1,7},{2},{3},{4},{5,6}} => [2,1,1,1,2] => [1,1,1,2,2] => ([(1,6),(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}} => [1,2,1,1,2] => [2,1,1,2,1] => ([(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) => 4

{{1},{2},{3},{4},{5,6,7}} => [1,1,1,1,3] => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4

{{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},{2,7},{3},{4},{5},{6}} => [1,2,1,1,1,1] => [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) => 5

{{1},{2},{3},{4},{5},{6,7}} => [1,1,1,1,1,2] => [1,1,1,1,2,1] => ([(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) => 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

{{1},{2},{3},{4},{5},{6},{7},{8}} => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 7

{{1},{2},{3},{4},{5},{6},{7,8}} => [1,1,1,1,1,1,2] => [1,1,1,1,1,2,1] => ([(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) => 6

{{1},{2},{3},{4},{5},{6},{7},{8},{9}} => [1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(3,4),(3,5),(3,6),(3,7),(3,8),(4,5),(4,6),(4,7),(4,8),(5,6),(5,7),(5,8),(6,7),(6,8),(7,8)],9) => 8

{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => [1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(0,8),(0,9),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8),(1,9),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8),(2,9),(3,4),(3,5),(3,6),(3,7),(3,8),(3,9),(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)],10) => 9

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

click to show known generating functions

$F_{1} = 1$

$F_{2} = 1 + q$

$F_{3} = 1 + 3\ q + q^{2}$

$F_{4} = 1 + 6\ q + 7\ q^{2} + q^{3}$

Description

The dimension of a graph.
The dimension of a graph is the least integer

$n$ such that there exists a representation of the graph in the Euclidean space of dimension

$n$ with all vertices distinct and all edges having unit length. Edges are allowed to intersect, however.

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.

Map

rotate front to back

Description

The front to back rotation of the entries of an integer composition.