Identifier
Values
[[1,2]] => 0 => [1] => ([],1) => 0
[[1],[2]] => 1 => [1] => ([],1) => 0
[[1,2,3]] => 00 => [2] => ([],2) => 0
[[1,3],[2]] => 10 => [1,1] => ([(0,1)],2) => 1
[[1,2],[3]] => 01 => [1,1] => ([(0,1)],2) => 1
[[1],[2],[3]] => 11 => [2] => ([],2) => 0
[[1,2,3,4]] => 000 => [3] => ([],3) => 0
[[1,3,4],[2]] => 100 => [1,2] => ([(1,2)],3) => 1
[[1,2,4],[3]] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 2
[[1,3],[2,4]] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 2
[[1,2],[3,4]] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 2
[[1,3],[2],[4]] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 2
[[1,2],[3],[4]] => 011 => [1,2] => ([(1,2)],3) => 1
[[1],[2],[3],[4]] => 111 => [3] => ([],3) => 0
[[1,2,3,4,5]] => 0000 => [4] => ([],4) => 0
[[1,3,4,5],[2]] => 1000 => [1,3] => ([(2,3)],4) => 1
[[1,2,4,5],[3]] => 0100 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
[[1,3,5],[2,4]] => 1010 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,5],[3,4]] => 0100 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
[[1,2,4],[3,5]] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,5],[2],[4]] => 1010 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,2,4],[3],[5]] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3],[2,5],[4]] => 1010 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3],[2,4],[5]] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
[[1,2],[3,4],[5]] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3],[2],[4],[5]] => 1011 => [1,1,2] => ([(1,2),(1,3),(2,3)],4) => 2
[[1,2],[3],[4],[5]] => 0111 => [1,3] => ([(2,3)],4) => 1
[[1],[2],[3],[4],[5]] => 1111 => [4] => ([],4) => 0
[[1,2,3,4,5,6]] => 00000 => [5] => ([],5) => 0
[[1,3,4,5,6],[2]] => 10000 => [1,4] => ([(3,4)],5) => 1
[[1,2,4,5,6],[3]] => 01000 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[[1,2,3,4,6],[5]] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,2,3,4,5],[6]] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[[1,3,5,6],[2,4]] => 10100 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,2,5,6],[3,4]] => 01000 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[[1,2,4,6],[3,5]] => 01010 => [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]] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,3,5,6],[2],[4]] => 10100 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,2,4,6],[3],[5]] => 01010 => [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
[[1,3,5],[2,4,6]] => 10101 => [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
[[1,2,4],[3,5,6]] => 01010 => [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
[[1,3,6],[2,5],[4]] => 10100 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,2,6],[3,4],[5]] => 01010 => [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
[[1,3,5],[2,6],[4]] => 10101 => [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
[[1,2,4],[3,6],[5]] => 01010 => [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
[[1,3,5],[2,4],[6]] => 10101 => [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
[[1,2,4],[3,5],[6]] => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,3,5],[2],[4],[6]] => 10101 => [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
[[1,2,4],[3],[5],[6]] => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,3],[2,5],[4,6]] => 10101 => [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]] => 01010 => [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
[[1,5],[2,6],[3],[4]] => 11101 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,3],[2,5],[4],[6]] => 10101 => [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
[[1,3],[2,4],[5],[6]] => 10111 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[[1,2],[3,4],[5],[6]] => 01011 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,6],[2],[3],[4],[5]] => 11110 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[[1,5],[2],[3],[4],[6]] => 11101 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,3],[2],[4],[5],[6]] => 10111 => [1,1,3] => ([(2,3),(2,4),(3,4)],5) => 2
[[1,2],[3],[4],[5],[6]] => 01111 => [1,4] => ([(3,4)],5) => 1
[[1],[2],[3],[4],[5],[6]] => 11111 => [5] => ([],5) => 0
[[1,2,3,4,5,6,7]] => 000000 => [6] => ([],6) => 0
[[1,3,4,5,6,7],[2]] => 100000 => [1,5] => ([(4,5)],6) => 1
[[1,2,4,5,6,7],[3]] => 010000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[[1,2,3,4,6,7],[5]] => 000100 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3,5,6,7],[2,4]] => 101000 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,5,6,7],[3,4]] => 010000 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[[1,2,4,6,7],[3,5]] => 010100 => [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
[[1,2,3,4,7],[5,6]] => 000100 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3,5,6,7],[2],[4]] => 101000 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,4,6,7],[3],[5]] => 010100 => [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],[7]] => 000011 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[[1,3,5,7],[2,4,6]] => 101010 => [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
[[1,2,4,7],[3,5,6]] => 010100 => [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
[[1,2,4,6],[3,5,7]] => 010101 => [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]] => 000100 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3,6,7],[2,5],[4]] => 101000 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,6,7],[3,4],[5]] => 010100 => [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
[[1,3,5,7],[2,6],[4]] => 101010 => [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
[[1,2,4,7],[3,6],[5]] => 010100 => [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
[[1,3,5,7],[2,4],[6]] => 101010 => [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
[[1,2,4,6],[3,7],[5]] => 010101 => [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
[[1,2,4,6],[3,5],[7]] => 010101 => [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
[[1,3,5,7],[2],[4],[6]] => 101010 => [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
[[1,2,4,6],[3],[5],[7]] => 010101 => [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
[[1,2,6],[3,4,7],[5]] => 010101 => [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
[[1,3,5],[2,6,7],[4]] => 101010 => [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
[[1,2,4],[3,6,7],[5]] => 010100 => [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
[[1,3,5],[2,4,7],[6]] => 101010 => [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
[[1,3,5],[2,4,6],[7]] => 101011 => [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
[[1,2,4],[3,5,6],[7]] => 010101 => [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
[[1,3,7],[2,5],[4,6]] => 101010 => [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
[[1,2,7],[3,4],[5,6]] => 010100 => [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],[5,7]] => 010101 => [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
[[1,3,5],[2,6],[4,7]] => 101011 => [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
[[1,2,4],[3,6],[5,7]] => 010101 => [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
[[1,3,5],[2,4],[6,7]] => 101010 => [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
[[1,3,7],[2,5],[4],[6]] => 101010 => [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
[[1,3,5],[2,7],[4],[6]] => 101010 => [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
[[1,2,6],[3,4],[5],[7]] => 010101 => [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
[[1,3,5],[2,6],[4],[7]] => 101011 => [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
[[1,2,4],[3,6],[5],[7]] => 010101 => [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
>>> Load all 230 entries. <<<
[[1,3,5],[2,4],[6],[7]] => 101011 => [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
[[1,2,4],[3,5],[6],[7]] => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,6,7],[2],[3],[4],[5]] => 111100 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6) => 2
[[1,3,5],[2],[4],[6],[7]] => 101011 => [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
[[1,2,4],[3],[5],[6],[7]] => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,5],[2,6],[3,7],[4]] => 111011 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3],[2,5],[4,7],[6]] => 101010 => [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
[[1,3],[2,5],[4,6],[7]] => 101011 => [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],[7]] => 010101 => [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
[[1,5],[2,6],[3],[4],[7]] => 111011 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3],[2,5],[4],[6],[7]] => 101011 => [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],[2,4],[5],[6],[7]] => 101111 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[[1,2],[3,4],[5],[6],[7]] => 010111 => [1,1,1,3] => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,5],[2],[3],[4],[6],[7]] => 111011 => [3,1,2] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3],[2],[4],[5],[6],[7]] => 101111 => [1,1,4] => ([(3,4),(3,5),(4,5)],6) => 2
[[1,2],[3],[4],[5],[6],[7]] => 011111 => [1,5] => ([(4,5)],6) => 1
[[1],[2],[3],[4],[5],[6],[7]] => 111111 => [6] => ([],6) => 0
[[1,2,3,4,5,6,7,8]] => 0000000 => [7] => ([],7) => 0
[[1,3,4,5,6,7,8],[2]] => 1000000 => [1,6] => ([(5,6)],7) => 1
[[1,2,4,5,6,7,8],[3]] => 0100000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[[1,2,3,4,6,7,8],[5]] => 0001000 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,3,5,6,7,8],[2,4]] => 1010000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,2,5,6,7,8],[3,4]] => 0100000 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[[1,2,4,6,7,8],[3,5]] => 0101000 => [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
[[1,2,3,4,7,8],[5,6]] => 0001000 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,3,5,6,7,8],[2],[4]] => 1010000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,2,4,6,7,8],[3],[5]] => 0101000 => [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
[[1,3,5,7,8],[2,4,6]] => 1010100 => [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
[[1,2,4,7,8],[3,5,6]] => 0101000 => [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
[[1,2,4,6,8],[3,5,7]] => 0101010 => [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
[[1,2,3,4,8],[5,6,7]] => 0001000 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,3,6,7,8],[2,5],[4]] => 1010000 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,2,6,7,8],[3,4],[5]] => 0101000 => [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
[[1,3,5,7,8],[2,6],[4]] => 1010100 => [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
[[1,2,4,7,8],[3,6],[5]] => 0101000 => [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
[[1,3,5,7,8],[2,4],[6]] => 1010100 => [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
[[1,2,4,6,8],[3,7],[5]] => 0101010 => [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
[[1,2,4,6,8],[3,5],[7]] => 0101010 => [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
[[1,3,5,7,8],[2],[4],[6]] => 1010100 => [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
[[1,2,4,6,8],[3],[5],[7]] => 0101010 => [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]] => 0000111 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[[1,3,5,7],[2,4,6,8]] => 1010101 => [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
[[1,2,4,6],[3,5,7,8]] => 0101010 => [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]] => 0001000 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,2,6,8],[3,4,7],[5]] => 0101010 => [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
[[1,3,5,8],[2,6,7],[4]] => 1010100 => [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
[[1,2,4,8],[3,6,7],[5]] => 0101000 => [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
[[1,3,5,8],[2,4,7],[6]] => 1010100 => [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
[[1,2,4,8],[3,5,6],[7]] => 0101010 => [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
[[1,3,5,7],[2,6,8],[4]] => 1010101 => [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
[[1,3,5,7],[2,4,8],[6]] => 1010101 => [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
[[1,2,4,6],[3,7,8],[5]] => 0101010 => [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
[[1,2,4,6],[3,5,8],[7]] => 0101010 => [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
[[1,3,5,7],[2,4,6],[8]] => 1010101 => [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
[[1,2,4,6],[3,5,7],[8]] => 0101011 => [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
[[1,3,7,8],[2,5],[4,6]] => 1010100 => [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
[[1,2,7,8],[3,4],[5,6]] => 0101000 => [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
[[1,2,6,8],[3,4],[5,7]] => 0101010 => [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
[[1,2,4,8],[3,6],[5,7]] => 0101010 => [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
[[1,3,5,8],[2,4],[6,7]] => 1010100 => [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
[[1,3,5,7],[2,6],[4,8]] => 1010101 => [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
[[1,3,5,7],[2,4],[6,8]] => 1010101 => [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
[[1,2,4,6],[3,7],[5,8]] => 0101011 => [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
[[1,2,4,6],[3,5],[7,8]] => 0101010 => [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
[[1,3,7,8],[2,5],[4],[6]] => 1010100 => [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
[[1,3,5,8],[2,7],[4],[6]] => 1010100 => [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
[[1,2,6,8],[3,4],[5],[7]] => 0101010 => [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
[[1,2,4,8],[3,6],[5],[7]] => 0101010 => [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
[[1,3,5,7],[2,8],[4],[6]] => 1010101 => [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
[[1,2,4,6],[3,8],[5],[7]] => 0101010 => [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
[[1,3,5,7],[2,6],[4],[8]] => 1010101 => [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
[[1,3,5,7],[2,4],[6],[8]] => 1010101 => [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
[[1,2,4,6],[3,7],[5],[8]] => 0101011 => [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
[[1,2,4,6],[3,5],[7],[8]] => 0101011 => [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
[[1,6,7,8],[2],[3],[4],[5]] => 1111000 => [4,3] => ([(2,6),(3,6),(4,6),(5,6)],7) => 2
[[1,3,5,7],[2],[4],[6],[8]] => 1010101 => [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
[[1,2,4,6],[3],[5],[7],[8]] => 0101011 => [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
[[1,3,7],[2,5,8],[4,6]] => 1010101 => [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
[[1,2,6],[3,4,8],[5,7]] => 0101010 => [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
[[1,2,4],[3,6,8],[5,7]] => 0101010 => [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
[[1,3,5],[2,4,8],[6,7]] => 1010100 => [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
[[1,2,6],[3,4,7],[5,8]] => 0101011 => [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
[[1,3,5],[2,6,7],[4,8]] => 1010101 => [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
[[1,3,5],[2,4,7],[6,8]] => 1010101 => [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
[[1,2,4],[3,5,6],[7,8]] => 0101010 => [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
[[1,3,7],[2,5,8],[4],[6]] => 1010101 => [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
[[1,3,5],[2,7,8],[4],[6]] => 1010100 => [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
[[1,2,6],[3,4,8],[5],[7]] => 0101010 => [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
[[1,2,4],[3,6,8],[5],[7]] => 0101010 => [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
[[1,2,6],[3,4,7],[5],[8]] => 0101011 => [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
[[1,3,5],[2,6,7],[4],[8]] => 1010101 => [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
[[1,3,5],[2,4,7],[6],[8]] => 1010101 => [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
[[1,3,5],[2,4,6],[7],[8]] => 1010111 => [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],[3,5,6],[7],[8]] => 0101011 => [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
[[1,3,8],[2,5],[4,7],[6]] => 1010100 => [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
[[1,2,8],[3,4],[5,6],[7]] => 0101010 => [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
[[1,3,7],[2,5],[4,8],[6]] => 1010101 => [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
[[1,3,5],[2,7],[4,8],[6]] => 1010101 => [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
[[1,2,6],[3,4],[5,8],[7]] => 0101010 => [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
[[1,2,4],[3,6],[5,8],[7]] => 0101010 => [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
[[1,3,7],[2,5],[4,6],[8]] => 1010101 => [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
[[1,2,6],[3,4],[5,7],[8]] => 0101011 => [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
[[1,3,5],[2,6],[4,7],[8]] => 1010111 => [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],[3,6],[5,7],[8]] => 0101011 => [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
[[1,3,5],[2,4],[6,7],[8]] => 1010101 => [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
[[1,3,7],[2,5],[4],[6],[8]] => 1010101 => [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
[[1,3,5],[2,7],[4],[6],[8]] => 1010101 => [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
[[1,2,6],[3,4],[5],[7],[8]] => 0101011 => [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
[[1,3,5],[2,6],[4],[7],[8]] => 1010111 => [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],[3,6],[5],[7],[8]] => 0101011 => [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
[[1,3,5],[2,4],[6],[7],[8]] => 1010111 => [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],[3,5],[6],[7],[8]] => 0101111 => [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],[8]] => 1010111 => [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],[3],[5],[6],[7],[8]] => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,5],[2,6],[3,7],[4,8]] => 1110111 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,3],[2,5],[4,7],[6,8]] => 1010101 => [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]] => 0101010 => [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
[[1,5],[2,6],[3,7],[4],[8]] => 1110111 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,3],[2,5],[4,7],[6],[8]] => 1010101 => [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
[[1,3],[2,5],[4,6],[7],[8]] => 1010111 => [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],[8]] => 0101011 => [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],[2,6],[3],[4],[7],[8]] => 1110111 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,3],[2,5],[4],[6],[7],[8]] => 1010111 => [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],[8]] => 1011111 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[[1,2],[3,4],[5],[6],[7],[8]] => 0101111 => [1,1,1,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,5],[2],[3],[4],[6],[7],[8]] => 1110111 => [3,1,3] => ([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,3],[2],[4],[5],[6],[7],[8]] => 1011111 => [1,1,5] => ([(4,5),(4,6),(5,6)],7) => 2
[[1,2],[3],[4],[5],[6],[7],[8]] => 0111111 => [1,6] => ([(5,6)],7) => 1
[[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111 => [7] => ([],7) => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The 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
descent word
Description
The descent word of a standard Young tableau.
For a standard Young tableau of size $n$ we set $w_i=1$ if $i+1$ is in a lower row than $i$, and $0$ otherwise, for $1\leq i < n$.
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
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.