Identifier
Values
[[1]] => [[1]] => [1] => ([],1) => 0
[[1,3],[2]] => [[1,2],[3]] => [2,1] => ([(0,2),(1,2)],3) => 2
[[1,3,4],[2]] => [[1,2,3],[4]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[[1,3],[2,4]] => [[1,3],[2,4]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[[1,3],[2],[4]] => [[1,3],[2],[4]] => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[[1,3,4,5],[2]] => [[1,2,3,4],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[[1,3,5],[2,4]] => [[1,2,4],[3,5]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,4],[2,5]] => [[1,3,4],[2,5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[[1,3,5],[2],[4]] => [[1,2,4],[3],[5]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3,4],[2],[5]] => [[1,3,4],[2],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[[1,3],[2,5],[4]] => [[1,2],[3,4],[5]] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[[1,3],[2,4],[5]] => [[1,4],[2,5],[3]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[[1,3],[2],[4],[5]] => [[1,4],[2],[3],[5]] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 2
[[1,3,4,5,6],[2]] => [[1,2,3,4,5],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[[1,3,5,6],[2,4]] => [[1,2,3,5],[4,6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,4,6],[2,5]] => [[1,2,4,5],[3,6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,4,5],[2,6]] => [[1,3,4,5],[2,6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[[1,3,5,6],[2],[4]] => [[1,2,3,5],[4],[6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,4,6],[2],[5]] => [[1,2,4,5],[3],[6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,4,5],[2],[6]] => [[1,3,4,5],[2],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[[1,3,5],[2,4,6]] => [[1,3,5],[2,4,6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,4],[2,5,6]] => [[1,2,5],[3,4,6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,6],[2,5],[4]] => [[1,2,3],[4,5],[6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,6],[2,4],[5]] => [[1,2,5],[3,6],[4]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,5],[2,6],[4]] => [[1,3,5],[2,4],[6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,4],[2,6],[5]] => [[1,2,5],[3,4],[6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,5],[2,4],[6]] => [[1,3,5],[2,6],[4]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,4],[2,5],[6]] => [[1,4,5],[2,6],[3]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[[1,3,6],[2],[4],[5]] => [[1,2,5],[3],[4],[6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,5],[2],[4],[6]] => [[1,3,5],[2],[4],[6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,4],[2],[5],[6]] => [[1,4,5],[2],[3],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[[1,3],[2,5],[4,6]] => [[1,3],[2,5],[4,6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3],[2,4],[5,6]] => [[1,2],[3,5],[4,6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3],[2,6],[4],[5]] => [[1,2],[3,5],[4],[6]] => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3],[2,5],[4],[6]] => [[1,3],[2,5],[4],[6]] => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3],[2,4],[5],[6]] => [[1,5],[2,6],[3],[4]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[[1,3],[2],[4],[5],[6]] => [[1,5],[2],[3],[4],[6]] => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 2
[[1,3,4,5,6,7],[2]] => [[1,2,3,4,5,6],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[[1,3,5,6,7],[2,4]] => [[1,2,3,4,6],[5,7]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,6,7],[2,5]] => [[1,2,3,5,6],[4,7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,5,7],[2,6]] => [[1,2,4,5,6],[3,7]] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,5,6],[2,7]] => [[1,3,4,5,6],[2,7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[[1,3,5,6,7],[2],[4]] => [[1,2,3,4,6],[5],[7]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,6,7],[2],[5]] => [[1,2,3,5,6],[4],[7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,5,7],[2],[6]] => [[1,2,4,5,6],[3],[7]] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,5,6],[2],[7]] => [[1,3,4,5,6],[2],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[[1,3,5,7],[2,4,6]] => [[1,2,4,6],[3,5,7]] => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,7],[2,5,6]] => [[1,2,3,6],[4,5,7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5,6],[2,4,7]] => [[1,3,4,6],[2,5,7]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,6],[2,5,7]] => [[1,3,5,6],[2,4,7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,5],[2,6,7]] => [[1,2,5,6],[3,4,7]] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,6,7],[2,5],[4]] => [[1,2,3,4],[5,6],[7]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,6,7],[2,4],[5]] => [[1,2,3,6],[4,7],[5]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5,7],[2,6],[4]] => [[1,2,4,6],[3,5],[7]] => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,7],[2,6],[5]] => [[1,2,3,6],[4,5],[7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5,7],[2,4],[6]] => [[1,2,4,6],[3,7],[5]] => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,7],[2,5],[6]] => [[1,2,5,6],[3,7],[4]] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5,6],[2,7],[4]] => [[1,3,4,6],[2,5],[7]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,6],[2,7],[5]] => [[1,3,5,6],[2,4],[7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,5],[2,7],[6]] => [[1,2,5,6],[3,4],[7]] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5,6],[2,4],[7]] => [[1,3,4,6],[2,7],[5]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,6],[2,5],[7]] => [[1,3,5,6],[2,7],[4]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,5],[2,6],[7]] => [[1,4,5,6],[2,7],[3]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[[1,3,6,7],[2],[4],[5]] => [[1,2,3,6],[4],[5],[7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5,7],[2],[4],[6]] => [[1,2,4,6],[3],[5],[7]] => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,7],[2],[5],[6]] => [[1,2,5,6],[3],[4],[7]] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5,6],[2],[4],[7]] => [[1,3,4,6],[2],[5],[7]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,6],[2],[5],[7]] => [[1,3,5,6],[2],[4],[7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4,5],[2],[6],[7]] => [[1,4,5,6],[2],[3],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[[1,3,6],[2,5,7],[4]] => [[1,3,4],[2,5,6],[7]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,6],[2,4,7],[5]] => [[1,3,6],[2,4,7],[5]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5],[2,6,7],[4]] => [[1,2,4],[3,5,6],[7]] => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4],[2,6,7],[5]] => [[1,2,3],[4,5,6],[7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5],[2,4,7],[6]] => [[1,2,6],[3,4,7],[5]] => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4],[2,5,7],[6]] => [[1,2,6],[3,5,7],[4]] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5],[2,4,6],[7]] => [[1,4,6],[2,5,7],[3]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4],[2,5,6],[7]] => [[1,3,6],[2,5,7],[4]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,7],[2,5],[4,6]] => [[1,2,4],[3,6],[5,7]] => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,7],[2,4],[5,6]] => [[1,2,3],[4,6],[5,7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,6],[2,5],[4,7]] => [[1,3,4],[2,6],[5,7]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,6],[2,4],[5,7]] => [[1,3,6],[2,4],[5,7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5],[2,6],[4,7]] => [[1,4,6],[2,5],[3,7]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4],[2,6],[5,7]] => [[1,3,6],[2,5],[4,7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5],[2,4],[6,7]] => [[1,2,6],[3,4],[5,7]] => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4],[2,5],[6,7]] => [[1,2,6],[3,5],[4,7]] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,7],[2,6],[4],[5]] => [[1,2,3],[4,6],[5],[7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,7],[2,5],[4],[6]] => [[1,2,4],[3,6],[5],[7]] => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,7],[2,4],[5],[6]] => [[1,2,6],[3,7],[4],[5]] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,6],[2,7],[4],[5]] => [[1,3,6],[2,4],[5],[7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5],[2,7],[4],[6]] => [[1,2,6],[3,4],[5],[7]] => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4],[2,7],[5],[6]] => [[1,2,6],[3,5],[4],[7]] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,6],[2,5],[4],[7]] => [[1,3,4],[2,6],[5],[7]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,6],[2,4],[5],[7]] => [[1,3,6],[2,7],[4],[5]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5],[2,6],[4],[7]] => [[1,4,6],[2,5],[3],[7]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4],[2,6],[5],[7]] => [[1,3,6],[2,5],[4],[7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5],[2,4],[6],[7]] => [[1,4,6],[2,7],[3],[5]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4],[2,5],[6],[7]] => [[1,5,6],[2,7],[3],[4]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[[1,3,7],[2],[4],[5],[6]] => [[1,2,6],[3],[4],[5],[7]] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,6],[2],[4],[5],[7]] => [[1,3,6],[2],[4],[5],[7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5],[2],[4],[6],[7]] => [[1,4,6],[2],[3],[5],[7]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4],[2],[5],[6],[7]] => [[1,5,6],[2],[3],[4],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
>>> Load all 111 entries. <<<
[[1,3],[2,6],[4,7],[5]] => [[1,3],[2,4],[5,6],[7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3],[2,5],[4,7],[6]] => [[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3],[2,4],[5,7],[6]] => [[1,2],[3,6],[4,7],[5]] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3],[2,5],[4,6],[7]] => [[1,4],[2,6],[3,7],[5]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3],[2,4],[5,6],[7]] => [[1,3],[2,6],[4,7],[5]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3],[2,7],[4],[5],[6]] => [[1,2],[3,6],[4],[5],[7]] => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3],[2,6],[4],[5],[7]] => [[1,3],[2,6],[4],[5],[7]] => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3],[2,5],[4],[6],[7]] => [[1,4],[2,6],[3],[5],[7]] => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3],[2,4],[5],[6],[7]] => [[1,6],[2,7],[3],[4],[5]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
[[1,3],[2],[4],[5],[6],[7]] => [[1,6],[2],[3],[4],[5],[7]] => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 2
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 diameter of a connected graph.
This is the greatest distance between any pair of vertices.
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
peak composition
Description
The composition corresponding to the peak set of a standard tableau.
Let $T$ be a standard tableau of size $n$.
An entry $i$ of $T$ is a descent if $i+1$ is in a lower row (in English notation), otherwise $i$ is an ascent.
An entry $2 \leq i \leq n-1$ is a peak, if $i-1$ is an ascent and $i$ is a descent.
This map returns the composition $c_1,\dots,c_k$ of $n$ such that $\{c_1, c_1+c_2,\dots, c_1+\dots+c_k\}$ is the peak set of $T$.
Map
Schützenberger involution
Description
Sends a standard tableau to the standard tableau obtained via the Schützenberger involution.