Identifier
Values
[[1,4],[2],[3]] => [[1,2],[3],[4]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1],[2],[3],[4]] => [[1,2],[3],[4]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,5],[2],[3]] => [[1,2],[3],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,5],[2],[4]] => [[1,2],[4],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,5],[3],[4]] => [[1,3],[4],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[2,5],[3],[4]] => [[2,3],[4],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1],[2],[3],[5]] => [[1,2],[3],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1],[2],[4],[5]] => [[1,2],[4],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1],[3],[4],[5]] => [[1,3],[4],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[2],[3],[4],[5]] => [[2,3],[4],[5]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,1,4],[2],[3]] => [[1,1,2],[3],[4]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,2,4],[2],[3]] => [[1,2,2],[3],[4]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,3,4],[2],[3]] => [[1,2,3],[3],[4]] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,4,4],[2],[3]] => [[1,2,4],[3],[4]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,1],[2],[3],[4]] => [[1,1,2],[3],[4]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,2],[2],[3],[4]] => [[1,2,2],[3],[4]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,3],[2],[3],[4]] => [[1,2,3],[3],[4]] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,4],[2],[3],[4]] => [[1,2,4],[3],[4]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,1,3,3],[2,2]] => [[1,1,2,2],[3,3]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1,3],[2,2],[3]] => [[1,1,2,2],[3,3]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1],[2,2],[3,3]] => [[1,1,2,2],[3,3]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,6],[2],[3]] => [[1,2],[3],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,6],[2],[4]] => [[1,2],[4],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,6],[2],[5]] => [[1,2],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,6],[3],[4]] => [[1,3],[4],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,6],[3],[5]] => [[1,3],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,6],[4],[5]] => [[1,4],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[2,6],[3],[4]] => [[2,3],[4],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[2,6],[3],[5]] => [[2,3],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[2,6],[4],[5]] => [[2,4],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[3,6],[4],[5]] => [[3,4],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1],[2],[3],[6]] => [[1,2],[3],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1],[2],[4],[6]] => [[1,2],[4],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1],[2],[5],[6]] => [[1,2],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1],[3],[4],[6]] => [[1,3],[4],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1],[3],[5],[6]] => [[1,3],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1],[4],[5],[6]] => [[1,4],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[2],[3],[4],[6]] => [[2,3],[4],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[2],[3],[5],[6]] => [[2,3],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[2],[4],[5],[6]] => [[2,4],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[3],[4],[5],[6]] => [[3,4],[5],[6]] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[[1,3,5],[2,4]] => [[1,2,4],[3,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[[1,1,5],[2],[3]] => [[1,1,2],[3],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,1,5],[2],[4]] => [[1,1,2],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,1,5],[3],[4]] => [[1,1,3],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,2,5],[2],[3]] => [[1,2,2],[3],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,2,5],[2],[4]] => [[1,2,2],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,3,5],[2],[3]] => [[1,2,3],[3],[5]] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,2,5],[3],[4]] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,3,5],[2],[4]] => [[1,2,4],[3],[5]] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,4,5],[2],[3]] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,5,5],[2],[3]] => [[1,2,5],[3],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,4,5],[2],[4]] => [[1,2,4],[4],[5]] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,5,5],[2],[4]] => [[1,2,5],[4],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,3,5],[3],[4]] => [[1,3,3],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,4,5],[3],[4]] => [[1,3,4],[4],[5]] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,5,5],[3],[4]] => [[1,3,5],[4],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[2,2,5],[3],[4]] => [[2,2,3],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[2,3,5],[3],[4]] => [[2,3,3],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[2,4,5],[3],[4]] => [[2,3,4],[4],[5]] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[2,5,5],[3],[4]] => [[2,3,5],[4],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,3],[2,4],[5]] => [[1,2,4],[3,5]] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[[1,4],[2,5],[3]] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,1],[2],[3],[5]] => [[1,1,2],[3],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,1],[2],[4],[5]] => [[1,1,2],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,1],[3],[4],[5]] => [[1,1,3],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,2],[2],[3],[5]] => [[1,2,2],[3],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,2],[2],[4],[5]] => [[1,2,2],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,3],[2],[3],[5]] => [[1,2,3],[3],[5]] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,2],[3],[4],[5]] => [[1,2,3],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,3],[2],[4],[5]] => [[1,2,4],[3],[5]] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,4],[2],[3],[5]] => [[1,2,5],[3],[4]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,5],[2],[3],[4]] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,5],[2],[3],[5]] => [[1,2,5],[3],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,4],[2],[4],[5]] => [[1,2,4],[4],[5]] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,5],[2],[4],[5]] => [[1,2,5],[4],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,3],[3],[4],[5]] => [[1,3,3],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,4],[3],[4],[5]] => [[1,3,4],[4],[5]] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,5],[3],[4],[5]] => [[1,3,5],[4],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[2,2],[3],[4],[5]] => [[2,2,3],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[2,3],[3],[4],[5]] => [[2,3,3],[4],[5]] => [5,4,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[2,4],[3],[4],[5]] => [[2,3,4],[4],[5]] => [5,3,1,2,4] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[2,5],[3],[4],[5]] => [[2,3,5],[4],[5]] => [4,3,1,2,5] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1],[2],[3],[4],[5]] => [[1,2],[3],[4],[5]] => [5,4,3,1,2] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 3
[[1,1,3,4],[2,2]] => [[1,1,2,2],[3,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1,4,4],[2,2]] => [[1,1,2,2],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1,3,4],[2,3]] => [[1,1,2,3],[3,4]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1,4,4],[2,3]] => [[1,1,2,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1,4,4],[3,3]] => [[1,1,3,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,2,3,4],[2,3]] => [[1,2,2,3],[3,4]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,2,4,4],[2,3]] => [[1,2,2,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,2,4,4],[3,3]] => [[1,2,3,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[2,2,4,4],[3,3]] => [[2,2,3,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1,1,4],[2],[3]] => [[1,1,1,2],[3],[4]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,1,2,4],[2],[3]] => [[1,1,2,2],[3],[4]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,1,3,4],[2],[3]] => [[1,1,2,3],[3],[4]] => [6,4,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,1,4,4],[2],[3]] => [[1,1,2,4],[3],[4]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,2,4],[2],[3]] => [[1,2,2,2],[3],[4]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,3,4],[2],[3]] => [[1,2,2,3],[3],[4]] => [6,4,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,4,4],[2],[3]] => [[1,2,2,4],[3],[4]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3,3,4],[2],[3]] => [[1,2,3,3],[3],[4]] => [6,3,1,2,4,5] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
>>> Load all 205 entries. <<<
[[1,3,4,4],[2],[3]] => [[1,2,3,4],[3],[4]] => [5,3,1,2,4,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,4,4,4],[2],[3]] => [[1,2,4,4],[3],[4]] => [4,3,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,1,3],[2,2],[4]] => [[1,1,2,2],[3,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1,4],[2,2],[3]] => [[1,1,2,2],[3],[4]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,1,4],[2,2],[4]] => [[1,1,2,2],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1,3],[2,3],[4]] => [[1,1,2,3],[3,4]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1,4],[2,3],[3]] => [[1,1,2,3],[3],[4]] => [6,4,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,1,4],[2,3],[4]] => [[1,1,2,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1,4],[2,4],[3]] => [[1,1,2,4],[3],[4]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,1,4],[3,3],[4]] => [[1,1,3,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,2,3],[2,3],[4]] => [[1,2,2,3],[3,4]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,2,4],[2,3],[3]] => [[1,2,2,3],[3],[4]] => [6,4,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,4],[2,3],[4]] => [[1,2,2,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,2,4],[2,4],[3]] => [[1,2,2,4],[3],[4]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,4],[3,3],[4]] => [[1,2,3,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,3,4],[2,4],[3]] => [[1,2,3,4],[3],[4]] => [5,3,1,2,4,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[2,2,4],[3,3],[4]] => [[2,2,3,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1,1],[2],[3],[4]] => [[1,1,1,2],[3],[4]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,1,2],[2],[3],[4]] => [[1,1,2,2],[3],[4]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,1,3],[2],[3],[4]] => [[1,1,2,3],[3],[4]] => [6,4,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,1,4],[2],[3],[4]] => [[1,1,2,4],[3],[4]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,2],[2],[3],[4]] => [[1,2,2,2],[3],[4]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,3],[2],[3],[4]] => [[1,2,2,3],[3],[4]] => [6,4,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,4],[2],[3],[4]] => [[1,2,2,4],[3],[4]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3,3],[2],[3],[4]] => [[1,2,3,3],[3],[4]] => [6,3,1,2,4,5] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3,4],[2],[3],[4]] => [[1,2,3,4],[3],[4]] => [5,3,1,2,4,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,4,4],[2],[3],[4]] => [[1,2,4,4],[3],[4]] => [4,3,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,1],[2,2],[3,4]] => [[1,1,2,2],[3,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1],[2,2],[4,4]] => [[1,1,2,2],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1],[2,3],[3,4]] => [[1,1,2,3],[3,4]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1],[2,3],[4,4]] => [[1,1,2,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1],[3,3],[4,4]] => [[1,1,3,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,2],[2,3],[3,4]] => [[1,2,2,3],[3,4]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,2],[2,3],[4,4]] => [[1,2,2,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,2],[3,3],[4,4]] => [[1,2,3,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[2,2],[3,3],[4,4]] => [[2,2,3,3],[4,4]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,1],[2,2],[3],[4]] => [[1,1,2,2],[3],[4]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,1],[2,3],[3],[4]] => [[1,1,2,3],[3],[4]] => [6,4,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,1],[2,4],[3],[4]] => [[1,1,2,4],[3],[4]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2],[2,3],[3],[4]] => [[1,2,2,3],[3],[4]] => [6,4,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2],[2,4],[3],[4]] => [[1,2,2,4],[3],[4]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3],[2,4],[3],[4]] => [[1,2,3,4],[3],[4]] => [5,3,1,2,4,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,1,1,3,3],[2,2]] => [[1,1,1,2,2],[3,3]] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[[1,1,2,3,3],[2,2]] => [[1,1,2,2,2],[3,3]] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[[1,1,3,3,3],[2,2]] => [[1,1,2,2,3],[3,3]] => [5,6,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[[1,1,1,3],[2,2],[3]] => [[1,1,1,2,2],[3,3]] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[[1,1,2,3],[2,2],[3]] => [[1,1,2,2,2],[3,3]] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[[1,1,3,3],[2,2],[3]] => [[1,1,2,2,3],[3,3]] => [5,6,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[[1,1,1],[2,2],[3,3]] => [[1,1,1,2,2],[3,3]] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[[1,1,2],[2,2],[3,3]] => [[1,1,2,2,2],[3,3]] => [6,7,1,2,3,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[[1,1,3],[2,2],[3,3]] => [[1,1,2,2,3],[3,3]] => [5,6,1,2,3,4,7] => ([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 4
[[1,2,3,6],[4],[5]] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,3],[4],[5],[6]] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,4,6],[3,5]] => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,2,4],[3,5],[6]] => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,2,4,6],[3],[5]] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,4],[3],[5],[6]] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,5,6],[3],[4]] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,5],[3,6],[4]] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,5],[3],[4],[6]] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,6],[3],[4],[5]] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2],[3],[4],[5],[6]] => [[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3,4,6],[2,5]] => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[[1,3,4],[2,5],[6]] => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[[1,3,5,6],[2,4]] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[[1,3,5],[2,4,6]] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[[1,3,5],[2,4],[6]] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[[1,3,6],[2,4],[5]] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3],[2,4],[5],[6]] => [[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3,4,6],[2],[5]] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3,4],[2],[5],[6]] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3,5,6],[2],[4]] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3,5],[2,6],[4]] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3,5],[2],[4],[6]] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3,6],[2],[4],[5]] => [[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => ([(0,4),(0,5),(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]] => [[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,5,6],[3,4]] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,2,5],[3,4],[6]] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,2,6],[3,4],[5]] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2],[3,4],[5],[6]] => [[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,4,5,6],[2],[3]] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,4,5],[2,6],[3]] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,4,6],[2,5],[3]] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[[1,4],[2,5],[3,6]] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[[1,4],[2,5],[3],[6]] => [[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[[1,4,5],[2],[3],[6]] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,4,6],[2],[3],[5]] => [[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => ([(0,5),(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]] => [[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2,6],[3,5],[4]] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2],[3,5],[4],[6]] => [[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3,6],[2,5],[4]] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3],[2,5],[4,6]] => [[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[[1,3],[2,5],[4],[6]] => [[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2],[3,5],[4,6]] => [[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,5,6],[2],[3],[4]] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,5],[2,6],[3],[4]] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => ([(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]] => [[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2],[3,6],[4],[5]] => [[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3],[2,4],[5,6]] => [[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[[1,3],[2,6],[4],[5]] => [[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,2],[3,4],[5,6]] => [[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,4],[2,6],[3],[5]] => [[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,6],[2],[3],[4],[5]] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => ([(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) => 3
[[1],[2],[3],[4],[5],[6]] => [[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => ([(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) => 3
search for individual values
searching the database for the individual values of this statistic
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).
Map
catabolism
Description
Remove the first row of the semistandard tableau and insert it back using column Schensted insertion, starting with the largest number.
The algorithm for column-inserting an entry $k$ into tableau $T$ is as follows:
If $k$ is larger than all entries in the first column, place $k$ at the bottom of the first column and the procedure is finished. Otherwise, place $k$ in the first column, replacing the smallest entry, $y$, greater or equal to than $k$. Now insert $y$ into the second column using the same procedure: if $y$ is greater than all entries in the second column, place it at the bottom of that column (provided that the result is still a tableau). Otherwise, place $y$ in the second column, replacing, or 'bumping', the smallest entry, $z$, larger than or equal to $y$. Continue the procedure until we have placed a bumped entry at the bottom of a column (or on its own in a new column).
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.