Identifier
Values
[[1,2,3]] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 1
[[1,2,3,4]] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,3],[4]] => [4,1,2,3] => ([(1,2),(2,3)],4) => ([(0,2),(2,1)],3) => 1
[[1,3],[2,4]] => [2,4,1,3] => ([(0,3),(1,2),(1,3)],4) => ([(0,2),(2,1)],3) => 1
[[1,2],[3,4]] => [3,4,1,2] => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,2,3,4,5]] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,3,5],[4]] => [4,1,2,3,5] => ([(0,4),(1,2),(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 1
[[1,2,3,4],[5]] => [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,3,5],[2,4]] => [2,4,1,3,5] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,2),(2,1)],3) => 1
[[1,2,5],[3,4]] => [3,4,1,2,5] => ([(0,3),(1,2),(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,3,4],[2,5]] => [2,5,1,3,4] => ([(0,4),(1,2),(1,4),(4,3)],5) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,4],[3,5]] => [3,5,1,2,4] => ([(0,3),(1,2),(1,4),(3,4)],5) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,2,3],[4,5]] => [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,3],[4],[5]] => [5,4,1,2,3] => ([(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 1
[[1,3],[2,4],[5]] => [5,2,4,1,3] => ([(1,4),(2,3),(2,4)],5) => ([(0,2),(2,1)],3) => 1
[[1,2],[3,4],[5]] => [5,3,4,1,2] => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,2,3,4,5,6]] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1
[[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => ([(1,5),(3,4),(4,2),(5,3)],6) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1
[[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => ([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => ([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => ([(0,5),(1,3),(1,5),(4,2),(5,4)],6) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => ([(0,4),(1,3),(1,5),(4,5),(5,2)],6) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => ([(0,4),(1,3),(1,5),(2,5),(4,2)],6) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1
[[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1
[[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => ([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => ([(0,3),(1,4),(3,5),(4,2),(4,5)],6) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => ([(0,5),(1,4),(1,5),(4,2),(5,3)],6) => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2
[[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(2,1)],3) => 1
[[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => ([(0,5),(1,5),(2,3),(3,4)],6) => ([(0,2),(2,1)],3) => 1
[[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => ([(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(2,1)],3) => 1
[[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => ([(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => ([(1,5),(2,3),(2,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => ([(1,4),(2,3),(2,5),(4,5)],6) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => ([(1,3),(2,4),(4,5)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => ([(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1
[[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => ([(0,4),(1,4),(1,5),(2,3),(2,5)],6) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => ([(0,5),(1,3),(2,4),(2,5)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => ([(0,5),(1,3),(2,4),(2,5)],6) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => ([(2,5),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 1
[[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,2,3,4,5,6,7]] => [1,2,3,4,5,6,7] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,3,5,6,7],[4]] => [4,1,2,3,5,6,7] => ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,3,4,6,7],[5]] => [5,1,2,3,4,6,7] => ([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,3,4,5,7],[6]] => [6,1,2,3,4,5,7] => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,3,4,5,6],[7]] => [7,1,2,3,4,5,6] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,3,5,6,7],[2,4]] => [2,4,1,3,5,6,7] => ([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,5,6,7],[3,4]] => [3,4,1,2,5,6,7] => ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,3,4,6,7],[2,5]] => [2,5,1,3,4,6,7] => ([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,4,6,7],[3,5]] => [3,5,1,2,4,6,7] => ([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,2,3,6,7],[4,5]] => [4,5,1,2,3,6,7] => ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3,4,5,7],[2,6]] => [2,6,1,3,4,5,7] => ([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,4,5,7],[3,6]] => [3,6,1,2,4,5,7] => ([(0,3),(1,4),(1,6),(2,5),(3,6),(4,5),(6,2)],7) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,2,3,5,7],[4,6]] => [4,6,1,2,3,5,7] => ([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,3,4,5,6],[2,7]] => [2,7,1,3,4,5,6] => ([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,4,5,6],[3,7]] => [3,7,1,2,4,5,6] => ([(0,4),(1,3),(1,6),(4,6),(5,2),(6,5)],7) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,2,3,6,7],[4],[5]] => [5,4,1,2,3,6,7] => ([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,3,5,7],[4],[6]] => [6,4,1,2,3,5,7] => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,3,4,7],[5],[6]] => [6,5,1,2,3,4,7] => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,3,5,6],[4],[7]] => [7,4,1,2,3,5,6] => ([(1,6),(2,3),(3,5),(5,6),(6,4)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,3,4,6],[5],[7]] => [7,5,1,2,3,4,6] => ([(1,3),(2,6),(3,5),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,3,4,5],[6],[7]] => [7,6,1,2,3,4,5] => ([(2,6),(4,5),(5,3),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,3,5,7],[2,4,6]] => [2,4,6,1,3,5,7] => ([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,5,7],[3,4,6]] => [3,4,6,1,2,5,7] => ([(0,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,3,4,7],[2,5,6]] => [2,5,6,1,3,4,7] => ([(0,6),(1,4),(1,6),(2,5),(3,5),(4,3),(6,2)],7) => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2
[[1,3,5,6],[2,4,7]] => [2,4,7,1,3,5,6] => ([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7) => ([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) => 2
[[1,3,6,7],[2,4],[5]] => [5,2,4,1,3,6,7] => ([(0,6),(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,6,7],[3,4],[5]] => [5,3,4,1,2,6,7] => ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,2,3,7],[4,6],[5]] => [5,4,6,1,2,3,7] => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 1
[[1,3,5,7],[2,4],[6]] => [6,2,4,1,3,5,7] => ([(0,4),(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,5,7],[3,4],[6]] => [6,3,4,1,2,5,7] => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,3,4,7],[2,5],[6]] => [6,2,5,1,3,4,7] => ([(0,6),(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,4,7],[3,5],[6]] => [6,3,5,1,2,4,7] => ([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,2,3,7],[4,5],[6]] => [6,4,5,1,2,3,7] => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,3,6],[4,7],[5]] => [5,4,7,1,2,3,6] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,3,5],[4,7],[6]] => [6,4,7,1,2,3,5] => ([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,3,4],[5,7],[6]] => [6,5,7,1,2,3,4] => ([(0,3),(1,6),(2,6),(3,5),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,3,5,6],[2,4],[7]] => [7,2,4,1,3,5,6] => ([(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,5,6],[3,4],[7]] => [7,3,4,1,2,5,6] => ([(1,4),(2,3),(3,6),(4,6),(6,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,3,4,6],[2,5],[7]] => [7,2,5,1,3,4,6] => ([(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,4,6],[3,5],[7]] => [7,3,5,1,2,4,6] => ([(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,2,3,6],[4,5],[7]] => [7,4,5,1,2,3,6] => ([(1,3),(2,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3,4,5],[2,6],[7]] => [7,2,6,1,3,4,5] => ([(1,6),(2,3),(2,6),(4,5),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,4,5],[3,6],[7]] => [7,3,6,1,2,4,5] => ([(1,4),(2,3),(2,6),(4,6),(6,5)],7) => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 2
[[1,2,3,5],[4,6],[7]] => [7,4,6,1,2,3,5] => ([(1,4),(2,3),(2,6),(4,5),(5,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,3,7],[4],[5],[6]] => [6,5,4,1,2,3,7] => ([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,3,6],[4],[5],[7]] => [7,5,4,1,2,3,6] => ([(1,6),(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,3,5],[4],[6],[7]] => [7,6,4,1,2,3,5] => ([(2,6),(3,4),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,3,4],[5],[6],[7]] => [7,6,5,1,2,3,4] => ([(3,4),(4,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,3,6],[2,4,7],[5]] => [5,2,4,7,1,3,6] => ([(0,5),(0,6),(1,4),(2,3),(2,4),(3,5),(3,6),(4,6)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,6],[3,4,7],[5]] => [5,3,4,7,1,2,6] => ([(0,5),(0,6),(1,3),(2,4),(3,6),(4,5),(4,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,2,3],[4,6,7],[5]] => [5,4,6,7,1,2,3] => ([(0,6),(1,6),(2,3),(3,5),(6,4)],7) => ([(0,2),(2,1)],3) => 1
[[1,3,5],[2,4,7],[6]] => [6,2,4,7,1,3,5] => ([(0,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7) => ([(0,2),(2,1)],3) => 1
>>> Load all 183 entries. <<<
[[1,2,5],[3,4,7],[6]] => [6,3,4,7,1,2,5] => ([(0,5),(1,3),(2,4),(3,6),(4,5),(4,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,3,4],[2,5,7],[6]] => [6,2,5,7,1,3,4] => ([(0,6),(1,5),(2,3),(2,5),(3,6),(5,4)],7) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,4],[3,5,7],[6]] => [6,3,5,7,1,2,4] => ([(0,6),(1,3),(2,4),(2,5),(3,5),(4,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,2,3],[4,5,7],[6]] => [6,4,5,7,1,2,3] => ([(0,6),(1,3),(2,4),(3,5),(4,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3,5],[2,4,6],[7]] => [7,2,4,6,1,3,5] => ([(1,5),(2,3),(2,5),(3,4),(3,6),(5,6)],7) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,2,5],[3,4,6],[7]] => [7,3,4,6,1,2,5] => ([(1,3),(2,4),(3,6),(4,5),(4,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,3,4],[2,5,6],[7]] => [7,2,5,6,1,3,4] => ([(1,6),(2,3),(2,6),(3,5),(6,4)],7) => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => 2
[[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(3,6),(4,6),(5,6)],7) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,7],[3,5],[4,6]] => [4,6,3,5,1,2,7] => ([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3,7],[2,4],[5,6]] => [5,6,2,4,1,3,7] => ([(0,5),(1,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => ([(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,3,6],[2,5],[4,7]] => [4,7,2,5,1,3,6] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(4,6),(5,6)],7) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,6],[3,5],[4,7]] => [4,7,3,5,1,2,6] => ([(0,5),(1,4),(2,3),(2,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3,6],[2,4],[5,7]] => [5,7,2,4,1,3,6] => ([(0,5),(1,3),(1,6),(2,4),(2,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,4,5],[2,6],[3,7]] => [3,7,2,6,1,4,5] => ([(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,3,5],[2,6],[4,7]] => [4,7,2,6,1,3,5] => ([(0,4),(1,4),(1,5),(2,3),(2,5),(2,6),(4,6)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,5],[3,6],[4,7]] => [4,7,3,6,1,2,5] => ([(0,5),(0,6),(1,4),(2,3),(2,5),(2,6),(4,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,3,4],[2,6],[5,7]] => [5,7,2,6,1,3,4] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(6,3)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,4],[3,6],[5,7]] => [5,7,3,6,1,2,4] => ([(0,5),(0,6),(1,4),(2,3),(2,5),(4,6)],7) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,3,5],[2,4],[6,7]] => [6,7,2,4,1,3,5] => ([(0,5),(1,3),(2,4),(2,5),(4,6),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3,7],[2,4],[5],[6]] => [6,5,2,4,1,3,7] => ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,7],[3,4],[5],[6]] => [6,5,3,4,1,2,7] => ([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,2,3],[4,7],[5],[6]] => [6,5,4,7,1,2,3] => ([(0,6),(1,6),(2,6),(3,4),(4,5)],7) => ([(0,2),(2,1)],3) => 1
[[1,3,6],[2,4],[5],[7]] => [7,5,2,4,1,3,6] => ([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,6],[3,4],[5],[7]] => [7,5,3,4,1,2,6] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,2,3],[4,6],[5],[7]] => [7,5,4,6,1,2,3] => ([(1,6),(2,6),(3,4),(4,5)],7) => ([(0,2),(2,1)],3) => 1
[[1,3,5],[2,4],[6],[7]] => [7,6,2,4,1,3,5] => ([(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 1
[[1,2,5],[3,4],[6],[7]] => [7,6,3,4,1,2,5] => ([(2,5),(3,4),(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,3,4],[2,5],[6],[7]] => [7,6,2,5,1,3,4] => ([(2,6),(3,4),(3,6),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,4],[3,5],[6],[7]] => [7,6,3,5,1,2,4] => ([(2,5),(3,4),(3,6),(5,6)],7) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,2,3],[4,5],[6],[7]] => [7,6,4,5,1,2,3] => ([(2,4),(3,5),(5,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,3],[4],[5],[6],[7]] => [7,6,5,4,1,2,3] => ([(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 1
[[1,3],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3] => ([(0,5),(1,5),(2,6),(3,4),(3,6)],7) => ([(0,2),(2,1)],3) => 1
[[1,2],[3,4],[5,7],[6]] => [6,5,7,3,4,1,2] => ([(0,6),(1,6),(2,5),(3,4)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,4],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,3],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3] => ([(1,5),(2,5),(2,6),(3,4),(3,6)],7) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2],[3,5],[4,6],[7]] => [7,4,6,3,5,1,2] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3],[2,4],[5,6],[7]] => [7,5,6,2,4,1,3] => ([(1,6),(2,5),(3,4),(3,6)],7) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3],[2,4],[5],[6],[7]] => [7,6,5,2,4,1,3] => ([(3,6),(4,5),(4,6)],7) => ([(0,2),(2,1)],3) => 1
[[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,2,3,4,5,6,8],[7]] => [7,1,2,3,4,5,6,8] => ([(0,7),(1,6),(2,7),(3,5),(4,3),(5,2),(6,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,2,3,4,5,6,7],[8]] => [8,1,2,3,4,5,6,7] => ([(1,7),(3,4),(4,6),(5,3),(6,2),(7,5)],8) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
[[1,2,3,5,8],[4,7],[6]] => [6,4,7,1,2,3,5,8] => ([(0,5),(1,5),(1,6),(2,3),(3,4),(4,6),(5,7),(6,7)],8) => ([(0,2),(2,1)],3) => 1
[[1,2,3,4,8],[5,7],[6]] => [6,5,7,1,2,3,4,8] => ([(0,3),(1,6),(2,6),(3,5),(4,7),(5,4),(6,7)],8) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,3,4,7],[5,8],[6]] => [6,5,8,1,2,3,4,7] => ([(0,3),(1,6),(1,7),(2,6),(2,7),(3,5),(4,7),(5,4)],8) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,3,4,6],[5,8],[7]] => [7,5,8,1,2,3,4,6] => ([(0,3),(1,6),(2,6),(2,7),(3,5),(4,7),(5,4)],8) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,3,4,5],[6,8],[7]] => [7,6,8,1,2,3,4,5] => ([(0,7),(1,7),(2,6),(4,5),(5,3),(6,4)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,4,5,6],[3,7],[8]] => [8,3,7,1,2,4,5,6] => ([(1,5),(2,4),(2,7),(5,7),(6,3),(7,6)],8) => ([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) => 2
[[1,2,3,4,8],[5],[6],[7]] => [7,6,5,1,2,3,4,8] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,3,4,7],[5],[6],[8]] => [8,6,5,1,2,3,4,7] => ([(1,4),(2,7),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,3,4,6],[5],[7],[8]] => [8,7,5,1,2,3,4,6] => ([(2,4),(3,7),(4,6),(5,7),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,3,4,5],[6],[7],[8]] => [8,7,6,1,2,3,4,5] => ([(3,4),(4,7),(6,5),(7,6)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,3,5,7],[2,4,8],[6]] => [6,2,4,8,1,3,5,7] => ([(0,7),(1,3),(1,7),(2,4),(2,5),(3,5),(3,6),(6,4),(7,6)],8) => ([(0,2),(2,1)],3) => 1
[[1,2,4,7],[3,5,8],[6]] => [6,3,5,8,1,2,4,7] => ([(0,5),(0,7),(1,3),(2,4),(2,6),(3,6),(4,5),(4,7),(6,7)],8) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2
[[1,2,3,4],[5,7,8],[6]] => [6,5,7,8,1,2,3,4] => ([(0,7),(1,7),(2,6),(5,3),(6,5),(7,4)],8) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,3,5,6],[2,7],[4,8]] => [4,8,2,7,1,3,5,6] => ([(0,5),(1,5),(1,6),(2,4),(2,6),(2,7),(5,7),(7,3)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1
[[1,3,5,6],[2,4],[7,8]] => [7,8,2,4,1,3,5,6] => ([(0,6),(1,3),(2,4),(2,6),(4,7),(6,7),(7,5)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,3,4],[5,8],[6],[7]] => [7,6,5,8,1,2,3,4] => ([(0,4),(1,7),(2,7),(3,7),(4,6),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,3,5,7],[2,4],[6],[8]] => [8,6,2,4,1,3,5,7] => ([(1,5),(2,6),(3,4),(3,5),(4,7),(5,7),(7,6)],8) => ([(0,2),(2,1)],3) => 1
[[1,2,3,4],[5,7],[6],[8]] => [8,6,5,7,1,2,3,4] => ([(1,4),(2,7),(3,7),(4,6),(6,5)],8) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,2,3,5],[4,6],[7],[8]] => [8,7,4,6,1,2,3,5] => ([(2,5),(3,4),(3,7),(5,6),(6,7)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,2,3,8],[4],[5],[6],[7]] => [7,6,5,4,1,2,3,8] => ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 1
[[1,2,3,7],[4],[5],[6],[8]] => [8,6,5,4,1,2,3,7] => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8) => ([(0,2),(2,1)],3) => 1
[[1,2,3,4],[5],[6],[7],[8]] => [8,7,6,5,1,2,3,4] => ([(4,5),(5,7),(7,6)],8) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,3,7],[2,4,8],[5,6]] => [5,6,2,4,8,1,3,7] => ([(0,5),(1,3),(2,4),(2,5),(3,6),(3,7),(4,6),(4,7),(5,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3,6],[2,5,8],[4,7]] => [4,7,2,5,8,1,3,6] => ([(0,6),(1,3),(1,7),(2,6),(2,7),(3,5),(6,4),(7,4),(7,5)],8) => ([(0,3),(2,1),(3,2)],4) => 2
[[1,3,6],[2,4,8],[5,7]] => [5,7,2,4,8,1,3,6] => ([(0,5),(1,3),(1,7),(2,4),(2,5),(3,6),(4,6),(4,7),(5,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,2,5],[3,6,8],[4,7]] => [4,7,3,6,8,1,2,5] => ([(0,5),(0,7),(1,4),(2,3),(2,5),(2,7),(3,6),(4,7),(5,6)],8) => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => 2
[[1,3,7],[2,4,8],[5],[6]] => [6,5,2,4,8,1,3,7] => ([(0,6),(0,7),(1,6),(1,7),(2,5),(3,4),(3,5),(4,6),(4,7),(5,7)],8) => ([(0,2),(2,1)],3) => 1
[[1,2,3],[4,6,7],[5],[8]] => [8,5,4,6,7,1,2,3] => ([(1,7),(2,7),(3,4),(4,6),(7,5)],8) => ([(0,2),(2,1)],3) => 1
[[1,3,5],[2,4,6],[7],[8]] => [8,7,2,4,6,1,3,5] => ([(2,6),(3,4),(3,6),(4,5),(4,7),(6,7)],8) => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 2
[[1,3,6],[2,4],[5,8],[7]] => [7,5,8,2,4,1,3,6] => ([(0,5),(1,6),(2,5),(2,7),(3,4),(3,6),(4,7),(6,7)],8) => ([(0,2),(2,1)],3) => 1
[[1,3,7],[2,4],[5,6],[8]] => [8,5,6,2,4,1,3,7] => ([(1,6),(2,5),(3,4),(3,6),(4,7),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3,6],[2,4],[5,7],[8]] => [8,5,7,2,4,1,3,6] => ([(1,6),(2,4),(2,7),(3,5),(3,6),(5,7),(6,7)],8) => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 2
[[1,3,4],[2,6],[5,7],[8]] => [8,5,7,2,6,1,3,4] => ([(1,7),(2,6),(2,7),(3,5),(3,6),(7,4)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,2,8],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2,8] => ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,3,7],[2,4],[5],[6],[8]] => [8,6,5,2,4,1,3,7] => ([(1,7),(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8) => ([(0,2),(2,1)],3) => 1
[[1,5],[2,6],[3,7],[4,8]] => [4,8,3,7,2,6,1,5] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1
[[1,3],[2,4],[5],[6],[7],[8]] => [8,7,6,5,2,4,1,3] => ([(4,7),(5,6),(5,7)],8) => ([(0,2),(2,1)],3) => 1
[[1,2],[3,4],[5],[6],[7],[8]] => [8,7,6,5,3,4,1,2] => ([(4,7),(5,6)],8) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2
[[1,2,3,4,5,6,7,9],[8]] => [8,1,2,3,4,5,6,7,9] => ([(0,8),(1,7),(2,8),(3,4),(4,6),(5,3),(6,2),(7,5)],9) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1
search for individual values
searching the database for the individual values of this statistic
Description
The global dimension of the incidence algebra of the lattice over the rational numbers.
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
Map
antichains of maximal size
Description
The lattice of antichains of maximal size in a poset.
The set of antichains of maximal size can be ordered by setting $A \leq B \leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow} B$, where $\mathop{\downarrow} A$ is the order ideal generated by $A$.
This is a sublattice of the lattice of all antichains with respect to the same order relation. In particular, it is distributive.
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.