Identifier
Values
[[1]] => [1] => [1] => ([],1) => 0
[[1],[2]] => [2,1] => [2,1] => ([(0,1)],2) => 1
[[1],[2],[3]] => [3,2,1] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => 1
[[1,3],[2,4]] => [2,4,1,3] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4) => 2
[[1,2],[3,4]] => [3,4,1,2] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4) => 3
[[1],[2],[3],[4]] => [4,3,2,1] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[[1,4],[2,5],[3]] => [3,2,5,1,4] => [3,5,2,1,4] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 3
[[1,3],[2,5],[4]] => [4,2,5,1,3] => [2,4,1,5,3] => ([(0,4),(1,3),(2,3),(2,4)],5) => 4
[[1,2],[3,5],[4]] => [4,3,5,1,2] => [4,3,1,5,2] => ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) => 3
[[1,3],[2,4],[5]] => [5,2,4,1,3] => [5,2,1,4,3] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) => 2
[[1,2],[3,4],[5]] => [5,3,4,1,2] => [3,1,5,4,2] => ([(0,3),(1,2),(1,4),(2,4),(3,4)],5) => 3
[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [6,4,2,1,3,5] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [6,3,1,4,2,5] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [5,2,1,6,3,4] => ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) => 3
[[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [5,1,6,3,2,4] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 3
[[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 3
[[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [6,3,2,1,4,5] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => [4,2,1,6,3,5] => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 4
[[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [4,1,6,3,2,5] => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => [5,2,1,3,6,4] => ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) => 3
[[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => [3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6) => 5
[[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [3,6,5,2,1,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [4,6,2,1,5,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) => 2
[[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => [6,4,3,1,5,2] => ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => [2,5,1,6,4,3] => ([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) => 4
[[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [5,3,1,6,4,2] => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [4,3,6,2,1,5] => ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [3,2,5,1,6,4] => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 4
[[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [2,5,4,1,6,3] => ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) => 4
[[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => [5,4,3,1,6,2] => ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [3,6,2,1,5,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 3
[[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => [2,4,1,6,5,3] => ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) => 4
[[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => [4,3,1,6,5,2] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) => 3
[[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => [6,2,1,5,4,3] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => [3,1,6,5,4,2] => ([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => ([(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) => 1
[[1,3,5,6],[2,4,7]] => [2,4,7,1,3,5,6] => [7,2,1,4,3,5,6] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 2
[[1,2,5,6],[3,4,7]] => [3,4,7,1,2,5,6] => [3,1,7,4,2,5,6] => ([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6),(5,6)],7) => 4
[[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [7,3,5,2,1,4,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,6],[2,5,7],[4]] => [4,2,5,7,1,3,6] => [7,2,4,1,5,3,6] => ([(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 2
[[1,2,6],[3,5,7],[4]] => [4,3,5,7,1,2,6] => [4,7,3,1,5,2,6] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,3,6],[2,4,7],[5]] => [5,2,4,7,1,3,6] => [5,7,2,1,4,3,6] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3
[[1,2,6],[3,4,7],[5]] => [5,3,4,7,1,2,6] => [3,5,1,7,4,2,6] => ([(0,5),(1,2),(1,4),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 4
[[1,4,5],[2,6,7],[3]] => [3,2,6,7,1,4,5] => [6,7,3,2,1,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 2
[[1,3,5],[2,6,7],[4]] => [4,2,6,7,1,3,5] => [4,6,2,1,7,3,5] => ([(0,1),(0,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 3
[[1,2,5],[3,6,7],[4]] => [4,3,6,7,1,2,5] => [4,6,1,7,3,2,5] => ([(0,3),(0,6),(1,2),(1,6),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 3
[[1,3,4],[2,6,7],[5]] => [5,2,6,7,1,3,4] => [5,6,2,1,3,7,4] => ([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3
[[1,2,4],[3,6,7],[5]] => [5,3,6,7,1,2,4] => [3,5,1,6,2,7,4] => ([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) => 4
[[1,2,3],[4,6,7],[5]] => [5,4,6,7,1,2,3] => [5,4,1,6,2,7,3] => ([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 3
[[1,3,5],[2,4,7],[6]] => [6,2,4,7,1,3,5] => [4,6,2,1,3,7,5] => ([(0,2),(1,5),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
[[1,2,5],[3,4,7],[6]] => [6,3,4,7,1,2,5] => [3,4,1,6,2,7,5] => ([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) => 5
[[1,3,4],[2,5,7],[6]] => [6,2,5,7,1,3,4] => [6,5,2,1,3,7,4] => ([(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,2,4],[3,5,7],[6]] => [6,3,5,7,1,2,4] => [6,3,1,5,2,7,4] => ([(0,5),(1,4),(1,6),(2,3),(2,4),(2,6),(3,5),(3,6),(4,6),(5,6)],7) => 3
[[1,2,3],[4,5,7],[6]] => [6,4,5,7,1,2,3] => [4,1,6,5,2,7,3] => ([(0,5),(1,6),(2,3),(2,4),(2,5),(3,4),(3,6),(4,6),(5,6)],7) => 3
[[1,3,5],[2,4,6],[7]] => [7,2,4,6,1,3,5] => [7,4,2,1,3,6,5] => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,2,5],[3,4,6],[7]] => [7,3,4,6,1,2,5] => [7,3,1,4,2,6,5] => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,4],[2,5,6],[7]] => [7,2,5,6,1,3,4] => [7,2,1,5,3,6,4] => ([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,2,4],[3,5,6],[7]] => [7,3,5,6,1,2,4] => [3,1,7,5,2,6,4] => ([(0,2),(1,5),(1,6),(2,4),(3,4),(3,5),(3,6),(4,6),(5,6)],7) => 4
[[1,2,3],[4,5,6],[7]] => [7,4,5,6,1,2,3] => [4,1,5,2,7,6,3] => ([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(5,6)],7) => 3
[[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [3,7,2,1,5,4,6] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 3
[[1,3,6],[2,5],[4,7]] => [4,7,2,5,1,3,6] => [2,4,1,7,5,3,6] => ([(0,6),(1,4),(2,5),(2,6),(3,4),(3,5),(5,6)],7) => 5
[[1,2,6],[3,5],[4,7]] => [4,7,3,5,1,2,6] => [4,3,1,7,5,2,6] => ([(0,5),(1,3),(1,4),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 4
[[1,3,6],[2,4],[5,7]] => [5,7,2,4,1,3,6] => [7,2,1,5,4,3,6] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,2,6],[3,4],[5,7]] => [5,7,3,4,1,2,6] => [3,1,7,5,4,2,6] => ([(0,5),(1,2),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[[1,4,5],[2,6],[3,7]] => [3,7,2,6,1,4,5] => [7,3,2,1,6,4,5] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) => 2
[[1,3,5],[2,6],[4,7]] => [4,7,2,6,1,3,5] => [4,2,1,7,6,3,5] => ([(0,4),(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5)],7) => 4
[[1,2,5],[3,6],[4,7]] => [4,7,3,6,1,2,5] => [4,1,7,6,3,2,5] => ([(0,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[[1,3,4],[2,6],[5,7]] => [5,7,2,6,1,3,4] => [5,2,1,7,3,6,4] => ([(0,1),(0,6),(1,6),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => 3
[[1,2,4],[3,6],[5,7]] => [5,7,3,6,1,2,4] => [5,1,7,3,2,6,4] => ([(0,6),(1,4),(1,5),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) => 3
[[1,3,5],[2,4],[6,7]] => [6,7,2,4,1,3,5] => [6,2,1,4,3,7,5] => ([(0,5),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) => 3
[[1,2,5],[3,4],[6,7]] => [6,7,3,4,1,2,5] => [3,1,6,4,2,7,5] => ([(0,4),(1,3),(2,5),(2,6),(3,5),(4,6),(5,6)],7) => 5
[[1,3,4],[2,5],[6,7]] => [6,7,2,5,1,3,4] => [6,2,1,3,7,5,4] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 3
[[1,2,4],[3,5],[6,7]] => [6,7,3,5,1,2,4] => [3,1,6,2,7,5,4] => ([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7) => 5
[[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [4,7,3,2,1,5,6] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,4,6],[2,7],[3],[5]] => [5,3,2,7,1,4,6] => [3,5,2,1,7,4,6] => ([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7) => 5
[[1,3,6],[2,7],[4],[5]] => [5,4,2,7,1,3,6] => [5,4,2,1,7,3,6] => ([(0,1),(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[[1,2,6],[3,7],[4],[5]] => [5,4,3,7,1,2,6] => [5,4,1,7,3,2,6] => ([(0,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[[1,4,5],[2,7],[3],[6]] => [6,3,2,7,1,4,5] => [3,6,2,1,4,7,5] => ([(0,6),(1,2),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 4
[[1,3,5],[2,7],[4],[6]] => [6,4,2,7,1,3,5] => [2,4,1,6,3,7,5] => ([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) => 6
[[1,2,5],[3,7],[4],[6]] => [6,4,3,7,1,2,5] => [4,3,1,6,2,7,5] => ([(0,3),(1,3),(1,4),(2,5),(2,6),(4,5),(4,6),(5,6)],7) => 5
[[1,3,4],[2,7],[5],[6]] => [6,5,2,7,1,3,4] => [6,2,1,5,3,7,4] => ([(0,5),(1,2),(1,6),(2,6),(3,4),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,2,4],[3,7],[5],[6]] => [6,5,3,7,1,2,4] => [3,1,6,5,2,7,4] => ([(0,6),(1,2),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 5
[[1,4,5],[2,6],[3],[7]] => [7,3,2,6,1,4,5] => [7,3,2,1,4,6,5] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3,5],[2,6],[4],[7]] => [7,4,2,6,1,3,5] => [4,2,1,7,3,6,5] => ([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) => 4
[[1,2,5],[3,6],[4],[7]] => [7,4,3,6,1,2,5] => [4,1,7,3,2,6,5] => ([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
[[1,3,4],[2,6],[5],[7]] => [7,5,2,6,1,3,4] => [5,2,1,3,7,6,4] => ([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => 3
[[1,2,4],[3,6],[5],[7]] => [7,5,3,6,1,2,4] => [3,1,5,2,7,6,4] => ([(0,5),(1,4),(1,5),(2,3),(2,6),(3,6),(4,6)],7) => 5
[[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [7,4,3,6,2,1,5] => ([(0,3),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [3,5,7,2,1,6,4] => ([(0,5),(0,6),(1,3),(1,4),(2,3),(2,5),(2,6),(3,4),(4,5),(4,6),(5,6)],7) => 3
[[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [5,4,7,2,1,6,3] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(4,5),(5,6)],7) => 2
[[1,2],[3,6],[4,7],[5]] => [5,4,7,3,6,1,2] => [5,7,4,3,1,6,2] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [6,3,7,2,1,5,4] => ([(0,1),(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 2
[[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => [4,2,6,1,7,5,3] => ([(0,3),(0,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(4,6),(5,6)],7) => 3
[[1,2],[3,5],[4,7],[6]] => [6,4,7,3,5,1,2] => [4,6,3,1,7,5,2] => ([(0,3),(0,6),(1,2),(1,4),(1,6),(2,4),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,3],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3] => [2,6,5,1,7,4,3] => ([(0,2),(1,5),(1,6),(2,3),(2,4),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[[1,2],[3,4],[5,7],[6]] => [6,5,7,3,4,1,2] => [6,5,3,1,7,4,2] => ([(0,3),(0,6),(1,2),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,4],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4] => [3,7,6,2,1,5,4] => ([(0,3),(0,4),(1,2),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,3],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3] => [4,7,2,1,6,5,3] => ([(0,1),(0,2),(0,6),(1,2),(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,2],[3,5],[4,6],[7]] => [7,4,6,3,5,1,2] => [7,4,3,1,6,5,2] => ([(0,1),(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,3],[2,4],[5,6],[7]] => [7,5,6,2,4,1,3] => [2,5,1,7,6,4,3] => ([(0,1),(1,4),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
>>> Load all 117 entries. <<<
[[1,2],[3,4],[5,6],[7]] => [7,5,6,3,4,1,2] => [5,3,1,7,6,4,2] => ([(0,3),(0,5),(1,2),(1,4),(1,6),(2,4),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [5,4,3,7,2,1,6] => ([(0,1),(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) => 3
[[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [4,3,2,6,1,7,5] => ([(0,2),(1,2),(1,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [3,2,6,5,1,7,4] => ([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
[[1,3],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3] => [2,6,5,4,1,7,3] => ([(0,6),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
[[1,2],[3,7],[4],[5],[6]] => [6,5,4,3,7,1,2] => [6,5,4,3,1,7,2] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [4,3,7,2,1,6,5] => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5),(4,6),(5,6)],7) => 3
[[1,4],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4] => [3,2,5,1,7,6,4] => ([(0,1),(0,6),(1,6),(2,3),(2,5),(3,5),(4,5),(4,6)],7) => 4
[[1,3],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3] => [2,5,4,1,7,6,3] => ([(0,5),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6)],7) => 4
[[1,2],[3,6],[4],[5],[7]] => [7,5,4,3,6,1,2] => [5,4,3,1,7,6,2] => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,4],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4] => [3,7,2,1,6,5,4] => ([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,3],[2,5],[4],[6],[7]] => [7,6,4,2,5,1,3] => [2,4,1,7,6,5,3] => ([(0,2),(1,2),(1,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[[1,2],[3,5],[4],[6],[7]] => [7,6,4,3,5,1,2] => [4,3,1,7,6,5,2] => ([(0,4),(0,5),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1,3],[2,4],[5],[6],[7]] => [7,6,5,2,4,1,3] => [7,2,1,6,5,4,3] => ([(0,1),(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[[1,2],[3,4],[5],[6],[7]] => [7,6,5,3,4,1,2] => [3,1,7,6,5,4,2] => ([(0,1),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => ([(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) => 1
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
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.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
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.