Identifier
Values
[[1,2]] => [1,2] => [.,[.,.]] => [2,1] => 1
[[1],[2]] => [2,1] => [[.,.],.] => [1,2] => 0
[[1,2,3]] => [1,2,3] => [.,[.,[.,.]]] => [3,2,1] => 3
[[1,3],[2]] => [2,1,3] => [[.,.],[.,.]] => [1,3,2] => 2
[[1,2],[3]] => [3,1,2] => [[.,[.,.]],.] => [2,1,3] => 1
[[1],[2],[3]] => [3,2,1] => [[[.,.],.],.] => [1,2,3] => 0
[[1,2,3,4]] => [1,2,3,4] => [.,[.,[.,[.,.]]]] => [4,3,2,1] => 6
[[1,3,4],[2]] => [2,1,3,4] => [[.,.],[.,[.,.]]] => [1,4,3,2] => 5
[[1,2,4],[3]] => [3,1,2,4] => [[.,[.,.]],[.,.]] => [2,1,4,3] => 4
[[1,2,3],[4]] => [4,1,2,3] => [[.,[.,[.,.]]],.] => [3,2,1,4] => 3
[[1,3],[2,4]] => [2,4,1,3] => [[.,.],[[.,.],.]] => [1,3,4,2] => 2
[[1,2],[3,4]] => [3,4,1,2] => [[.,[.,.]],[.,.]] => [2,1,4,3] => 4
[[1,4],[2],[3]] => [3,2,1,4] => [[[.,.],.],[.,.]] => [1,2,4,3] => 3
[[1,3],[2],[4]] => [4,2,1,3] => [[[.,.],[.,.]],.] => [1,3,2,4] => 2
[[1,2],[3],[4]] => [4,3,1,2] => [[[.,[.,.]],.],.] => [2,1,3,4] => 1
[[1],[2],[3],[4]] => [4,3,2,1] => [[[[.,.],.],.],.] => [1,2,3,4] => 0
[[1,2,3,4,5]] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => 10
[[1,3,4,5],[2]] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => 9
[[1,2,4,5],[3]] => [3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 8
[[1,2,3,5],[4]] => [4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 7
[[1,2,3,4],[5]] => [5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => 6
[[1,3,5],[2,4]] => [2,4,1,3,5] => [[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => 6
[[1,2,5],[3,4]] => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => 8
[[1,3,4],[2,5]] => [2,5,1,3,4] => [[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => 5
[[1,2,4],[3,5]] => [3,5,1,2,4] => [[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => 4
[[1,2,3],[4,5]] => [4,5,1,2,3] => [[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => 7
[[1,4,5],[2],[3]] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => 7
[[1,3,5],[2],[4]] => [4,2,1,3,5] => [[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => 6
[[1,2,5],[3],[4]] => [4,3,1,2,5] => [[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => 5
[[1,3,4],[2],[5]] => [5,2,1,3,4] => [[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => 5
[[1,2,4],[3],[5]] => [5,3,1,2,4] => [[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => 4
[[1,2,3],[4],[5]] => [5,4,1,2,3] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => 3
[[1,4],[2,5],[3]] => [3,2,5,1,4] => [[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => 3
[[1,3],[2,5],[4]] => [4,2,5,1,3] => [[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => 6
[[1,2],[3,5],[4]] => [4,3,5,1,2] => [[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => 5
[[1,3],[2,4],[5]] => [5,2,4,1,3] => [[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => 2
[[1,2],[3,4],[5]] => [5,3,4,1,2] => [[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => 4
[[1,5],[2],[3],[4]] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => 4
[[1,4],[2],[3],[5]] => [5,3,2,1,4] => [[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => 3
[[1,3],[2],[4],[5]] => [5,4,2,1,3] => [[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => 2
[[1,2],[3],[4],[5]] => [5,4,3,1,2] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => 1
[[1],[2],[3],[4],[5]] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5] => 0
[[1,2,3,4,5,6]] => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => 15
[[1,3,4,5,6],[2]] => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => 14
[[1,2,4,5,6],[3]] => [3,1,2,4,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 13
[[1,2,3,5,6],[4]] => [4,1,2,3,5,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 12
[[1,2,3,4,6],[5]] => [5,1,2,3,4,6] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 11
[[1,2,3,4,5],[6]] => [6,1,2,3,4,5] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => 10
[[1,3,5,6],[2,4]] => [2,4,1,3,5,6] => [[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => 11
[[1,2,5,6],[3,4]] => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => 13
[[1,3,4,6],[2,5]] => [2,5,1,3,4,6] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 10
[[1,2,4,6],[3,5]] => [3,5,1,2,4,6] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 9
[[1,2,3,6],[4,5]] => [4,5,1,2,3,6] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 12
[[1,3,4,5],[2,6]] => [2,6,1,3,4,5] => [[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => 9
[[1,2,4,5],[3,6]] => [3,6,1,2,4,5] => [[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => 8
[[1,2,3,5],[4,6]] => [4,6,1,2,3,5] => [[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => 7
[[1,2,3,4],[5,6]] => [5,6,1,2,3,4] => [[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => 11
[[1,4,5,6],[2],[3]] => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => 12
[[1,3,5,6],[2],[4]] => [4,2,1,3,5,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => 11
[[1,2,5,6],[3],[4]] => [4,3,1,2,5,6] => [[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => 10
[[1,3,4,6],[2],[5]] => [5,2,1,3,4,6] => [[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => 10
[[1,2,4,6],[3],[5]] => [5,3,1,2,4,6] => [[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => 9
[[1,2,3,6],[4],[5]] => [5,4,1,2,3,6] => [[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => 8
[[1,3,4,5],[2],[6]] => [6,2,1,3,4,5] => [[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => 9
[[1,2,4,5],[3],[6]] => [6,3,1,2,4,5] => [[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => 8
[[1,2,3,5],[4],[6]] => [6,4,1,2,3,5] => [[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => 7
[[1,2,3,4],[5],[6]] => [6,5,1,2,3,4] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => 6
[[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => [[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => 6
[[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => [[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => 8
[[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => [[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => 10
[[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => [[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => 9
[[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => [[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => 12
[[1,4,6],[2,5],[3]] => [3,2,5,1,4,6] => [[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => 8
[[1,3,6],[2,5],[4]] => [4,2,5,1,3,6] => [[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => 11
[[1,2,6],[3,5],[4]] => [4,3,5,1,2,6] => [[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => 10
[[1,3,6],[2,4],[5]] => [5,2,4,1,3,6] => [[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => 7
[[1,2,6],[3,4],[5]] => [5,3,4,1,2,6] => [[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => 9
[[1,4,5],[2,6],[3]] => [3,2,6,1,4,5] => [[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => 7
[[1,3,5],[2,6],[4]] => [4,2,6,1,3,5] => [[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => 6
[[1,2,5],[3,6],[4]] => [4,3,6,1,2,5] => [[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => 5
[[1,3,4],[2,6],[5]] => [5,2,6,1,3,4] => [[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => 10
[[1,2,4],[3,6],[5]] => [5,3,6,1,2,4] => [[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => 9
[[1,2,3],[4,6],[5]] => [5,4,6,1,2,3] => [[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => 8
[[1,3,5],[2,4],[6]] => [6,2,4,1,3,5] => [[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => 6
[[1,2,5],[3,4],[6]] => [6,3,4,1,2,5] => [[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => 8
[[1,3,4],[2,5],[6]] => [6,2,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => 5
[[1,2,4],[3,5],[6]] => [6,3,5,1,2,4] => [[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => 4
[[1,2,3],[4,5],[6]] => [6,4,5,1,2,3] => [[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => 7
[[1,5,6],[2],[3],[4]] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => 9
[[1,4,6],[2],[3],[5]] => [5,3,2,1,4,6] => [[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => 8
[[1,3,6],[2],[4],[5]] => [5,4,2,1,3,6] => [[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => 7
[[1,2,6],[3],[4],[5]] => [5,4,3,1,2,6] => [[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => 6
[[1,4,5],[2],[3],[6]] => [6,3,2,1,4,5] => [[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => 7
[[1,3,5],[2],[4],[6]] => [6,4,2,1,3,5] => [[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => 6
[[1,2,5],[3],[4],[6]] => [6,4,3,1,2,5] => [[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => 5
[[1,3,4],[2],[5],[6]] => [6,5,2,1,3,4] => [[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => 5
[[1,2,4],[3],[5],[6]] => [6,5,3,1,2,4] => [[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => 4
[[1,2,3],[4],[5],[6]] => [6,5,4,1,2,3] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => 3
[[1,4],[2,5],[3,6]] => [3,6,2,5,1,4] => [[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => 3
[[1,3],[2,5],[4,6]] => [4,6,2,5,1,3] => [[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => 6
[[1,2],[3,5],[4,6]] => [4,6,3,5,1,2] => [[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => 5
>>> Load all 225 entries. <<<
[[1,3],[2,4],[5,6]] => [5,6,2,4,1,3] => [[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => 7
[[1,2],[3,4],[5,6]] => [5,6,3,4,1,2] => [[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => 9
[[1,5],[2,6],[3],[4]] => [4,3,2,6,1,5] => [[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => 4
[[1,4],[2,6],[3],[5]] => [5,3,2,6,1,4] => [[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => 8
[[1,3],[2,6],[4],[5]] => [5,4,2,6,1,3] => [[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => 7
[[1,2],[3,6],[4],[5]] => [5,4,3,6,1,2] => [[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => 6
[[1,4],[2,5],[3],[6]] => [6,3,2,5,1,4] => [[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => 3
[[1,3],[2,5],[4],[6]] => [6,4,2,5,1,3] => [[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => 6
[[1,2],[3,5],[4],[6]] => [6,4,3,5,1,2] => [[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => 5
[[1,3],[2,4],[5],[6]] => [6,5,2,4,1,3] => [[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => 2
[[1,2],[3,4],[5],[6]] => [6,5,3,4,1,2] => [[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => 4
[[1,6],[2],[3],[4],[5]] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => 5
[[1,5],[2],[3],[4],[6]] => [6,4,3,2,1,5] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => 4
[[1,4],[2],[3],[5],[6]] => [6,5,3,2,1,4] => [[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => 3
[[1,3],[2],[4],[5],[6]] => [6,5,4,2,1,3] => [[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => 2
[[1,2],[3],[4],[5],[6]] => [6,5,4,3,1,2] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => 1
[[1],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => 0
[[1,3,5,6,7],[2,4]] => [2,4,1,3,5,6,7] => [[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => 17
[[1,3,4,6,7],[2,5]] => [2,5,1,3,4,6,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 16
[[1,4,5,6,7],[2],[3]] => [3,2,1,4,5,6,7] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => 18
[[1,3,5,6,7],[2],[4]] => [4,2,1,3,5,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => 17
[[1,3,4,6,7],[2],[5]] => [5,2,1,3,4,6,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => 16
[[1,3,5,7],[2,4,6]] => [2,4,6,1,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => 12
[[1,3,4,7],[2,5,6]] => [2,5,6,1,3,4,7] => [[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => 16
[[1,3,5,6],[2,4,7]] => [2,4,7,1,3,5,6] => [[.,.],[[.,.],[[.,[.,.]],.]]] => [1,3,6,5,7,4,2] => 11
[[1,3,4,6],[2,5,7]] => [2,5,7,1,3,4,6] => [[.,.],[[.,[.,.]],[[.,.],.]]] => [1,4,3,6,7,5,2] => 10
[[1,4,6,7],[2,5],[3]] => [3,2,5,1,4,6,7] => [[[.,.],.],[[.,.],[.,[.,.]]]] => [1,2,4,7,6,5,3] => 14
[[1,3,6,7],[2,5],[4]] => [4,2,5,1,3,6,7] => [[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => 17
[[1,3,6,7],[2,4],[5]] => [5,2,4,1,3,6,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => 13
[[1,4,5,7],[2,6],[3]] => [3,2,6,1,4,5,7] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => 13
[[1,3,5,7],[2,6],[4]] => [4,2,6,1,3,5,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => 12
[[1,3,4,7],[2,6],[5]] => [5,2,6,1,3,4,7] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => 16
[[1,3,5,7],[2,4],[6]] => [6,2,4,1,3,5,7] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => 12
[[1,3,4,7],[2,5],[6]] => [6,2,5,1,3,4,7] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => 11
[[1,4,5,6],[2,7],[3]] => [3,2,7,1,4,5,6] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [1,2,6,5,4,7,3] => 12
[[1,3,5,6],[2,7],[4]] => [4,2,7,1,3,5,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => 11
[[1,3,4,6],[2,7],[5]] => [5,2,7,1,3,4,6] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => 10
[[1,3,5,6],[2,4],[7]] => [7,2,4,1,3,5,6] => [[[.,.],[[.,.],[.,[.,.]]]],.] => [1,3,6,5,4,2,7] => 11
[[1,3,4,6],[2,5],[7]] => [7,2,5,1,3,4,6] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => 10
[[1,5,6,7],[2],[3],[4]] => [4,3,2,1,5,6,7] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => 15
[[1,4,6,7],[2],[3],[5]] => [5,3,2,1,4,6,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => 14
[[1,3,6,7],[2],[4],[5]] => [5,4,2,1,3,6,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => 13
[[1,4,5,7],[2],[3],[6]] => [6,3,2,1,4,5,7] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => 13
[[1,3,5,7],[2],[4],[6]] => [6,4,2,1,3,5,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => 12
[[1,3,4,7],[2],[5],[6]] => [6,5,2,1,3,4,7] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => 11
[[1,4,5,6],[2],[3],[7]] => [7,3,2,1,4,5,6] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7] => 12
[[1,3,5,6],[2],[4],[7]] => [7,4,2,1,3,5,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => 11
[[1,3,4,6],[2],[5],[7]] => [7,5,2,1,3,4,6] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => 10
[[1,4,6],[2,5,7],[3]] => [3,2,5,7,1,4,6] => [[[.,.],.],[[.,.],[[.,.],.]]] => [1,2,4,6,7,5,3] => 8
[[1,3,6],[2,5,7],[4]] => [4,2,5,7,1,3,6] => [[[.,.],[.,.]],[.,[[.,.],.]]] => [1,3,2,6,7,5,4] => 11
[[1,3,6],[2,4,7],[5]] => [5,2,4,7,1,3,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => 7
[[1,4,5],[2,6,7],[3]] => [3,2,6,7,1,4,5] => [[[.,.],.],[[.,[.,.]],[.,.]]] => [1,2,5,4,7,6,3] => 13
[[1,3,5],[2,6,7],[4]] => [4,2,6,7,1,3,5] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => 12
[[1,3,4],[2,6,7],[5]] => [5,2,6,7,1,3,4] => [[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => 16
[[1,3,5],[2,4,7],[6]] => [6,2,4,7,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => 12
[[1,3,4],[2,5,7],[6]] => [6,2,5,7,1,3,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => 11
[[1,3,5],[2,4,6],[7]] => [7,2,4,6,1,3,5] => [[[.,.],[[.,.],[[.,.],.]]],.] => [1,3,5,6,4,2,7] => 6
[[1,3,4],[2,5,6],[7]] => [7,2,5,6,1,3,4] => [[[.,.],[[.,[.,.]],[.,.]]],.] => [1,4,3,6,5,2,7] => 10
[[1,4,7],[2,5],[3,6]] => [3,6,2,5,1,4,7] => [[[.,.],.],[[[.,.],.],[.,.]]] => [1,2,4,5,7,6,3] => 9
[[1,3,7],[2,5],[4,6]] => [4,6,2,5,1,3,7] => [[[.,.],[.,.]],[[.,.],[.,.]]] => [1,3,2,5,7,6,4] => 12
[[1,3,7],[2,4],[5,6]] => [5,6,2,4,1,3,7] => [[[.,.],[[.,.],.]],[.,[.,.]]] => [1,3,4,2,7,6,5] => 13
[[1,4,6],[2,5],[3,7]] => [3,7,2,5,1,4,6] => [[[.,.],.],[[[.,.],[.,.]],.]] => [1,2,4,6,5,7,3] => 8
[[1,3,6],[2,5],[4,7]] => [4,7,2,5,1,3,6] => [[[.,.],[.,.]],[[.,[.,.]],.]] => [1,3,2,6,5,7,4] => 11
[[1,3,6],[2,4],[5,7]] => [5,7,2,4,1,3,6] => [[[.,.],[[.,.],.]],[[.,.],.]] => [1,3,4,2,6,7,5] => 7
[[1,4,5],[2,6],[3,7]] => [3,7,2,6,1,4,5] => [[[.,.],.],[[[.,[.,.]],.],.]] => [1,2,5,4,6,7,3] => 7
[[1,3,5],[2,6],[4,7]] => [4,7,2,6,1,3,5] => [[[.,.],[.,.]],[[[.,.],.],.]] => [1,3,2,5,6,7,4] => 6
[[1,3,4],[2,6],[5,7]] => [5,7,2,6,1,3,4] => [[[.,.],[.,[.,.]]],[[.,.],.]] => [1,4,3,2,6,7,5] => 10
[[1,3,5],[2,4],[6,7]] => [6,7,2,4,1,3,5] => [[[.,.],[[.,.],[.,.]]],[.,.]] => [1,3,5,4,2,7,6] => 12
[[1,3,4],[2,5],[6,7]] => [6,7,2,5,1,3,4] => [[[.,.],[[.,[.,.]],.]],[.,.]] => [1,4,3,5,2,7,6] => 11
[[1,5,7],[2,6],[3],[4]] => [4,3,2,6,1,5,7] => [[[[.,.],.],.],[[.,.],[.,.]]] => [1,2,3,5,7,6,4] => 10
[[1,4,7],[2,6],[3],[5]] => [5,3,2,6,1,4,7] => [[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => 14
[[1,3,7],[2,6],[4],[5]] => [5,4,2,6,1,3,7] => [[[[.,.],[.,.]],.],[.,[.,.]]] => [1,3,2,4,7,6,5] => 13
[[1,4,7],[2,5],[3],[6]] => [6,3,2,5,1,4,7] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => 9
[[1,3,7],[2,5],[4],[6]] => [6,4,2,5,1,3,7] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => 12
[[1,3,7],[2,4],[5],[6]] => [6,5,2,4,1,3,7] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => 8
[[1,5,6],[2,7],[3],[4]] => [4,3,2,7,1,5,6] => [[[[.,.],.],.],[[.,[.,.]],.]] => [1,2,3,6,5,7,4] => 9
[[1,4,6],[2,7],[3],[5]] => [5,3,2,7,1,4,6] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => 8
[[1,3,6],[2,7],[4],[5]] => [5,4,2,7,1,3,6] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => 7
[[1,4,5],[2,7],[3],[6]] => [6,3,2,7,1,4,5] => [[[[.,.],.],[.,[.,.]]],[.,.]] => [1,2,5,4,3,7,6] => 13
[[1,3,5],[2,7],[4],[6]] => [6,4,2,7,1,3,5] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => 12
[[1,3,4],[2,7],[5],[6]] => [6,5,2,7,1,3,4] => [[[[.,.],[.,[.,.]]],.],[.,.]] => [1,4,3,2,5,7,6] => 11
[[1,4,6],[2,5],[3],[7]] => [7,3,2,5,1,4,6] => [[[[.,.],.],[[.,.],[.,.]]],.] => [1,2,4,6,5,3,7] => 8
[[1,3,6],[2,5],[4],[7]] => [7,4,2,5,1,3,6] => [[[[.,.],[.,.]],[.,[.,.]]],.] => [1,3,2,6,5,4,7] => 11
[[1,3,6],[2,4],[5],[7]] => [7,5,2,4,1,3,6] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => 7
[[1,4,5],[2,6],[3],[7]] => [7,3,2,6,1,4,5] => [[[[.,.],.],[[.,[.,.]],.]],.] => [1,2,5,4,6,3,7] => 7
[[1,3,5],[2,6],[4],[7]] => [7,4,2,6,1,3,5] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => 6
[[1,3,4],[2,6],[5],[7]] => [7,5,2,6,1,3,4] => [[[[.,.],[.,[.,.]]],[.,.]],.] => [1,4,3,2,6,5,7] => 10
[[1,3,5],[2,4],[6],[7]] => [7,6,2,4,1,3,5] => [[[[.,.],[[.,.],[.,.]]],.],.] => [1,3,5,4,2,6,7] => 6
[[1,3,4],[2,5],[6],[7]] => [7,6,2,5,1,3,4] => [[[[.,.],[[.,[.,.]],.]],.],.] => [1,4,3,5,2,6,7] => 5
[[1,6,7],[2],[3],[4],[5]] => [5,4,3,2,1,6,7] => [[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => 11
[[1,5,7],[2],[3],[4],[6]] => [6,4,3,2,1,5,7] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => 10
[[1,4,7],[2],[3],[5],[6]] => [6,5,3,2,1,4,7] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => 9
[[1,3,7],[2],[4],[5],[6]] => [6,5,4,2,1,3,7] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => 8
[[1,5,6],[2],[3],[4],[7]] => [7,4,3,2,1,5,6] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7] => 9
[[1,4,6],[2],[3],[5],[7]] => [7,5,3,2,1,4,6] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => 8
[[1,3,6],[2],[4],[5],[7]] => [7,5,4,2,1,3,6] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => 7
[[1,4,5],[2],[3],[6],[7]] => [7,6,3,2,1,4,5] => [[[[[.,.],.],[.,[.,.]]],.],.] => [1,2,5,4,3,6,7] => 7
[[1,3,5],[2],[4],[6],[7]] => [7,6,4,2,1,3,5] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => 6
[[1,3,4],[2],[5],[6],[7]] => [7,6,5,2,1,3,4] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7] => 5
[[1,5],[2,6],[3,7],[4]] => [4,3,7,2,6,1,5] => [[[[.,.],.],.],[[[.,.],.],.]] => [1,2,3,5,6,7,4] => 4
[[1,4],[2,6],[3,7],[5]] => [5,3,7,2,6,1,4] => [[[[.,.],.],[.,.]],[[.,.],.]] => [1,2,4,3,6,7,5] => 8
[[1,3],[2,6],[4,7],[5]] => [5,4,7,2,6,1,3] => [[[[.,.],[.,.]],.],[[.,.],.]] => [1,3,2,4,6,7,5] => 7
[[1,4],[2,5],[3,7],[6]] => [6,3,7,2,5,1,4] => [[[[.,.],.],[[.,.],.]],[.,.]] => [1,2,4,5,3,7,6] => 9
[[1,3],[2,5],[4,7],[6]] => [6,4,7,2,5,1,3] => [[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => 12
[[1,3],[2,4],[5,7],[6]] => [6,5,7,2,4,1,3] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,3,4,2,5,7,6] => 8
[[1,4],[2,5],[3,6],[7]] => [7,3,6,2,5,1,4] => [[[[.,.],.],[[[.,.],.],.]],.] => [1,2,4,5,6,3,7] => 3
[[1,3],[2,5],[4,6],[7]] => [7,4,6,2,5,1,3] => [[[[.,.],[.,.]],[[.,.],.]],.] => [1,3,2,5,6,4,7] => 6
[[1,3],[2,4],[5,6],[7]] => [7,5,6,2,4,1,3] => [[[[.,.],[[.,.],.]],[.,.]],.] => [1,3,4,2,6,5,7] => 7
[[1,6],[2,7],[3],[4],[5]] => [5,4,3,2,7,1,6] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,2,3,4,6,7,5] => 5
[[1,5],[2,7],[3],[4],[6]] => [6,4,3,2,7,1,5] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => 10
[[1,4],[2,7],[3],[5],[6]] => [6,5,3,2,7,1,4] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,2,4,3,5,7,6] => 9
[[1,3],[2,7],[4],[5],[6]] => [6,5,4,2,7,1,3] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,3,2,4,5,7,6] => 8
[[1,5],[2,6],[3],[4],[7]] => [7,4,3,2,6,1,5] => [[[[[.,.],.],.],[[.,.],.]],.] => [1,2,3,5,6,4,7] => 4
[[1,4],[2,6],[3],[5],[7]] => [7,5,3,2,6,1,4] => [[[[[.,.],.],[.,.]],[.,.]],.] => [1,2,4,3,6,5,7] => 8
[[1,3],[2,6],[4],[5],[7]] => [7,5,4,2,6,1,3] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7] => 7
[[1,4],[2,5],[3],[6],[7]] => [7,6,3,2,5,1,4] => [[[[[.,.],.],[[.,.],.]],.],.] => [1,2,4,5,3,6,7] => 3
[[1,3],[2,5],[4],[6],[7]] => [7,6,4,2,5,1,3] => [[[[[.,.],[.,.]],[.,.]],.],.] => [1,3,2,5,4,6,7] => 6
[[1,3],[2,4],[5],[6],[7]] => [7,6,5,2,4,1,3] => [[[[[.,.],[[.,.],.]],.],.],.] => [1,3,4,2,5,6,7] => 2
[[1,7],[2],[3],[4],[5],[6]] => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => 6
[[1,6],[2],[3],[4],[5],[7]] => [7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7] => 5
[[1,5],[2],[3],[4],[6],[7]] => [7,6,4,3,2,1,5] => [[[[[[.,.],.],.],[.,.]],.],.] => [1,2,3,5,4,6,7] => 4
[[1,4],[2],[3],[5],[6],[7]] => [7,6,5,3,2,1,4] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7] => 3
[[1,3],[2],[4],[5],[6],[7]] => [7,6,5,4,2,1,3] => [[[[[[.,.],[.,.]],.],.],.],.] => [1,3,2,4,5,6,7] => 2
[[1],[2],[3],[4],[5],[6],[7]] => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => 0
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Description
The makl of a permutation.
According to [1], this is the sum of the number of occurrences of the vincular patterns $(1\underline{32})$, $(\underline{31}2)$, $(\underline{32}1)$ and $(\underline{21})$, where matches of the underlined letters must be adjacent.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
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.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.