Identifier
Values
[.,.] => [1] => [1] => [1] => 0
[.,[.,.]] => [2,1] => [1,2] => [1,2] => 1
[[.,.],.] => [1,2] => [2,1] => [2,1] => 0
[.,[.,[.,.]]] => [3,2,1] => [1,2,3] => [1,2,3] => 1
[.,[[.,.],.]] => [2,3,1] => [2,1,3] => [2,1,3] => 1
[[.,.],[.,.]] => [1,3,2] => [2,3,1] => [3,1,2] => 1
[[.,[.,.]],.] => [2,1,3] => [3,1,2] => [2,3,1] => 1
[[[.,.],.],.] => [1,2,3] => [3,2,1] => [3,2,1] => 0
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 1
[.,[.,[[.,.],.]]] => [3,4,2,1] => [3,1,2,4] => [2,3,1,4] => 2
[.,[[.,.],[.,.]]] => [2,4,3,1] => [2,1,3,4] => [2,1,3,4] => 1
[.,[[.,[.,.]],.]] => [3,2,4,1] => [2,3,1,4] => [3,1,2,4] => 1
[.,[[[.,.],.],.]] => [2,3,4,1] => [3,2,1,4] => [3,2,1,4] => 1
[[.,.],[.,[.,.]]] => [1,4,3,2] => [2,3,4,1] => [4,1,2,3] => 1
[[.,.],[[.,.],.]] => [1,3,4,2] => [3,2,4,1] => [4,2,1,3] => 1
[[.,[.,.]],[.,.]] => [2,1,4,3] => [3,4,1,2] => [3,4,1,2] => 2
[[[.,.],.],[.,.]] => [1,2,4,3] => [3,4,2,1] => [4,3,1,2] => 1
[[.,[.,[.,.]]],.] => [3,2,1,4] => [4,1,2,3] => [2,3,4,1] => 1
[[.,[[.,.],.]],.] => [2,3,1,4] => [4,2,1,3] => [3,2,4,1] => 1
[[[.,.],[.,.]],.] => [1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 1
[[[.,[.,.]],.],.] => [2,1,3,4] => [4,3,1,2] => [3,4,2,1] => 1
[[[[.,.],.],.],.] => [1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [1,2,3,4,5] => [1,2,3,4,5] => 1
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [4,1,2,3,5] => [2,3,4,1,5] => 2
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [3,1,2,4,5] => [2,3,1,4,5] => 2
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [3,4,1,2,5] => [3,4,1,2,5] => 2
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [4,3,1,2,5] => [3,4,2,1,5] => 2
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [2,1,3,4,5] => [2,1,3,4,5] => 1
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [4,2,1,3,5] => [3,2,4,1,5] => 2
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [2,3,1,4,5] => [3,1,2,4,5] => 1
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [3,2,1,4,5] => [3,2,1,4,5] => 1
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [2,3,4,1,5] => [4,1,2,3,5] => 1
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [3,2,4,1,5] => [4,2,1,3,5] => 1
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [3,4,2,1,5] => [4,3,1,2,5] => 1
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [4,2,3,1,5] => [4,2,3,1,5] => 2
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [4,3,2,1,5] => [4,3,2,1,5] => 1
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [2,3,4,5,1] => [5,1,2,3,4] => 1
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [4,2,3,5,1] => [5,2,3,1,4] => 2
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [3,2,4,5,1] => [5,2,1,3,4] => 1
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [3,4,2,5,1] => [5,3,1,2,4] => 1
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [4,3,2,5,1] => [5,3,2,1,4] => 1
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [3,4,5,1,2] => [4,5,1,2,3] => 2
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [4,3,5,1,2] => [4,5,2,1,3] => 2
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [3,4,5,2,1] => [5,4,1,2,3] => 1
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [4,3,5,2,1] => [5,4,2,1,3] => 1
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [4,5,1,2,3] => [3,4,5,1,2] => 2
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [4,5,2,1,3] => [4,3,5,1,2] => 2
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [4,5,2,3,1] => [5,3,4,1,2] => 2
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [4,5,3,1,2] => [4,5,3,1,2] => 2
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [4,5,3,2,1] => [5,4,3,1,2] => 1
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [5,1,2,3,4] => [2,3,4,5,1] => 1
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [5,3,1,2,4] => [3,4,2,5,1] => 2
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [5,2,1,3,4] => [3,2,4,5,1] => 1
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [5,2,3,1,4] => [4,2,3,5,1] => 1
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [5,3,2,1,4] => [4,3,2,5,1] => 1
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [5,2,3,4,1] => [5,2,3,4,1] => 1
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [5,3,2,4,1] => [5,3,2,4,1] => 1
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [5,3,4,1,2] => [4,5,2,3,1] => 2
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [5,3,4,2,1] => [5,4,2,3,1] => 1
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [5,4,1,2,3] => [3,4,5,2,1] => 1
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [5,4,2,1,3] => [4,3,5,2,1] => 1
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [5,4,2,3,1] => [5,3,4,2,1] => 1
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [5,4,3,1,2] => [4,5,3,2,1] => 1
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [5,4,3,2,1] => [5,4,3,2,1] => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 1
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [5,1,2,3,4,6] => [2,3,4,5,1,6] => 2
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [4,1,2,3,5,6] => [2,3,4,1,5,6] => 2
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [4,5,1,2,3,6] => [3,4,5,1,2,6] => 2
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [5,4,1,2,3,6] => [3,4,5,2,1,6] => 2
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [3,1,2,4,5,6] => [2,3,1,4,5,6] => 2
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [5,3,1,2,4,6] => [3,4,2,5,1,6] => 3
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [3,4,1,2,5,6] => [3,4,1,2,5,6] => 2
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [4,3,1,2,5,6] => [3,4,2,1,5,6] => 2
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [3,4,5,1,2,6] => [4,5,1,2,3,6] => 2
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [4,3,5,1,2,6] => [4,5,2,1,3,6] => 2
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [4,5,3,1,2,6] => [4,5,3,1,2,6] => 2
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [5,3,4,1,2,6] => [4,5,2,3,1,6] => 3
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [5,4,3,1,2,6] => [4,5,3,2,1,6] => 2
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [2,1,3,4,5,6] => [2,1,3,4,5,6] => 1
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [5,2,1,3,4,6] => [3,2,4,5,1,6] => 2
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [4,2,1,3,5,6] => [3,2,4,1,5,6] => 2
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [4,5,2,1,3,6] => [4,3,5,1,2,6] => 2
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [5,4,2,1,3,6] => [4,3,5,2,1,6] => 2
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [2,3,1,4,5,6] => [3,1,2,4,5,6] => 1
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [5,2,3,1,4,6] => [4,2,3,5,1,6] => 2
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [3,2,1,4,5,6] => [3,2,1,4,5,6] => 1
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [5,3,2,1,4,6] => [4,3,2,5,1,6] => 2
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [2,3,4,1,5,6] => [4,1,2,3,5,6] => 1
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [3,2,4,1,5,6] => [4,2,1,3,5,6] => 1
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [3,4,2,1,5,6] => [4,3,1,2,5,6] => 1
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [4,2,3,1,5,6] => [4,2,3,1,5,6] => 2
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [4,3,2,1,5,6] => [4,3,2,1,5,6] => 1
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [2,3,4,5,1,6] => [5,1,2,3,4,6] => 1
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [4,2,3,5,1,6] => [5,2,3,1,4,6] => 2
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [3,2,4,5,1,6] => [5,2,1,3,4,6] => 1
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [3,4,2,5,1,6] => [5,3,1,2,4,6] => 1
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [4,3,2,5,1,6] => [5,3,2,1,4,6] => 1
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [3,4,5,2,1,6] => [5,4,1,2,3,6] => 1
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [4,3,5,2,1,6] => [5,4,2,1,3,6] => 1
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [4,5,2,3,1,6] => [5,3,4,1,2,6] => 2
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [4,5,3,2,1,6] => [5,4,3,1,2,6] => 1
>>> Load all 267 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [5,2,3,4,1,6] => [5,2,3,4,1,6] => 2
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [5,3,2,4,1,6] => [5,3,2,4,1,6] => 2
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [5,3,4,2,1,6] => [5,4,2,3,1,6] => 2
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [5,4,2,3,1,6] => [5,3,4,2,1,6] => 2
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [5,4,3,2,1,6] => [5,4,3,2,1,6] => 1
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [2,3,4,5,6,1] => [6,1,2,3,4,5] => 1
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [5,2,3,4,6,1] => [6,2,3,4,1,5] => 2
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [4,2,3,5,6,1] => [6,2,3,1,4,5] => 2
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [4,5,2,3,6,1] => [6,3,4,1,2,5] => 2
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [5,4,2,3,6,1] => [6,3,4,2,1,5] => 2
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [3,2,4,5,6,1] => [6,2,1,3,4,5] => 1
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [5,3,2,4,6,1] => [6,3,2,4,1,5] => 2
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [3,4,2,5,6,1] => [6,3,1,2,4,5] => 1
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [4,3,2,5,6,1] => [6,3,2,1,4,5] => 1
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [3,4,5,2,6,1] => [6,4,1,2,3,5] => 1
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [4,3,5,2,6,1] => [6,4,2,1,3,5] => 1
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [4,5,3,2,6,1] => [6,4,3,1,2,5] => 1
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [5,3,4,2,6,1] => [6,4,2,3,1,5] => 2
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [5,4,3,2,6,1] => [6,4,3,2,1,5] => 1
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [3,4,5,6,1,2] => [5,6,1,2,3,4] => 2
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [5,3,4,6,1,2] => [5,6,2,3,1,4] => 3
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [4,3,5,6,1,2] => [5,6,2,1,3,4] => 2
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [4,5,3,6,1,2] => [5,6,3,1,2,4] => 2
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [5,4,3,6,1,2] => [5,6,3,2,1,4] => 2
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [3,4,5,6,2,1] => [6,5,1,2,3,4] => 1
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [5,3,4,6,2,1] => [6,5,2,3,1,4] => 2
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [4,3,5,6,2,1] => [6,5,2,1,3,4] => 1
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [4,5,3,6,2,1] => [6,5,3,1,2,4] => 1
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [5,4,3,6,2,1] => [6,5,3,2,1,4] => 1
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [4,5,6,1,2,3] => [4,5,6,1,2,3] => 2
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [5,4,6,1,2,3] => [4,5,6,2,1,3] => 2
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [4,5,6,2,1,3] => [5,4,6,1,2,3] => 2
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [5,4,6,2,1,3] => [5,4,6,2,1,3] => 2
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [4,5,6,2,3,1] => [6,4,5,1,2,3] => 2
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [5,4,6,2,3,1] => [6,4,5,2,1,3] => 2
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [4,5,6,3,1,2] => [5,6,4,1,2,3] => 2
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [5,4,6,3,1,2] => [5,6,4,2,1,3] => 2
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [4,5,6,3,2,1] => [6,5,4,1,2,3] => 1
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [5,4,6,3,2,1] => [6,5,4,2,1,3] => 1
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [5,6,1,2,3,4] => [3,4,5,6,1,2] => 2
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [5,6,3,1,2,4] => [4,5,3,6,1,2] => 3
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [5,6,2,1,3,4] => [4,3,5,6,1,2] => 2
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [5,6,2,3,1,4] => [5,3,4,6,1,2] => 2
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [5,6,3,2,1,4] => [5,4,3,6,1,2] => 2
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [5,6,2,3,4,1] => [6,3,4,5,1,2] => 2
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [5,6,3,2,4,1] => [6,4,3,5,1,2] => 2
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => [5,6,3,4,1,2] => 3
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [5,6,3,4,2,1] => [6,5,3,4,1,2] => 2
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [5,6,4,1,2,3] => [4,5,6,3,1,2] => 2
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [5,6,4,2,1,3] => [5,4,6,3,1,2] => 2
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [5,6,4,2,3,1] => [6,4,5,3,1,2] => 2
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [5,6,4,3,1,2] => [5,6,4,3,1,2] => 2
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [5,6,4,3,2,1] => [6,5,4,3,1,2] => 1
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [6,1,2,3,4,5] => [2,3,4,5,6,1] => 1
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [6,4,1,2,3,5] => [3,4,5,2,6,1] => 2
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [6,3,1,2,4,5] => [3,4,2,5,6,1] => 2
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [6,3,4,1,2,5] => [4,5,2,3,6,1] => 2
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [6,4,3,1,2,5] => [4,5,3,2,6,1] => 2
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [6,2,1,3,4,5] => [3,2,4,5,6,1] => 1
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [6,4,2,1,3,5] => [4,3,5,2,6,1] => 2
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [6,2,3,1,4,5] => [4,2,3,5,6,1] => 1
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [6,3,2,1,4,5] => [4,3,2,5,6,1] => 1
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [6,2,3,4,1,5] => [5,2,3,4,6,1] => 1
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [6,3,2,4,1,5] => [5,3,2,4,6,1] => 1
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [6,3,4,2,1,5] => [5,4,2,3,6,1] => 1
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [6,4,2,3,1,5] => [5,3,4,2,6,1] => 2
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [6,4,3,2,1,5] => [5,4,3,2,6,1] => 1
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [6,2,3,4,5,1] => [6,2,3,4,5,1] => 1
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [6,4,2,3,5,1] => [6,3,4,2,5,1] => 2
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [6,3,2,4,5,1] => [6,3,2,4,5,1] => 1
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [6,3,4,2,5,1] => [6,4,2,3,5,1] => 1
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [6,4,3,2,5,1] => [6,4,3,2,5,1] => 1
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [6,3,4,5,1,2] => [5,6,2,3,4,1] => 2
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [6,4,3,5,1,2] => [5,6,3,2,4,1] => 2
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [6,3,4,5,2,1] => [6,5,2,3,4,1] => 1
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [6,4,3,5,2,1] => [6,5,3,2,4,1] => 1
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [6,4,5,1,2,3] => [4,5,6,2,3,1] => 2
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [6,4,5,2,1,3] => [5,4,6,2,3,1] => 2
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [6,4,5,2,3,1] => [6,4,5,2,3,1] => 2
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [6,4,5,3,1,2] => [5,6,4,2,3,1] => 2
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [6,4,5,3,2,1] => [6,5,4,2,3,1] => 1
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [6,5,1,2,3,4] => [3,4,5,6,2,1] => 1
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [6,5,3,1,2,4] => [4,5,3,6,2,1] => 2
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [6,5,2,1,3,4] => [4,3,5,6,2,1] => 1
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [6,5,2,3,1,4] => [5,3,4,6,2,1] => 1
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [6,5,3,2,1,4] => [5,4,3,6,2,1] => 1
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [6,5,2,3,4,1] => [6,3,4,5,2,1] => 1
[[[[.,.],[[.,.],.]],.],.] => [1,3,4,2,5,6] => [6,5,3,2,4,1] => [6,4,3,5,2,1] => 1
[[[[.,[.,.]],[.,.]],.],.] => [2,1,4,3,5,6] => [6,5,3,4,1,2] => [5,6,3,4,2,1] => 2
[[[[[.,.],.],[.,.]],.],.] => [1,2,4,3,5,6] => [6,5,3,4,2,1] => [6,5,3,4,2,1] => 1
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [6,5,4,1,2,3] => [4,5,6,3,2,1] => 1
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [6,5,4,2,1,3] => [5,4,6,3,2,1] => 1
[[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6] => [6,5,4,2,3,1] => [6,4,5,3,2,1] => 1
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [6,5,4,3,1,2] => [5,6,4,3,2,1] => 1
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [6,5,4,3,2,1] => [6,5,4,3,2,1] => 0
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 1
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1] => [6,1,2,3,4,5,7] => [2,3,4,5,6,1,7] => 2
[.,[.,[.,[.,[[.,.],[.,.]]]]]] => [5,7,6,4,3,2,1] => [5,1,2,3,4,6,7] => [2,3,4,5,1,6,7] => 2
[.,[.,[.,[[.,.],[.,[.,.]]]]]] => [4,7,6,5,3,2,1] => [4,1,2,3,5,6,7] => [2,3,4,1,5,6,7] => 2
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1] => [4,5,6,1,2,3,7] => [4,5,6,1,2,3,7] => 2
[.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1] => [6,5,4,1,2,3,7] => [4,5,6,3,2,1,7] => 2
[.,[.,[[.,.],[.,[.,[.,.]]]]]] => [3,7,6,5,4,2,1] => [3,1,2,4,5,6,7] => [2,3,1,4,5,6,7] => 2
[.,[.,[[.,.],[[[.,.],.],.]]]] => [3,5,6,7,4,2,1] => [6,5,3,1,2,4,7] => [4,5,3,6,2,1,7] => 3
[.,[.,[[.,[.,.]],[.,[.,.]]]]] => [4,3,7,6,5,2,1] => [3,4,1,2,5,6,7] => [3,4,1,2,5,6,7] => 2
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [3,4,5,6,1,2,7] => [5,6,1,2,3,4,7] => 2
[.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1] => [5,6,3,4,1,2,7] => [5,6,3,4,1,2,7] => 3
[.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1] => [6,5,4,3,1,2,7] => [5,6,4,3,2,1,7] => 2
[.,[[.,.],[.,[.,[.,[.,.]]]]]] => [2,7,6,5,4,3,1] => [2,1,3,4,5,6,7] => [2,1,3,4,5,6,7] => 1
[.,[[.,.],[[[[.,.],.],.],.]]] => [2,4,5,6,7,3,1] => [6,5,4,2,1,3,7] => [5,4,6,3,2,1,7] => 2
[.,[[.,[.,.]],[.,[.,[.,.]]]]] => [3,2,7,6,5,4,1] => [2,3,1,4,5,6,7] => [3,1,2,4,5,6,7] => 1
[.,[[[.,.],.],[.,[.,[.,.]]]]] => [2,3,7,6,5,4,1] => [3,2,1,4,5,6,7] => [3,2,1,4,5,6,7] => 1
[.,[[[.,.],.],[[[.,.],.],.]]] => [2,3,5,6,7,4,1] => [6,5,3,2,1,4,7] => [5,4,3,6,2,1,7] => 2
[.,[[.,[.,[.,.]]],[.,[.,.]]]] => [4,3,2,7,6,5,1] => [2,3,4,1,5,6,7] => [4,1,2,3,5,6,7] => 1
[.,[[[[.,.],.],.],[.,[.,.]]]] => [2,3,4,7,6,5,1] => [4,3,2,1,5,6,7] => [4,3,2,1,5,6,7] => 1
[.,[[[[.,.],.],.],[[.,.],.]]] => [2,3,4,6,7,5,1] => [6,4,3,2,1,5,7] => [5,4,3,2,6,1,7] => 2
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [5,4,3,2,7,6,1] => [2,3,4,5,1,6,7] => [5,1,2,3,4,6,7] => 1
[.,[[[[[.,.],.],.],.],[.,.]]] => [2,3,4,5,7,6,1] => [5,4,3,2,1,6,7] => [5,4,3,2,1,6,7] => 1
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [2,3,4,5,6,1,7] => [6,1,2,3,4,5,7] => 1
[.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1] => [6,4,2,3,5,1,7] => [6,3,4,2,5,1,7] => 3
[.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1] => [6,4,3,2,5,1,7] => [6,4,3,2,5,1,7] => 2
[.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1] => [6,5,2,3,4,1,7] => [6,3,4,5,2,1,7] => 2
[.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1] => [6,5,3,2,4,1,7] => [6,4,3,5,2,1,7] => 2
[.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1] => [6,5,3,4,2,1,7] => [6,5,3,4,2,1,7] => 2
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [6,5,4,3,2,1,7] => [6,5,4,3,2,1,7] => 1
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [1,7,6,5,4,3,2] => [2,3,4,5,6,7,1] => [7,1,2,3,4,5,6] => 1
[[.,.],[.,[.,[.,[[.,.],.]]]]] => [1,6,7,5,4,3,2] => [6,2,3,4,5,7,1] => [7,2,3,4,5,1,6] => 2
[[.,.],[.,[.,[[.,.],[.,.]]]]] => [1,5,7,6,4,3,2] => [5,2,3,4,6,7,1] => [7,2,3,4,1,5,6] => 2
[[.,.],[.,[[.,.],[.,[.,.]]]]] => [1,4,7,6,5,3,2] => [4,2,3,5,6,7,1] => [7,2,3,1,4,5,6] => 2
[[.,.],[.,[[.,[.,.]],[.,.]]]] => [1,5,4,7,6,3,2] => [4,5,2,3,6,7,1] => [7,3,4,1,2,5,6] => 2
[[.,.],[[.,.],[.,[.,[.,.]]]]] => [1,3,7,6,5,4,2] => [3,2,4,5,6,7,1] => [7,2,1,3,4,5,6] => 1
[[.,.],[[.,.],[[.,.],[.,.]]]] => [1,3,5,7,6,4,2] => [5,3,2,4,6,7,1] => [7,3,2,4,1,5,6] => 2
[[.,.],[[.,[.,.]],[.,[.,.]]]] => [1,4,3,7,6,5,2] => [3,4,2,5,6,7,1] => [7,3,1,2,4,5,6] => 1
[[.,.],[[[.,.],.],[.,[.,.]]]] => [1,3,4,7,6,5,2] => [4,3,2,5,6,7,1] => [7,3,2,1,4,5,6] => 1
[[.,.],[[.,[.,[.,.]]],[.,.]]] => [1,5,4,3,7,6,2] => [3,4,5,2,6,7,1] => [7,4,1,2,3,5,6] => 1
[[.,.],[[.,[[.,.],.]],[.,.]]] => [1,4,5,3,7,6,2] => [4,3,5,2,6,7,1] => [7,4,2,1,3,5,6] => 1
[[.,.],[[.,[.,[.,[.,.]]]],.]] => [1,6,5,4,3,7,2] => [3,4,5,6,2,7,1] => [7,5,1,2,3,4,6] => 1
[[.,[.,.]],[.,[.,[.,[.,.]]]]] => [2,1,7,6,5,4,3] => [3,4,5,6,7,1,2] => [6,7,1,2,3,4,5] => 2
[[.,[.,.]],[.,[[.,[.,.]],.]]] => [2,1,6,5,7,4,3] => [5,6,3,4,7,1,2] => [6,7,3,4,1,2,5] => 3
[[[.,.],.],[.,[.,[.,[.,.]]]]] => [1,2,7,6,5,4,3] => [3,4,5,6,7,2,1] => [7,6,1,2,3,4,5] => 1
[[.,[.,[.,.]]],[.,[.,[.,.]]]] => [3,2,1,7,6,5,4] => [4,5,6,7,1,2,3] => [5,6,7,1,2,3,4] => 2
[[[.,.],[.,.]],[.,[.,[.,.]]]] => [1,3,2,7,6,5,4] => [4,5,6,7,2,3,1] => [7,5,6,1,2,3,4] => 2
[[[[.,.],.],.],[.,[.,[.,.]]]] => [1,2,3,7,6,5,4] => [4,5,6,7,3,2,1] => [7,6,5,1,2,3,4] => 1
[[.,[[.,.],[.,.]]],[.,[.,.]]] => [2,4,3,1,7,6,5] => [5,6,7,2,1,3,4] => [5,4,6,7,1,2,3] => 2
[[.,[[.,[.,.]],.]],[.,[.,.]]] => [3,2,4,1,7,6,5] => [5,6,7,2,3,1,4] => [6,4,5,7,1,2,3] => 2
[[[.,.],[.,[.,.]]],[.,[.,.]]] => [1,4,3,2,7,6,5] => [5,6,7,2,3,4,1] => [7,4,5,6,1,2,3] => 2
[[[.,[.,.]],[.,.]],[.,[.,.]]] => [2,1,4,3,7,6,5] => [5,6,7,3,4,1,2] => [6,7,4,5,1,2,3] => 3
[[[[.,.],.],[.,.]],[.,[.,.]]] => [1,2,4,3,7,6,5] => [5,6,7,3,4,2,1] => [7,6,4,5,1,2,3] => 2
[[[[[.,.],.],.],.],[.,[.,.]]] => [1,2,3,4,7,6,5] => [5,6,7,4,3,2,1] => [7,6,5,4,1,2,3] => 1
[[.,[.,[.,[.,[.,.]]]]],[.,.]] => [5,4,3,2,1,7,6] => [6,7,1,2,3,4,5] => [3,4,5,6,7,1,2] => 2
[[[.,[[.,.],.]],[.,.]],[.,.]] => [2,3,1,5,4,7,6] => [6,7,4,5,2,1,3] => [6,5,7,3,4,1,2] => 3
[[[[.,.],[.,.]],[.,.]],[.,.]] => [1,3,2,5,4,7,6] => [6,7,4,5,2,3,1] => [7,5,6,3,4,1,2] => 3
[[[[[.,.],.],.],[.,.]],[.,.]] => [1,2,3,5,4,7,6] => [6,7,4,5,3,2,1] => [7,6,5,3,4,1,2] => 2
[[[[[[.,.],.],.],.],.],[.,.]] => [1,2,3,4,5,7,6] => [6,7,5,4,3,2,1] => [7,6,5,4,3,1,2] => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [7,1,2,3,4,5,6] => [2,3,4,5,6,7,1] => 1
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [5,6,4,3,2,1,7] => [7,5,1,2,3,4,6] => [3,4,5,6,2,7,1] => 2
[[.,[.,[.,[[.,.],[.,.]]]]],.] => [4,6,5,3,2,1,7] => [7,4,1,2,3,5,6] => [3,4,5,2,6,7,1] => 2
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [3,6,5,4,2,1,7] => [7,3,1,2,4,5,6] => [3,4,2,5,6,7,1] => 2
[[.,[.,[[.,[.,.]],[.,.]]]],.] => [4,3,6,5,2,1,7] => [7,3,4,1,2,5,6] => [4,5,2,3,6,7,1] => 2
[[.,[[.,.],[.,[.,[.,.]]]]],.] => [2,6,5,4,3,1,7] => [7,2,1,3,4,5,6] => [3,2,4,5,6,7,1] => 1
[[.,[[.,.],[[.,.],[.,.]]]],.] => [2,4,6,5,3,1,7] => [7,4,2,1,3,5,6] => [4,3,5,2,6,7,1] => 2
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [3,2,6,5,4,1,7] => [7,2,3,1,4,5,6] => [4,2,3,5,6,7,1] => 1
[[.,[[[.,.],.],[.,[.,.]]]],.] => [2,3,6,5,4,1,7] => [7,3,2,1,4,5,6] => [4,3,2,5,6,7,1] => 1
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [4,3,2,6,5,1,7] => [7,2,3,4,1,5,6] => [5,2,3,4,6,7,1] => 1
[[.,[[.,[[.,.],.]],[.,.]]],.] => [3,4,2,6,5,1,7] => [7,3,2,4,1,5,6] => [5,3,2,4,6,7,1] => 1
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [5,4,3,2,6,1,7] => [7,2,3,4,5,1,6] => [6,2,3,4,5,7,1] => 1
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 0
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Description
The number of right outer peaks of a permutation.
A right outer peak in a permutation $w = [w_1,..., w_n]$ is either a position $i$ such that $w_{i-1} < w_i > w_{i+1}$ or $n$ if $w_n > w_{n-1}$.
In other words, it is a peak in the word $[w_1,..., w_n,0]$.
Map
inverse
Description
Sends a permutation to its inverse.
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.
Map
weak order rowmotion
Description
Return the reversal of the permutation obtained by inverting the corresponding Laguerre heap.
This map is the composite of Mp00241invert Laguerre heap and Mp00064reverse.
Conjecturally, it is also the rowmotion on the weak order:
Any semidistributive lattice $L$ has a canonical labeling of the edges of its Hasse diagram by its join irreducible elements (see [1] and [2]). Rowmotion on this lattice is the bijection which takes an element $x \in L$ with a given set of down-labels to the unique element $y \in L$ which has that set as its up-labels (see [2] and [3]). For example, if the lattice is the distributive lattice $J(P)$ of order ideals of a finite poset $P$, then this reduces to ordinary rowmotion on the order ideals of $P$.
The weak order (a.k.a. permutohedral order) on the permutations in $S_n$ is a semidistributive lattice. In this way, we obtain an action of rowmotion on the set of permutations in $S_n$.
Note that the dynamics of weak order rowmotion is poorly understood. A collection of nontrivial homomesies is described in Corollary 6.14 of [4].