Identifier
Values
[.,.] => [1] => [1] => 0
[.,[.,.]] => [2,1] => [2,1] => 0
[[.,.],.] => [1,2] => [1,2] => 0
[.,[.,[.,.]]] => [3,2,1] => [3,2,1] => 0
[.,[[.,.],.]] => [2,3,1] => [2,1,3] => 1
[[.,.],[.,.]] => [3,1,2] => [3,1,2] => 0
[[.,[.,.]],.] => [2,1,3] => [1,3,2] => 0
[[[.,.],.],.] => [1,2,3] => [1,2,3] => 0
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [4,3,1,2] => 0
[.,[.,[[.,.],.]]] => [3,4,2,1] => [3,2,4,1] => 1
[.,[[.,.],[.,.]]] => [4,2,3,1] => [4,3,2,1] => 0
[.,[[.,[.,.]],.]] => [3,2,4,1] => [2,1,3,4] => 1
[.,[[[.,.],.],.]] => [2,3,4,1] => [2,1,4,3] => 1
[[.,.],[.,[.,.]]] => [4,3,1,2] => [4,2,1,3] => 0
[[.,.],[[.,.],.]] => [3,4,1,2] => [3,1,4,2] => 1
[[.,[.,.]],[.,.]] => [4,2,1,3] => [4,2,3,1] => 0
[[[.,.],.],[.,.]] => [4,1,2,3] => [4,1,3,2] => 0
[[.,[.,[.,.]]],.] => [3,2,1,4] => [1,4,3,2] => 0
[[.,[[.,.],.]],.] => [2,3,1,4] => [1,4,2,3] => 0
[[[.,.],[.,.]],.] => [3,1,2,4] => [1,3,4,2] => 0
[[[.,[.,.]],.],.] => [2,1,3,4] => [1,3,2,4] => 0
[[[[.,.],.],.],.] => [1,2,3,4] => [1,2,3,4] => 0
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [5,4,1,2,3] => 0
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [4,3,5,1,2] => 1
[.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1] => [5,4,2,1,3] => 0
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [3,2,4,5,1] => 1
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [3,2,5,4,1] => 1
[.,[[.,.],[.,[.,.]]]] => [5,4,2,3,1] => [5,4,1,3,2] => 0
[.,[[.,.],[[.,.],.]]] => [4,5,2,3,1] => [4,3,5,2,1] => 1
[.,[[.,[.,.]],[.,.]]] => [5,3,2,4,1] => [5,4,3,1,2] => 0
[.,[[[.,.],.],[.,.]]] => [5,2,3,4,1] => [5,4,3,2,1] => 0
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [2,1,3,4,5] => 1
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [2,1,4,3,5] => 1
[.,[[[.,.],[.,.]],.]] => [4,2,3,5,1] => [2,1,3,5,4] => 1
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [2,1,5,3,4] => 1
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [2,1,5,4,3] => 1
[[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2] => [5,3,1,2,4] => 0
[[.,.],[.,[[.,.],.]]] => [4,5,3,1,2] => [4,2,5,1,3] => 1
[[.,.],[[.,.],[.,.]]] => [5,3,4,1,2] => [5,3,2,1,4] => 0
[[.,.],[[.,[.,.]],.]] => [4,3,5,1,2] => [3,1,4,5,2] => 1
[[.,.],[[[.,.],.],.]] => [3,4,5,1,2] => [3,1,5,4,2] => 1
[[.,[.,.]],[.,[.,.]]] => [5,4,2,1,3] => [5,3,1,4,2] => 0
[[.,[.,.]],[[.,.],.]] => [4,5,2,1,3] => [4,2,5,3,1] => 1
[[[.,.],.],[.,[.,.]]] => [5,4,1,2,3] => [5,2,1,4,3] => 0
[[[.,.],.],[[.,.],.]] => [4,5,1,2,3] => [4,1,5,3,2] => 1
[[.,[.,[.,.]]],[.,.]] => [5,3,2,1,4] => [5,3,4,2,1] => 0
[[.,[[.,.],.]],[.,.]] => [5,2,3,1,4] => [5,3,4,1,2] => 0
[[[.,.],[.,.]],[.,.]] => [5,3,1,2,4] => [5,2,4,3,1] => 0
[[[.,[.,.]],.],[.,.]] => [5,2,1,3,4] => [5,2,4,1,3] => 0
[[[[.,.],.],.],[.,.]] => [5,1,2,3,4] => [5,1,4,2,3] => 0
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [1,5,4,3,2] => 0
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [1,5,4,2,3] => 0
[[.,[[.,.],[.,.]]],.] => [4,2,3,1,5] => [1,5,3,4,2] => 0
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [1,5,3,2,4] => 0
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [1,5,2,3,4] => 0
[[[.,.],[.,[.,.]]],.] => [4,3,1,2,5] => [1,4,5,3,2] => 0
[[[.,.],[[.,.],.]],.] => [3,4,1,2,5] => [1,4,5,2,3] => 0
[[[.,[.,.]],[.,.]],.] => [4,2,1,3,5] => [1,4,3,5,2] => 0
[[[[.,.],.],[.,.]],.] => [4,1,2,3,5] => [1,3,4,5,2] => 0
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [1,4,3,2,5] => 0
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [1,4,2,3,5] => 0
[[[[.,.],[.,.]],.],.] => [3,1,2,4,5] => [1,3,4,2,5] => 0
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [1,3,2,4,5] => 0
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [6,5,1,2,3,4] => 0
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [5,4,6,1,2,3] => 1
[.,[.,[.,[[.,.],[.,.]]]]] => [6,4,5,3,2,1] => [6,5,2,1,3,4] => 0
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [4,3,5,6,1,2] => 1
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [4,3,6,5,1,2] => 1
[.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1] => [6,5,1,3,2,4] => 0
[.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1] => [5,4,6,2,1,3] => 1
[.,[.,[[.,[.,.]],[.,.]]]] => [6,4,3,5,2,1] => [6,5,3,1,2,4] => 0
[.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1] => [6,5,3,2,1,4] => 0
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [3,2,4,5,6,1] => 1
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [3,2,5,4,6,1] => 1
[.,[.,[[[.,.],[.,.]],.]]] => [5,3,4,6,2,1] => [3,2,4,6,5,1] => 1
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [3,2,6,4,5,1] => 1
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [3,2,6,5,4,1] => 1
[.,[[.,.],[.,[.,[.,.]]]]] => [6,5,4,2,3,1] => [6,5,1,2,4,3] => 0
[.,[[.,.],[.,[[.,.],.]]]] => [5,6,4,2,3,1] => [5,4,6,1,3,2] => 1
[.,[[.,.],[[.,.],[.,.]]]] => [6,4,5,2,3,1] => [6,5,2,1,4,3] => 0
[.,[[.,.],[[.,[.,.]],.]]] => [5,4,6,2,3,1] => [4,3,5,6,2,1] => 1
[.,[[.,.],[[[.,.],.],.]]] => [4,5,6,2,3,1] => [4,3,6,5,2,1] => 1
[.,[[.,[.,.]],[.,[.,.]]]] => [6,5,3,2,4,1] => [6,5,1,4,2,3] => 0
[.,[[.,[.,.]],[[.,.],.]]] => [5,6,3,2,4,1] => [5,4,6,3,1,2] => 1
[.,[[[.,.],.],[.,[.,.]]]] => [6,5,2,3,4,1] => [6,5,1,4,3,2] => 0
[.,[[[.,.],.],[[.,.],.]]] => [5,6,2,3,4,1] => [5,4,6,3,2,1] => 1
[.,[[.,[.,[.,.]]],[.,.]]] => [6,4,3,2,5,1] => [6,5,4,1,2,3] => 0
[.,[[.,[[.,.],.]],[.,.]]] => [6,3,4,2,5,1] => [6,5,4,2,1,3] => 0
[.,[[[.,.],[.,.]],[.,.]]] => [6,4,2,3,5,1] => [6,5,4,1,3,2] => 0
[.,[[[.,[.,.]],.],[.,.]]] => [6,3,2,4,5,1] => [6,5,4,3,1,2] => 0
[.,[[[[.,.],.],.],[.,.]]] => [6,2,3,4,5,1] => [6,5,4,3,2,1] => 0
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [2,1,3,4,5,6] => 1
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [2,1,4,3,5,6] => 1
[.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1] => [2,1,3,5,4,6] => 1
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [2,1,5,3,4,6] => 1
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [2,1,5,4,3,6] => 1
[.,[[[.,.],[.,[.,.]]],.]] => [5,4,2,3,6,1] => [2,1,3,4,6,5] => 1
[.,[[[.,.],[[.,.],.]],.]] => [4,5,2,3,6,1] => [2,1,4,3,6,5] => 1
[.,[[[.,[.,.]],[.,.]],.]] => [5,3,2,4,6,1] => [2,1,3,6,4,5] => 1
[.,[[[[.,.],.],[.,.]],.]] => [5,2,3,4,6,1] => [2,1,3,6,5,4] => 1
>>> Load all 255 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [2,1,6,3,4,5] => 1
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [2,1,6,4,3,5] => 1
[.,[[[[.,.],[.,.]],.],.]] => [4,2,3,5,6,1] => [2,1,6,3,5,4] => 1
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [2,1,6,5,3,4] => 1
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [2,1,6,5,4,3] => 1
[[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2] => [6,4,1,2,3,5] => 0
[[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2] => [5,3,6,1,2,4] => 1
[[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2] => [6,4,2,1,3,5] => 0
[[.,.],[.,[[.,[.,.]],.]]] => [5,4,6,3,1,2] => [4,2,5,6,1,3] => 1
[[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2] => [4,2,6,5,1,3] => 1
[[.,.],[[.,.],[.,[.,.]]]] => [6,5,3,4,1,2] => [6,4,1,3,2,5] => 0
[[.,.],[[.,.],[[.,.],.]]] => [5,6,3,4,1,2] => [5,3,6,2,1,4] => 1
[[.,.],[[.,[.,.]],[.,.]]] => [6,4,3,5,1,2] => [6,4,3,1,2,5] => 0
[[.,.],[[[.,.],.],[.,.]]] => [6,3,4,5,1,2] => [6,4,3,2,1,5] => 0
[[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2] => [3,1,4,5,6,2] => 1
[[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2] => [3,1,5,4,6,2] => 1
[[.,.],[[[.,.],[.,.]],.]] => [5,3,4,6,1,2] => [3,1,4,6,5,2] => 1
[[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2] => [3,1,6,4,5,2] => 1
[[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2] => [3,1,6,5,4,2] => 1
[[.,[.,.]],[.,[.,[.,.]]]] => [6,5,4,2,1,3] => [6,4,1,2,5,3] => 0
[[.,[.,.]],[.,[[.,.],.]]] => [5,6,4,2,1,3] => [5,3,6,1,4,2] => 1
[[.,[.,.]],[[.,.],[.,.]]] => [6,4,5,2,1,3] => [6,4,2,1,5,3] => 0
[[.,[.,.]],[[.,[.,.]],.]] => [5,4,6,2,1,3] => [4,2,5,6,3,1] => 1
[[.,[.,.]],[[[.,.],.],.]] => [4,5,6,2,1,3] => [4,2,6,5,3,1] => 1
[[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3] => [6,3,1,2,5,4] => 0
[[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3] => [5,2,6,1,4,3] => 1
[[[.,.],.],[[.,.],[.,.]]] => [6,4,5,1,2,3] => [6,3,2,1,5,4] => 0
[[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3] => [4,1,5,6,3,2] => 1
[[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3] => [4,1,6,5,3,2] => 1
[[.,[.,[.,.]]],[.,[.,.]]] => [6,5,3,2,1,4] => [6,4,1,5,3,2] => 0
[[.,[.,[.,.]]],[[.,.],.]] => [5,6,3,2,1,4] => [5,3,6,4,2,1] => 1
[[.,[[.,.],.]],[.,[.,.]]] => [6,5,2,3,1,4] => [6,4,1,5,2,3] => 0
[[.,[[.,.],.]],[[.,.],.]] => [5,6,2,3,1,4] => [5,3,6,4,1,2] => 1
[[[.,.],[.,.]],[.,[.,.]]] => [6,5,3,1,2,4] => [6,3,1,5,4,2] => 0
[[[.,.],[.,.]],[[.,.],.]] => [5,6,3,1,2,4] => [5,2,6,4,3,1] => 1
[[[.,[.,.]],.],[.,[.,.]]] => [6,5,2,1,3,4] => [6,3,1,5,2,4] => 0
[[[.,[.,.]],.],[[.,.],.]] => [5,6,2,1,3,4] => [5,2,6,4,1,3] => 1
[[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4] => [6,2,1,5,3,4] => 0
[[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4] => [5,1,6,4,2,3] => 1
[[.,[.,[.,[.,.]]]],[.,.]] => [6,4,3,2,1,5] => [6,4,5,3,2,1] => 0
[[.,[.,[[.,.],.]]],[.,.]] => [6,3,4,2,1,5] => [6,4,5,3,1,2] => 0
[[.,[[.,.],[.,.]]],[.,.]] => [6,4,2,3,1,5] => [6,4,5,2,3,1] => 0
[[.,[[.,[.,.]],.]],[.,.]] => [6,3,2,4,1,5] => [6,4,5,2,1,3] => 0
[[.,[[[.,.],.],.]],[.,.]] => [6,2,3,4,1,5] => [6,4,5,1,2,3] => 0
[[[.,.],[.,[.,.]]],[.,.]] => [6,4,3,1,2,5] => [6,3,5,4,2,1] => 0
[[[.,.],[[.,.],.]],[.,.]] => [6,3,4,1,2,5] => [6,3,5,4,1,2] => 0
[[[.,[.,.]],[.,.]],[.,.]] => [6,4,2,1,3,5] => [6,3,5,2,4,1] => 0
[[[[.,.],.],[.,.]],[.,.]] => [6,4,1,2,3,5] => [6,2,5,3,4,1] => 0
[[[.,[.,[.,.]]],.],[.,.]] => [6,3,2,1,4,5] => [6,3,5,2,1,4] => 0
[[[.,[[.,.],.]],.],[.,.]] => [6,2,3,1,4,5] => [6,3,5,1,2,4] => 0
[[[[.,.],[.,.]],.],[.,.]] => [6,3,1,2,4,5] => [6,2,5,3,1,4] => 0
[[[[.,[.,.]],.],.],[.,.]] => [6,2,1,3,4,5] => [6,2,5,1,3,4] => 0
[[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5] => [6,1,5,2,3,4] => 0
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [1,6,5,4,3,2] => 0
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [1,6,5,4,2,3] => 0
[[.,[.,[[.,.],[.,.]]]],.] => [5,3,4,2,1,6] => [1,6,5,3,4,2] => 0
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [1,6,5,3,2,4] => 0
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [1,6,5,2,3,4] => 0
[[.,[[.,.],[.,[.,.]]]],.] => [5,4,2,3,1,6] => [1,6,4,5,3,2] => 0
[[.,[[.,.],[[.,.],.]]],.] => [4,5,2,3,1,6] => [1,6,4,5,2,3] => 0
[[.,[[.,[.,.]],[.,.]]],.] => [5,3,2,4,1,6] => [1,6,4,3,5,2] => 0
[[.,[[[.,.],.],[.,.]]],.] => [5,2,3,4,1,6] => [1,6,3,4,5,2] => 0
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [1,6,4,3,2,5] => 0
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [1,6,4,2,3,5] => 0
[[.,[[[.,.],[.,.]],.]],.] => [4,2,3,5,1,6] => [1,6,3,4,2,5] => 0
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [1,6,3,2,4,5] => 0
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [1,6,2,3,4,5] => 0
[[[.,.],[.,[.,[.,.]]]],.] => [5,4,3,1,2,6] => [1,5,6,4,3,2] => 0
[[[.,.],[.,[[.,.],.]]],.] => [4,5,3,1,2,6] => [1,5,6,4,2,3] => 0
[[[.,.],[[.,.],[.,.]]],.] => [5,3,4,1,2,6] => [1,5,6,3,4,2] => 0
[[[.,.],[[.,[.,.]],.]],.] => [4,3,5,1,2,6] => [1,5,6,3,2,4] => 0
[[[.,.],[[[.,.],.],.]],.] => [3,4,5,1,2,6] => [1,5,6,2,3,4] => 0
[[[.,[.,.]],[.,[.,.]]],.] => [5,4,2,1,3,6] => [1,5,4,6,3,2] => 0
[[[.,[.,.]],[[.,.],.]],.] => [4,5,2,1,3,6] => [1,5,4,6,2,3] => 0
[[[[.,.],.],[.,[.,.]]],.] => [5,4,1,2,3,6] => [1,4,5,6,3,2] => 0
[[[[.,.],.],[[.,.],.]],.] => [4,5,1,2,3,6] => [1,4,5,6,2,3] => 0
[[[.,[.,[.,.]]],[.,.]],.] => [5,3,2,1,4,6] => [1,5,4,3,6,2] => 0
[[[.,[[.,.],.]],[.,.]],.] => [5,2,3,1,4,6] => [1,5,3,4,6,2] => 0
[[[[.,.],[.,.]],[.,.]],.] => [5,3,1,2,4,6] => [1,4,5,3,6,2] => 0
[[[[.,[.,.]],.],[.,.]],.] => [5,2,1,3,4,6] => [1,4,3,5,6,2] => 0
[[[[[.,.],.],.],[.,.]],.] => [5,1,2,3,4,6] => [1,3,4,5,6,2] => 0
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [1,5,4,3,2,6] => 0
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [1,5,4,2,3,6] => 0
[[[.,[[.,.],[.,.]]],.],.] => [4,2,3,1,5,6] => [1,5,3,4,2,6] => 0
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [1,5,3,2,4,6] => 0
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [1,5,2,3,4,6] => 0
[[[[.,.],[.,[.,.]]],.],.] => [4,3,1,2,5,6] => [1,4,5,3,2,6] => 0
[[[[.,.],[[.,.],.]],.],.] => [3,4,1,2,5,6] => [1,4,5,2,3,6] => 0
[[[[.,[.,.]],[.,.]],.],.] => [4,2,1,3,5,6] => [1,4,3,5,2,6] => 0
[[[[[.,.],.],[.,.]],.],.] => [4,1,2,3,5,6] => [1,3,4,5,2,6] => 0
[[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6] => [1,4,3,2,5,6] => 0
[[[[.,[[.,.],.]],.],.],.] => [2,3,1,4,5,6] => [1,4,2,3,5,6] => 0
[[[[[.,.],[.,.]],.],.],.] => [3,1,2,4,5,6] => [1,3,4,2,5,6] => 0
[[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6] => [1,3,2,4,5,6] => 0
[[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6] => [1,2,3,4,5,6] => 0
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1] => [7,6,1,2,3,4,5] => 0
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1] => [5,4,6,7,1,2,3] => 1
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1] => [3,2,4,5,6,7,1] => 1
[.,[[.,[.,[.,[.,.]]]],[.,.]]] => [7,5,4,3,2,6,1] => [7,6,5,1,2,3,4] => 0
[.,[[[.,[.,[.,.]]],.],[.,.]]] => [7,4,3,2,5,6,1] => [7,6,5,4,1,2,3] => 0
[.,[[[[.,[.,.]],.],.],[.,.]]] => [7,3,2,4,5,6,1] => [7,6,5,4,3,1,2] => 0
[.,[[[[[.,.],.],.],.],[.,.]]] => [7,2,3,4,5,6,1] => [7,6,5,4,3,2,1] => 0
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1] => [2,1,3,4,5,6,7] => 1
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [5,4,3,6,2,7,1] => [2,1,6,3,4,5,7] => 1
[.,[[[.,[.,.]],[.,[.,.]]],.]] => [6,5,3,2,4,7,1] => [2,1,3,4,7,5,6] => 1
[.,[[[.,[.,[.,.]]],[.,.]],.]] => [6,4,3,2,5,7,1] => [2,1,3,7,4,5,6] => 1
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1] => [2,1,7,3,4,5,6] => 1
[.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1] => [2,1,7,6,5,4,3] => 1
[[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2] => [7,5,1,2,3,4,6] => 0
[[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2] => [5,3,6,7,1,2,4] => 1
[[.,[[.,.],[[.,.],.]]],[.,.]] => [7,4,5,2,3,1,6] => [7,5,6,3,4,1,2] => 0
[[.,[[[[.,.],.],.],.]],[.,.]] => [7,2,3,4,5,1,6] => [7,5,6,1,2,3,4] => 0
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7] => [1,7,6,5,4,3,2] => 0
[[.,[.,[[.,.],[.,[.,.]]]]],.] => [6,5,3,4,2,1,7] => [1,7,6,4,5,3,2] => 0
[[.,[[.,[.,.]],[.,[.,.]]]],.] => [6,5,3,2,4,1,7] => [1,7,5,4,6,3,2] => 0
[[.,[[[.,.],.],[.,[.,.]]]],.] => [6,5,2,3,4,1,7] => [1,7,4,5,6,3,2] => 0
[[.,[[.,[.,[.,.]]],[.,.]]],.] => [6,4,3,2,5,1,7] => [1,7,5,4,3,6,2] => 0
[[.,[[[.,.],[.,.]],[.,.]]],.] => [6,4,2,3,5,1,7] => [1,7,4,5,3,6,2] => 0
[[.,[[[[[.,.],.],.],.],.]],.] => [2,3,4,5,6,1,7] => [1,7,2,3,4,5,6] => 0
[[[.,.],[.,[.,[.,[.,.]]]]],.] => [6,5,4,3,1,2,7] => [1,6,7,5,4,3,2] => 0
[[[.,.],[[[[.,.],.],.],.]],.] => [3,4,5,6,1,2,7] => [1,6,7,2,3,4,5] => 0
[[[.,[.,.]],[.,[.,[.,.]]]],.] => [6,5,4,2,1,3,7] => [1,6,5,7,4,3,2] => 0
[[[[.,.],.],[.,[.,[.,.]]]],.] => [6,5,4,1,2,3,7] => [1,5,6,7,4,3,2] => 0
[[[[.,.],.],[[[.,.],.],.]],.] => [4,5,6,1,2,3,7] => [1,5,6,7,2,3,4] => 0
[[[.,[.,[.,.]]],[.,[.,.]]],.] => [6,5,3,2,1,4,7] => [1,6,5,4,7,3,2] => 0
[[[[.,.],[.,.]],[.,[.,.]]],.] => [6,5,3,1,2,4,7] => [1,5,6,4,7,3,2] => 0
[[[[[.,.],.],.],[.,[.,.]]],.] => [6,5,1,2,3,4,7] => [1,4,5,6,7,3,2] => 0
[[[[[.,.],.],.],[[.,.],.]],.] => [5,6,1,2,3,4,7] => [1,4,5,6,7,2,3] => 0
[[[.,[.,[.,[.,.]]]],[.,.]],.] => [6,4,3,2,1,5,7] => [1,6,5,4,3,7,2] => 0
[[[[[.,.],.],[.,.]],[.,.]],.] => [6,4,1,2,3,5,7] => [1,4,5,6,3,7,2] => 0
[[[[[.,.],[.,.]],.],[.,.]],.] => [6,3,1,2,4,5,7] => [1,4,5,3,6,7,2] => 0
[[[[[.,[.,.]],.],.],[.,.]],.] => [6,2,1,3,4,5,7] => [1,4,3,5,6,7,2] => 0
[[[[[[.,.],.],.],.],[.,.]],.] => [6,1,2,3,4,5,7] => [1,3,4,5,6,7,2] => 0
[[[[[.,.],.],[.,[.,.]]],.],.] => [5,4,1,2,3,6,7] => [1,4,5,6,3,2,7] => 0
[[[[[.,.],.],[[.,.],.]],.],.] => [4,5,1,2,3,6,7] => [1,4,5,6,2,3,7] => 0
[[[[[.,.],[.,.]],[.,.]],.],.] => [5,3,1,2,4,6,7] => [1,4,5,3,6,2,7] => 0
[[[[[.,[.,.]],.],[.,.]],.],.] => [5,2,1,3,4,6,7] => [1,4,3,5,6,2,7] => 0
[[[[[[.,.],.],.],[.,.]],.],.] => [5,1,2,3,4,6,7] => [1,3,4,5,6,2,7] => 0
[[[[[.,.],[.,[.,.]]],.],.],.] => [4,3,1,2,5,6,7] => [1,4,5,3,2,6,7] => 0
[[[[[.,.],[[.,.],.]],.],.],.] => [3,4,1,2,5,6,7] => [1,4,5,2,3,6,7] => 0
[[[[[.,[.,.]],[.,.]],.],.],.] => [4,2,1,3,5,6,7] => [1,4,3,5,2,6,7] => 0
[[[[[[.,.],.],[.,.]],.],.],.] => [4,1,2,3,5,6,7] => [1,3,4,5,2,6,7] => 0
[[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7] => [1,4,3,2,5,6,7] => 0
[[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7] => [1,4,2,3,5,6,7] => 0
[[[[[[.,.],[.,.]],.],.],.],.] => [3,1,2,4,5,6,7] => [1,3,4,2,5,6,7] => 0
[[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7] => [1,3,2,4,5,6,7] => 0
[[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => 0
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1] => [8,7,1,2,3,4,5,6] => 0
[.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1] => [2,1,8,7,6,5,4,3] => 1
[[.,.],[[[[.,[.,.]],.],.],[.,.]]] => [8,4,3,5,6,7,1,2] => [8,6,5,4,3,1,2,7] => 0
[[.,[.,[.,.]]],[[[[.,.],.],.],.]] => [5,6,7,8,3,2,1,4] => [5,3,8,7,6,4,2,1] => 1
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]] => [8,6,4,3,2,1,5,7] => [8,5,7,4,3,2,6,1] => 0
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8] => [1,8,7,6,5,4,3,2] => 0
[[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8] => [1,2,3,4,5,6,7,8] => 0
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Description
The number of occurrences of the vincular pattern |21-3 in a permutation.
This is the number of occurrences of the pattern $213$, where the first matched entry is the first entry of the permutation and the other two matched entries are consecutive.
In other words, this is the number of ascents whose bottom value is strictly smaller and the top value is strictly larger than the first entry of the permutation.
Map
ones to leading
Description
The unique permutation obtained by applying the Foata-Riordan map to obtain a Prüfer code, then prepending zero and cyclically shifting.
Let $c_1,\dots, c_{n-1}$ be the Prüfer code obtained via the Foata-Riordan map described in [1, eq (1.2)] and let $c_0 = 0$.
This map returns the a unique permutation $q_1,\dots, q_n$ such that $q_i - c_{i-1}$ is constant modulo $n+1$.
This map is Mp00299ones to leading restricted to permutations.
Map
to 132-avoiding permutation
Description
Return a 132-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 maximal element of the Sylvester class.