Identifier
Values
[.,.] => [1,0] => [[1],[]] => 1
[.,[.,.]] => [1,0,1,0] => [[1,1],[]] => 1
[[.,.],.] => [1,1,0,0] => [[2],[]] => 1
[.,[.,[.,.]]] => [1,0,1,0,1,0] => [[1,1,1],[]] => 1
[.,[[.,.],.]] => [1,0,1,1,0,0] => [[2,1],[]] => 1
[[.,.],[.,.]] => [1,1,1,0,0,0] => [[2,2],[]] => 2
[[.,[.,.]],.] => [1,1,0,0,1,0] => [[2,2],[1]] => 1
[[[.,.],.],.] => [1,1,0,1,0,0] => [[3],[]] => 1
[.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => [[1,1,1,1],[]] => 1
[.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => [[2,1,1],[]] => 1
[.,[[.,.],[.,.]]] => [1,0,1,1,1,0,0,0] => [[2,2,1],[]] => 2
[.,[[.,[.,.]],.]] => [1,0,1,1,0,0,1,0] => [[2,2,1],[1]] => 1
[.,[[[.,.],.],.]] => [1,0,1,1,0,1,0,0] => [[3,1],[]] => 1
[[.,.],[.,[.,.]]] => [1,1,1,0,0,0,1,0] => [[2,2,2],[1]] => 2
[[.,.],[[.,.],.]] => [1,1,1,0,0,1,0,0] => [[3,2],[]] => 2
[[.,[.,.]],[.,.]] => [1,1,1,0,1,0,0,0] => [[2,2,2],[]] => 2
[[[.,.],.],[.,.]] => [1,1,1,1,0,0,0,0] => [[3,3],[]] => 2
[[.,[.,[.,.]]],.] => [1,1,0,0,1,0,1,0] => [[2,2,2],[1,1]] => 1
[[.,[[.,.],.]],.] => [1,1,0,0,1,1,0,0] => [[3,2],[1]] => 1
[[[.,.],[.,.]],.] => [1,1,0,1,1,0,0,0] => [[3,3],[1]] => 2
[[[.,[.,.]],.],.] => [1,1,0,1,0,0,1,0] => [[3,3],[2]] => 1
[[[[.,.],.],.],.] => [1,1,0,1,0,1,0,0] => [[4],[]] => 1
[.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1],[]] => 1
[.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1],[]] => 1
[.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1],[]] => 2
[.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1],[1]] => 1
[.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,0,1,0,0] => [[3,1,1],[]] => 1
[.,[[.,.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1],[1]] => 2
[.,[[.,.],[[.,.],.]]] => [1,0,1,1,1,0,0,1,0,0] => [[3,2,1],[]] => 2
[.,[[.,[.,.]],[.,.]]] => [1,0,1,1,1,0,1,0,0,0] => [[2,2,2,1],[]] => 2
[.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0] => [[3,3,1],[]] => 2
[.,[[.,[.,[.,.]]],.]] => [1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1],[1,1]] => 1
[.,[[.,[[.,.],.]],.]] => [1,0,1,1,0,0,1,1,0,0] => [[3,2,1],[1]] => 1
[.,[[[.,.],[.,.]],.]] => [1,0,1,1,0,1,1,0,0,0] => [[3,3,1],[1]] => 2
[.,[[[.,[.,.]],.],.]] => [1,0,1,1,0,1,0,0,1,0] => [[3,3,1],[2]] => 1
[.,[[[[.,.],.],.],.]] => [1,0,1,1,0,1,0,1,0,0] => [[4,1],[]] => 1
[[.,.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2],[1,1]] => 2
[[.,.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,1,0,0] => [[3,2,2],[1]] => 2
[[.,.],[[.,.],[.,.]]] => [1,1,1,0,0,1,1,0,0,0] => [[3,3,2],[1]] => 3
[[.,.],[[.,[.,.]],.]] => [1,1,1,0,0,1,0,0,1,0] => [[3,3,2],[2]] => 2
[[.,.],[[[.,.],.],.]] => [1,1,1,0,0,1,0,1,0,0] => [[4,2],[]] => 2
[[.,[.,.]],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0] => [[2,2,2,2],[1]] => 2
[[.,[.,.]],[[.,.],.]] => [1,1,1,0,1,0,0,1,0,0] => [[3,2,2],[]] => 2
[[[.,.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0] => [[3,3,3],[2]] => 2
[[[.,.],.],[[.,.],.]] => [1,1,1,1,0,0,0,1,0,0] => [[4,3],[]] => 2
[[.,[.,[.,[.,.]]]],.] => [1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2],[1,1,1]] => 1
[[.,[.,[[.,.],.]]],.] => [1,1,0,0,1,0,1,1,0,0] => [[3,2,2],[1,1]] => 1
[[.,[[.,.],[.,.]]],.] => [1,1,0,0,1,1,1,0,0,0] => [[3,3,2],[1,1]] => 2
[[.,[[.,[.,.]],.]],.] => [1,1,0,0,1,1,0,0,1,0] => [[3,3,2],[2,1]] => 1
[[.,[[[.,.],.],.]],.] => [1,1,0,0,1,1,0,1,0,0] => [[4,2],[1]] => 1
[[[.,.],[.,[.,.]]],.] => [1,1,0,1,1,0,0,0,1,0] => [[3,3,3],[2,1]] => 2
[[[.,.],[[.,.],.]],.] => [1,1,0,1,1,0,0,1,0,0] => [[4,3],[1]] => 2
[[[.,[.,.]],[.,.]],.] => [1,1,0,1,1,0,1,0,0,0] => [[3,3,3],[1,1]] => 2
[[[[.,.],.],[.,.]],.] => [1,1,0,1,1,1,0,0,0,0] => [[4,4],[1]] => 2
[[[.,[.,[.,.]]],.],.] => [1,1,0,1,0,0,1,0,1,0] => [[3,3,3],[2,2]] => 1
[[[.,[[.,.],.]],.],.] => [1,1,0,1,0,0,1,1,0,0] => [[4,3],[2]] => 1
[[[[.,.],[.,.]],.],.] => [1,1,0,1,0,1,1,0,0,0] => [[4,4],[2]] => 2
[[[[.,[.,.]],.],.],.] => [1,1,0,1,0,1,0,0,1,0] => [[4,4],[3]] => 1
[[[[[.,.],.],.],.],.] => [1,1,0,1,0,1,0,1,0,0] => [[5],[]] => 1
[.,[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1],[]] => 1
[.,[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1],[]] => 1
[.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[2,2,1,1,1],[]] => 2
[.,[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1],[1]] => 1
[.,[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1],[]] => 1
[.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [[2,2,2,1,1],[1]] => 2
[.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [[3,2,1,1],[]] => 2
[.,[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1],[1,1]] => 1
[.,[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1],[1]] => 1
[.,[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [[3,3,1,1],[1]] => 2
[.,[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1],[2]] => 1
[.,[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1],[]] => 1
[.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [[2,2,2,2,1],[1,1]] => 2
[.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [[3,2,2,1],[1]] => 2
[.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [[3,3,2,1],[2]] => 2
[.,[[.,.],[[[.,.],.],.]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[4,2,1],[]] => 2
[.,[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1],[1,1,1]] => 1
[.,[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1],[1,1]] => 1
[.,[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [[3,3,2,1],[1,1]] => 2
[.,[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1],[2,1]] => 1
[.,[[.,[[[.,.],.],.]],.]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1],[1]] => 1
[.,[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [[3,3,3,1],[2,1]] => 2
[.,[[[.,.],[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [[4,3,1],[1]] => 2
[.,[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1],[2,2]] => 1
[.,[[[.,[[.,.],.]],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1],[2]] => 1
[.,[[[[.,.],[.,.]],.],.]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [[4,4,1],[2]] => 2
[.,[[[[.,[.,.]],.],.],.]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1],[3]] => 1
[.,[[[[[.,.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1],[]] => 1
[[.,.],[.,[.,[.,[.,.]]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1]] => 2
[[.,.],[.,[.,[[.,.],.]]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1]] => 2
[[.,.],[.,[[.,[.,.]],.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1]] => 2
[[.,.],[.,[[[.,.],.],.]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [[4,2,2],[1]] => 2
[[.,.],[[.,[.,[.,.]]],.]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2]] => 2
[[.,.],[[.,[[.,.],.]],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [[4,3,2],[2]] => 2
[[.,.],[[[.,[.,.]],.],.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [[4,4,2],[3]] => 2
[[.,.],[[[[.,.],.],.],.]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [[5,2],[]] => 2
[[.,[.,[.,[.,[.,.]]]]],.] => [1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2],[1,1,1,1]] => 1
[[.,[.,[.,[[.,.],.]]]],.] => [1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2],[1,1,1]] => 1
[[.,[.,[[.,.],[.,.]]]],.] => [1,1,0,0,1,0,1,1,1,0,0,0] => [[3,3,2,2],[1,1,1]] => 2
[[.,[.,[[.,[.,.]],.]]],.] => [1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2],[2,1,1]] => 1
[[.,[.,[[[.,.],.],.]]],.] => [1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2],[1,1]] => 1
[[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,0,1,1,1,0,0,0,1,0] => [[3,3,3,2],[2,1,1]] => 2
>>> Load all 187 entries. <<<
[[.,[[.,.],[[.,.],.]]],.] => [1,1,0,0,1,1,1,0,0,1,0,0] => [[4,3,2],[1,1]] => 2
[[.,[[.,[.,[.,.]]],.]],.] => [1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2],[2,2,1]] => 1
[[.,[[.,[[.,.],.]],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2],[2,1]] => 1
[[.,[[[.,.],[.,.]],.]],.] => [1,1,0,0,1,1,0,1,1,0,0,0] => [[4,4,2],[2,1]] => 2
[[.,[[[.,[.,.]],.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2],[3,1]] => 1
[[.,[[[[.,.],.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2],[1]] => 1
[[[.,.],[.,[.,[.,.]]]],.] => [1,1,0,1,1,0,0,0,1,0,1,0] => [[3,3,3,3],[2,2,1]] => 2
[[[.,.],[.,[[.,.],.]]],.] => [1,1,0,1,1,0,0,0,1,1,0,0] => [[4,3,3],[2,1]] => 2
[[[.,.],[[.,[.,.]],.]],.] => [1,1,0,1,1,0,0,1,0,0,1,0] => [[4,4,3],[3,1]] => 2
[[[.,.],[[[.,.],.],.]],.] => [1,1,0,1,1,0,0,1,0,1,0,0] => [[5,3],[1]] => 2
[[[.,[.,[.,[.,.]]]],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3],[2,2,2]] => 1
[[[.,[.,[[.,.],.]]],.],.] => [1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3],[2,2]] => 1
[[[.,[[.,.],[.,.]]],.],.] => [1,1,0,1,0,0,1,1,1,0,0,0] => [[4,4,3],[2,2]] => 2
[[[.,[[.,[.,.]],.]],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3],[3,2]] => 1
[[[.,[[[.,.],.],.]],.],.] => [1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3],[2]] => 1
[[[[.,.],[.,[.,.]]],.],.] => [1,1,0,1,0,1,1,0,0,0,1,0] => [[4,4,4],[3,2]] => 2
[[[[.,.],[[.,.],.]],.],.] => [1,1,0,1,0,1,1,0,0,1,0,0] => [[5,4],[2]] => 2
[[[[.,[.,[.,.]]],.],.],.] => [1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4],[3,3]] => 1
[[[[.,[[.,.],.]],.],.],.] => [1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4],[3]] => 1
[[[[[.,.],[.,.]],.],.],.] => [1,1,0,1,0,1,0,1,1,0,0,0] => [[5,5],[3]] => 2
[[[[[.,[.,.]],.],.],.],.] => [1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5],[4]] => 1
[[[[[[.,.],.],.],.],.],.] => [1,1,0,1,0,1,0,1,0,1,0,0] => [[6],[]] => 1
[.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,1,1,1,1,1,1],[]] => 1
[.,[.,[.,[.,[.,[[.,.],.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[2,1,1,1,1,1],[]] => 1
[.,[.,[.,[.,[[.,[.,.]],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [[2,2,1,1,1,1],[1]] => 1
[.,[.,[.,[.,[[[.,.],.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[3,1,1,1,1],[]] => 1
[.,[.,[.,[[.,[.,[.,.]]],.]]]] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [[2,2,2,1,1,1],[1,1]] => 1
[.,[.,[.,[[.,[[.,.],.]],.]]]] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [[3,2,1,1,1],[1]] => 1
[.,[.,[.,[[[.,[.,.]],.],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [[3,3,1,1,1],[2]] => 1
[.,[.,[.,[[[[.,.],.],.],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[4,1,1,1],[]] => 1
[.,[.,[[.,[.,[.,[.,.]]]],.]]] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [[2,2,2,2,1,1],[1,1,1]] => 1
[.,[.,[[.,[.,[[.,.],.]]],.]]] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [[3,2,2,1,1],[1,1]] => 1
[.,[.,[[.,[[.,[.,.]],.]],.]]] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [[3,3,2,1,1],[2,1]] => 1
[.,[.,[[.,[[[.,.],.],.]],.]]] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [[4,2,1,1],[1]] => 1
[.,[.,[[[.,[.,[.,.]]],.],.]]] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [[3,3,3,1,1],[2,2]] => 1
[.,[.,[[[.,[[.,.],.]],.],.]]] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [[4,3,1,1],[2]] => 1
[.,[.,[[[[.,[.,.]],.],.],.]]] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [[4,4,1,1],[3]] => 1
[.,[.,[[[[[.,.],.],.],.],.]]] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[5,1,1],[]] => 1
[.,[[.,[.,[.,[.,[.,.]]]]],.]] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,1],[1,1,1,1]] => 1
[.,[[.,[.,[.,[[.,.],.]]]],.]] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,1],[1,1,1]] => 1
[.,[[.,[.,[[.,[.,.]],.]]],.]] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,1],[2,1,1]] => 1
[.,[[.,[.,[[[.,.],.],.]]],.]] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [[4,2,2,1],[1,1]] => 1
[.,[[.,[[.,[.,[.,.]]],.]],.]] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,1],[2,2,1]] => 1
[.,[[.,[[.,[[.,.],.]],.]],.]] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [[4,3,2,1],[2,1]] => 1
[.,[[.,[[[.,[.,.]],.],.]],.]] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [[4,4,2,1],[3,1]] => 1
[.,[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [[5,2,1],[1]] => 1
[.,[[[.,[.,[.,[.,.]]]],.],.]] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,1],[2,2,2]] => 1
[.,[[[.,[.,[[.,.],.]]],.],.]] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [[4,3,3,1],[2,2]] => 1
[.,[[[.,[[.,[.,.]],.]],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [[4,4,3,1],[3,2]] => 1
[.,[[[.,[[[.,.],.],.]],.],.]] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [[5,3,1],[2]] => 1
[.,[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [[4,4,4,1],[3,3]] => 1
[.,[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [[5,4,1],[3]] => 1
[.,[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [[5,5,1],[4]] => 1
[.,[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[6,1],[]] => 1
[[.,[.,[.,[.,[.,[.,.]]]]]],.] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [[2,2,2,2,2,2],[1,1,1,1,1]] => 1
[[.,[.,[.,[.,[[.,.],.]]]]],.] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[3,2,2,2,2],[1,1,1,1]] => 1
[[.,[.,[.,[[.,[.,.]],.]]]],.] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [[3,3,2,2,2],[2,1,1,1]] => 1
[[.,[.,[.,[[[.,.],.],.]]]],.] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[4,2,2,2],[1,1,1]] => 1
[[.,[.,[[.,[.,[.,.]]],.]]],.] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [[3,3,3,2,2],[2,2,1,1]] => 1
[[.,[.,[[.,[[.,.],.]],.]]],.] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[4,3,2,2],[2,1,1]] => 1
[[.,[.,[[[.,[.,.]],.],.]]],.] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [[4,4,2,2],[3,1,1]] => 1
[[.,[.,[[[[.,.],.],.],.]]],.] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[5,2,2],[1,1]] => 1
[[.,[[.,[.,[.,[.,.]]]],.]],.] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [[3,3,3,3,2],[2,2,2,1]] => 1
[[.,[[.,[.,[[.,.],.]]],.]],.] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[4,3,3,2],[2,2,1]] => 1
[[.,[[.,[[.,[.,.]],.]],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [[4,4,3,2],[3,2,1]] => 1
[[.,[[.,[[[.,.],.],.]],.]],.] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[5,3,2],[2,1]] => 1
[[.,[[[.,[.,[.,.]]],.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [[4,4,4,2],[3,3,1]] => 1
[[.,[[[.,[[.,.],.]],.],.]],.] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[5,4,2],[3,1]] => 1
[[.,[[[[.,[.,.]],.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [[5,5,2],[4,1]] => 1
[[.,[[[[[.,.],.],.],.],.]],.] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [[6,2],[1]] => 1
[[[.,[.,[.,[.,[.,.]]]]],.],.] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [[3,3,3,3,3],[2,2,2,2]] => 1
[[[.,[.,[.,[[.,.],.]]]],.],.] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[4,3,3,3],[2,2,2]] => 1
[[[.,[.,[[.,[.,.]],.]]],.],.] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [[4,4,3,3],[3,2,2]] => 1
[[[.,[.,[[[.,.],.],.]]],.],.] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[5,3,3],[2,2]] => 1
[[[.,[[.,[.,[.,.]]],.]],.],.] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [[4,4,4,3],[3,3,2]] => 1
[[[.,[[.,[[.,.],.]],.]],.],.] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[5,4,3],[3,2]] => 1
[[[.,[[[.,[.,.]],.],.]],.],.] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [[5,5,3],[4,2]] => 1
[[[.,[[[[.,.],.],.],.]],.],.] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [[6,3],[2]] => 1
[[[[.,[.,[.,[.,.]]]],.],.],.] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [[4,4,4,4],[3,3,3]] => 1
[[[[.,[.,[[.,.],.]]],.],.],.] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[5,4,4],[3,3]] => 1
[[[[.,[[.,[.,.]],.]],.],.],.] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [[5,5,4],[4,3]] => 1
[[[[.,[[[.,.],.],.]],.],.],.] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [[6,4],[3]] => 1
[[[[[.,[.,[.,.]]],.],.],.],.] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [[5,5,5],[4,4]] => 1
[[[[[.,[[.,.],.]],.],.],.],.] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [[6,5],[4]] => 1
[[[[[[.,[.,.]],.],.],.],.],.] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [[6,6],[5]] => 1
[[[[[[[.,.],.],.],.],.],.],.] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[7],[]] => 1
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Description
The Frobenius rank of a skew partition.
This is the minimal number of border strips in a border strip decomposition of the skew partition.
Map
skew partition
Description
The parallelogram polyomino corresponding to a Dyck path, interpreted as a skew partition.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
This map returns the skew partition definded by the diagram of $\gamma(D)$.
Map
pruning number to logarithmic height
Description
Francon's map from binary trees to Dyck paths.
This bijection sends the pruning number of the binary tree, St000396The register function (or Horton-Strahler number) of a binary tree., to the logarithmic height of the Dyck path, St000920The logarithmic height of a Dyck path.. The implementation is a literal translation of Knuth's [2].