Identifier
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00034: Dyck paths —to binary tree: up step, left tree, down step, right tree⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Images
[1] => [1,0] => [.,.] => [1]
[2] => [1,0,1,0] => [.,[.,.]] => [2,1]
[1,1] => [1,1,0,0] => [[.,.],.] => [1,2]
[3] => [1,0,1,0,1,0] => [.,[.,[.,.]]] => [3,2,1]
[2,1] => [1,0,1,1,0,0] => [.,[[.,.],.]] => [2,3,1]
[1,1,1] => [1,1,0,1,0,0] => [[.,[.,.]],.] => [2,1,3]
[4] => [1,0,1,0,1,0,1,0] => [.,[.,[.,[.,.]]]] => [4,3,2,1]
[3,1] => [1,0,1,0,1,1,0,0] => [.,[.,[[.,.],.]]] => [3,4,2,1]
[2,2] => [1,1,1,0,0,0] => [[[.,.],.],.] => [1,2,3]
[2,1,1] => [1,0,1,1,0,1,0,0] => [.,[[.,[.,.]],.]] => [3,2,4,1]
[1,1,1,1] => [1,1,0,1,0,1,0,0] => [[.,[.,[.,.]]],.] => [3,2,1,4]
[5] => [1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1]
[4,1] => [1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1]
[3,2] => [1,0,1,1,1,0,0,0] => [.,[[[.,.],.],.]] => [2,3,4,1]
[3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1]
[2,2,1] => [1,1,1,0,0,1,0,0] => [[[.,.],[.,.]],.] => [1,3,2,4]
[2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1]
[1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5]
[6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1]
[5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1]
[4,2] => [1,0,1,0,1,1,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1]
[4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1]
[3,3] => [1,1,1,0,1,0,0,0] => [[[.,[.,.]],.],.] => [2,1,3,4]
[3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [.,[[[.,.],[.,.]],.]] => [2,4,3,5,1]
[3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1]
[2,2,2] => [1,1,1,1,0,0,0,0] => [[[[.,.],.],.],.] => [1,2,3,4]
[2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [[[.,.],[.,[.,.]]],.] => [1,4,3,2,5]
[2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1]
[1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6]
[7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1]
[6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1]
[5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1]
[5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => [6,5,7,4,3,2,1]
[4,3] => [1,0,1,1,1,0,1,0,0,0] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1]
[4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1]
[4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1]
[3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [[[.,[.,.]],[.,.]],.] => [2,1,4,3,5]
[3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1]
[3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1]
[3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => [6,5,4,3,7,2,1]
[2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [[[[.,.],.],[.,.]],.] => [1,2,4,3,5]
[2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6]
[2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1]
[1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,.]]]]]],.] => [6,5,4,3,2,1,7]
[8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1]
[7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1]
[6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1]
[6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [7,6,8,5,4,3,2,1]
[5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1]
[5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => [4,6,5,7,3,2,1]
[5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]] => [7,6,5,8,4,3,2,1]
[4,4] => [1,1,1,0,1,0,1,0,0,0] => [[[.,[.,[.,.]]],.],.] => [3,2,1,4,5]
[4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1]
[4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1]
[4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => [3,6,5,4,7,2,1]
[4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1]
[3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [[[.,[[.,.],.]],.],.] => [2,3,1,4,5]
[3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6]
[3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1]
[3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,[.,.]]]],.]] => [2,6,5,4,3,7,1]
[3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]] => [7,6,5,4,3,8,2,1]
[2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [[[[.,[.,.]],.],.],.] => [2,1,3,4,5]
[2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6]
[2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,.]]]]],.] => [1,6,5,4,3,2,7]
[2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1]
[1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [7,6,5,4,3,2,1,8]
[9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1]
[8,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1]
[7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1]
[7,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]] => [8,7,9,6,5,4,3,2,1]
[6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1]
[6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[.,[[[.,.],[.,.]],.]]]]] => [5,7,6,8,4,3,2,1]
[6,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]] => [8,7,6,9,5,4,3,2,1]
[5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1]
[5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => [4,3,6,5,7,2,1]
[5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1]
[5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[.,[[[.,.],[.,[.,.]]],.]]]] => [4,7,6,5,8,3,2,1]
[5,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]] => [8,7,6,5,9,4,3,2,1]
[4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6]
[4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1]
[4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => [3,2,6,5,4,7,1]
[4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [.,[.,[[[[.,.],.],[.,.]],.]]] => [3,4,6,5,7,2,1]
[4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [.,[.,[[[.,.],[.,[.,[.,.]]]],.]]] => [3,7,6,5,4,8,2,1]
[4,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]] => [8,7,6,5,4,9,3,2,1]
[3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5]
[3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6]
[3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,[.,.]]]],.] => [2,1,6,5,4,3,7]
[3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1]
[3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[[.,.],.],[.,[.,.]]],.]] => [2,3,6,5,4,7,1]
[3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,[.,[.,.]]]]],.]] => [2,7,6,5,4,3,8,1]
[3,1,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]] => [8,7,6,5,4,3,9,2,1]
[2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6]
[2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,[.,.]]]],.] => [1,2,6,5,4,3,7]
[2,2,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,7,6,5,4,3,2,8]
[2,1,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1]
[1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [8,7,6,5,4,3,2,1,9]
[10] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1]
[9,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1]
[8,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1]
[8,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]] => [9,8,10,7,6,5,4,3,2,1]
[7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [.,[.,[.,[.,[[[.,[.,.]],.],.]]]]] => [6,5,7,8,4,3,2,1]
>>> Load all 335 entries. <<<
[7,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]] => [6,8,7,9,5,4,3,2,1]
[7,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]] => [9,8,7,10,6,5,4,3,2,1]
[6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => [5,4,3,6,7,2,1]
[6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [.,[.,[.,[[[.,[.,.]],[.,.]],.]]]] => [5,4,7,6,8,3,2,1]
[6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1]
[6,2,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]] => [5,8,7,6,9,4,3,2,1]
[6,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]] => [9,8,7,6,10,5,4,3,2,1]
[5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6]
[5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => [4,3,2,6,5,7,1]
[5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[[.,.],.]],.],.]]] => [4,5,3,6,7,2,1]
[5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [.,[.,[[[.,[.,.]],[.,[.,.]]],.]]] => [4,3,7,6,5,8,2,1]
[5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [.,[.,[.,[[[[.,.],.],[.,.]],.]]]] => [4,5,7,6,8,3,2,1]
[5,2,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]] => [4,8,7,6,5,9,3,2,1]
[5,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]] => [9,8,7,6,5,10,4,3,2,1]
[4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6]
[4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,[.,.]]],[.,[.,.]]],.] => [3,2,1,6,5,4,7]
[4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1]
[4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,[[.,.],.]],[.,.]],.]] => [3,4,2,6,5,7,1]
[4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[.,[.,.]],[.,[.,[.,.]]]],.]] => [3,2,7,6,5,4,8,1]
[4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [.,[.,[[[[.,[.,.]],.],.],.]]] => [4,3,5,6,7,2,1]
[4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [.,[.,[[[[.,.],.],[.,[.,.]]],.]]] => [3,4,7,6,5,8,2,1]
[4,2,1,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]] => [3,8,7,6,5,4,9,2,1]
[4,1,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]] => [9,8,7,6,5,4,10,3,2,1]
[3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6]
[3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6]
[3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[[.,[[.,.],.]],[.,[.,.]]],.] => [2,3,1,6,5,4,7]
[3,3,1,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,[.,[.,.]]]]],.] => [2,1,7,6,5,4,3,8]
[3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,.]],.]] => [3,2,4,6,5,7,1]
[3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => [2,3,7,6,5,4,8,1]
[3,2,1,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]] => [2,8,7,6,5,4,3,9,1]
[3,1,1,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]] => [9,8,7,6,5,4,3,10,2,1]
[2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,.]]],.],.],.] => [3,2,1,4,5,6]
[2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[[[.,[.,.]],.],[.,[.,.]]],.] => [2,1,3,6,5,4,7]
[2,2,2,1,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,[.,[.,.]]]]],.] => [1,2,7,6,5,4,3,8]
[2,2,1,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.] => [1,8,7,6,5,4,3,2,9]
[2,1,1,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]] => [9,8,7,6,5,4,3,2,10,1]
[1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.] => [9,8,7,6,5,4,3,2,1,10]
[10,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]] => [10,11,9,8,7,6,5,4,3,2,1]
[9,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1]
[9,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]] => [10,9,11,8,7,6,5,4,3,2,1]
[7,4] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1]
[7,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1]
[6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1]
[6,4,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [.,[.,[[[.,[.,[.,.]]],[.,.]],.]]] => [5,4,3,7,6,8,2,1]
[6,3,2] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1]
[5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,.]]]],[.,.]],.] => [4,3,2,1,6,5,7]
[5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1]
[5,4,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,.]]],[.,[.,.]]],.]] => [4,3,2,7,6,5,8,1]
[5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1]
[5,3,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [.,[.,[[[.,[[.,.],.]],[.,.]],.]]] => [4,5,3,7,6,8,2,1]
[5,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1]
[4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6]
[4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[[.,[.,[[.,.],.]]],[.,.]],.] => [3,4,2,1,6,5,7]
[4,4,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [[[.,[.,[.,.]]],[.,[.,[.,.]]]],.] => [3,2,1,7,6,5,4,8]
[4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [.,[[[[[.,.],.],.],[.,.]],.]] => [2,3,4,6,5,7,1]
[4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [4,3,5,2,6,7,1]
[4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],.]],[.,[.,.]]],.]] => [3,4,2,7,6,5,8,1]
[4,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [.,[.,[[[[.,[.,.]],.],[.,.]],.]]] => [4,3,5,7,6,8,2,1]
[3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [[[[[.,.],[.,.]],.],.],.] => [1,3,2,4,5,6]
[3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[[[[.,.],.],.],[.,[.,.]]],.] => [1,2,3,6,5,4,7]
[3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,.]],.] => [3,2,4,1,6,5,7]
[3,3,2,1,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [[[.,[[.,.],.]],[.,[.,[.,.]]]],.] => [2,3,1,7,6,5,4,8]
[3,3,1,1,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.] => [2,1,8,7,6,5,4,3,9]
[3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1]
[3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[[.,[.,.]],.],[.,[.,.]]],.]] => [3,2,4,7,6,5,8,1]
[2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[[[.,[.,[.,.]]],.],[.,.]],.] => [3,2,1,4,6,5,7]
[2,2,2,2,1,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [[[[.,[.,.]],.],[.,[.,[.,.]]]],.] => [2,1,3,7,6,5,4,8]
[2,2,2,1,1,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.] => [1,2,8,7,6,5,4,3,9]
[2,2,1,1,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.] => [1,9,8,7,6,5,4,3,2,10]
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.] => [10,9,8,7,6,5,4,3,2,1,11]
[10,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]] => [9,10,11,8,7,6,5,4,3,2,1]
[8,2,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1]
[7,5] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,[.,.]]]],.],.]]] => [6,5,4,3,7,8,2,1]
[6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,.]]]]],.],.] => [5,4,3,2,1,6,7]
[6,5,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,[.,[.,[.,.]]]],[.,.]],.]] => [5,4,3,2,7,6,8,1]
[6,4,2] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,[.,[[.,.],.]]],.],.]]] => [5,6,4,3,7,8,2,1]
[6,4,1,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]] => [5,4,3,8,7,6,9,2,1]
[6,3,3] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1]
[5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[.,[[.,.],.]]]],.],.] => [4,5,3,2,1,6,7]
[5,5,1,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,[.,[.,.]]]],[.,[.,.]]],.] => [4,3,2,1,7,6,5,8]
[5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1]
[5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [.,[[[.,[.,[[.,.],.]]],[.,.]],.]] => [4,5,3,2,7,6,8,1]
[5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [.,[.,[[[[[.,.],.],.],[.,.]],.]]] => [3,4,5,7,6,8,2,1]
[5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[[.,[[.,[.,.]],.]],.],.]]] => [5,4,6,3,7,8,2,1]
[4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[.,[.,.]],.],.],.],.] => [2,1,3,4,5,6]
[4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[[.,[[[.,.],.],.]],[.,.]],.] => [2,3,4,1,6,5,7]
[4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[[.,[.,[[.,[.,.]],.]]],.],.] => [4,3,5,2,1,6,7]
[4,4,2,1,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [[[.,[.,[[.,.],.]]],[.,[.,.]]],.] => [3,4,2,1,7,6,5,8]
[4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [.,[[[[[.,.],[.,.]],.],.],.]] => [2,4,3,5,6,7,1]
[4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => [2,3,4,7,6,5,8,1]
[4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[[.,[[.,[.,.]],.]],[.,.]],.]] => [4,3,5,2,7,6,8,1]
[4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[[[.,[.,[.,.]]],.],.],.]]] => [5,4,3,6,7,8,2,1]
[3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6]
[3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[[[[.,.],[.,.]],.],[.,.]],.] => [1,3,2,4,6,5,7]
[3,3,3,1,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],[.,[.,[.,.]]]],.] => [1,2,3,7,6,5,4,8]
[3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[[.,[[.,[.,[.,.]]],.]],.],.] => [4,3,2,5,1,6,7]
[3,3,2,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [[[.,[[.,[.,.]],.]],[.,[.,.]]],.] => [3,2,4,1,7,6,5,8]
[3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [.,[[[[.,[.,[.,.]]],.],[.,.]],.]] => [4,3,2,5,7,6,8,1]
[2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,[.,.]]]],.],.],.] => [4,3,2,1,5,6,7]
[2,2,2,2,2,1,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [[[[.,[.,[.,.]]],.],[.,[.,.]]],.] => [3,2,1,4,7,6,5,8]
[9,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [.,[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]] => [8,7,6,9,10,5,4,3,2,1]
[7,6] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1]
[7,3,3] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1]
[7,2,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [.,[.,[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]]] => [7,6,8,9,10,5,4,3,2,1]
[6,6,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,.]],.] => [5,4,3,2,1,7,6,8]
[6,5,2] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[[[.,[.,[.,[[.,.],.]]]],.],.]] => [5,6,4,3,2,7,8,1]
[6,4,3] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[.,[[[.,.],.],.]],.],.]]] => [4,5,6,3,7,8,2,1]
[5,5,3] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[[.,[.,[[[.,.],.],.]]],.],.] => [3,4,5,2,1,6,7]
[5,5,2,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [[[.,[.,[.,[[.,.],.]]]],[.,.]],.] => [4,5,3,2,1,7,6,8]
[5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1]
[5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[[.,[[[.,.],.],.]],[.,.]],.]] => [3,4,5,2,7,6,8,1]
[5,4,2,2] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1]
[5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[[[[.,.],[.,.]],.],.],.]]] => [3,5,4,6,7,8,2,1]
[4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[[[[.,[.,.]],.],.],[.,.]],.] => [2,1,3,4,6,5,7]
[4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[[.,[[[.,.],[.,.]],.]],.],.] => [2,4,3,5,1,6,7]
[4,4,3,1,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [[[.,[[[.,.],.],.]],[.,[.,.]]],.] => [2,3,4,1,7,6,5,8]
[4,4,2,2,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [[[.,[.,[[.,[.,.]],.]]],[.,.]],.] => [4,3,5,2,1,7,6,8]
[4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1]
[4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => [2,4,3,5,7,6,8,1]
[4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[[[.,[[.,[.,[.,.]]],.]],.],.]] => [5,4,3,6,2,7,8,1]
[3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[.,.],.],.],.],[.,.]],.] => [1,2,3,4,6,5,7]
[3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[[[[.,.],[.,[.,.]]],.],.],.] => [1,4,3,2,5,6,7]
[3,3,3,2,1,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [[[[[.,.],[.,.]],.],[.,[.,.]]],.] => [1,3,2,4,7,6,5,8]
[3,3,3,1,1,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.] => [1,2,3,8,7,6,5,4,9]
[3,3,2,2,2,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [[[.,[[.,[.,[.,.]]],.]],[.,.]],.] => [4,3,2,5,1,7,6,8]
[3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1]
[2,2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [[[[.,[.,[.,[.,.]]]],.],[.,.]],.] => [4,3,2,1,5,7,6,8]
[8,6] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]] => [7,6,5,4,3,8,9,2,1]
[8,3,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1]
[7,7] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],.],.] => [6,5,4,3,2,1,7,8]
[7,6,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]] => [6,5,4,3,2,8,7,9,1]
[6,6,2] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[.,[.,[[.,.],.]]]]],.],.] => [5,6,4,3,2,1,7,8]
[6,6,1,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.] => [5,4,3,2,1,8,7,6,9]
[6,5,3] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1]
[6,4,4] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[[[[.,[.,.]],.],.],.],.]]] => [4,3,5,6,7,8,2,1]
[5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[[.,[[[.,[.,.]],.],.]],.],.] => [3,2,4,5,1,6,7]
[5,5,3,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [[[.,[.,[[[.,.],.],.]]],[.,.]],.] => [3,4,5,2,1,7,6,8]
[5,5,2,2] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [[[.,[.,[.,[[.,[.,.]],.]]]],.],.] => [5,4,6,3,2,1,7,8]
[5,5,1,1,1,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]],.] => [4,3,2,1,9,8,7,6,5,10]
[5,4,4,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[[[[.,[.,.]],.],.],[.,.]],.]] => [3,2,4,5,7,6,8,1]
[5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[[[.,[[[.,.],[.,.]],.]],.],.]] => [3,5,4,6,2,7,8,1]
[5,3,3,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1]
[4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[[[[.,[.,.]],[.,.]],.],.],.] => [2,1,4,3,5,6,7]
[4,4,4,1,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [[[[[.,[.,.]],.],.],[.,[.,.]]],.] => [2,1,3,4,7,6,5,8]
[4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[[.,[[[[.,.],.],.],.]],.],.] => [2,3,4,5,1,6,7]
[4,4,3,2,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [[[.,[[[.,.],[.,.]],.]],[.,.]],.] => [2,4,3,5,1,7,6,8]
[4,4,2,2,2] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [[[.,[.,[[.,[.,[.,.]]],.]]],.],.] => [5,4,3,6,2,1,7,8]
[4,3,3,3,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => [2,3,4,5,7,6,8,1]
[4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => [2,5,4,3,6,7,8,1]
[3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[[[[[.,.],.],[.,.]],.],.],.] => [1,2,4,3,5,6,7]
[3,3,3,3,1,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [[[[[[.,.],.],.],.],[.,[.,.]]],.] => [1,2,3,4,7,6,5,8]
[3,3,3,2,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [[[[[.,.],[.,[.,.]]],.],[.,.]],.] => [1,4,3,2,5,7,6,8]
[3,3,2,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [[[.,[[.,[.,[.,[.,.]]]],.]],.],.] => [5,4,3,2,6,1,7,8]
[2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,[.,[.,.]]]]],.],.],.] => [5,4,3,2,1,6,7,8]
[8,7] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]] => [7,6,5,4,3,2,8,9,1]
[7,7,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.] => [6,5,4,3,2,1,8,7,9]
[6,6,3] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [[[.,[.,[.,[[[.,.],.],.]]]],.],.] => [4,5,6,3,2,1,7,8]
[6,5,4] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[[[.,[[[.,[.,.]],.],.]],.],.]] => [4,3,5,6,2,7,8,1]
[6,3,3,3] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1]
[5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[[[[.,[.,[.,.]]],.],.],.],.] => [3,2,1,4,5,6,7]
[5,5,4,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [[[.,[[[.,[.,.]],.],.]],[.,.]],.] => [3,2,4,5,1,7,6,8]
[5,5,3,2] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [[[.,[.,[[[.,.],[.,.]],.]]],.],.] => [3,5,4,6,2,1,7,8]
[5,4,4,2] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[[[[[.,[.,.]],[.,.]],.],.],.]] => [3,2,5,4,6,7,8,1]
[5,4,3,3] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1]
[5,4,3,2,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[[.,[[[.,.],[.,.]],.]],[.,.]],.]] => [3,5,4,6,2,8,7,9,1]
[4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[[[[.,[[.,.],.]],.],.],.],.] => [2,3,1,4,5,6,7]
[4,4,4,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [[[[[.,[.,.]],[.,.]],.],[.,.]],.] => [2,1,4,3,5,7,6,8]
[4,4,3,3,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [[[.,[[[[.,.],.],.],.]],[.,.]],.] => [2,3,4,5,1,7,6,8]
[4,4,3,2,2] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [[[.,[[[.,.],[.,[.,.]]],.]],.],.] => [2,5,4,3,6,1,7,8]
[4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => [2,3,5,4,6,7,8,1]
[3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[[[[.,[.,.]],.],.],.],.],.] => [2,1,3,4,5,6,7]
[3,3,3,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [[[[[[.,.],.],[.,.]],.],[.,.]],.] => [1,2,4,3,5,7,6,8]
[3,3,3,3,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0] => [[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.] => [1,2,3,4,8,7,6,5,9]
[3,3,3,2,2,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [[[[[.,.],[.,[.,[.,.]]]],.],.],.] => [1,5,4,3,2,6,7,8]
[3,2,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [6,5,4,3,2,7,8,9,1]
[8,8] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.] => [7,6,5,4,3,2,1,8,9]
[7,7,2] => [1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => [6,7,5,4,3,2,1,8,9]
[7,3,3,3] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1]
[6,6,4] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [[[.,[.,[[[.,[.,.]],.],.]]],.],.] => [4,3,5,6,2,1,7,8]
[6,5,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1]
[5,5,5,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [[[[[.,[.,[.,.]]],.],.],[.,.]],.] => [3,2,1,4,5,7,6,8]
[5,5,4,2] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [[[.,[[[.,[.,.]],[.,.]],.]],.],.] => [3,2,5,4,6,1,7,8]
[5,5,3,3] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [[[.,[.,[[[[.,.],.],.],.]]],.],.] => [3,4,5,6,2,1,7,8]
[5,4,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1]
[4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7]
[4,4,4,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [[[[[.,[[.,.],.]],.],.],[.,.]],.] => [2,3,1,4,5,7,6,8]
[4,4,4,2,2] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [[[[[.,[.,.]],[.,[.,.]]],.],.],.] => [2,1,5,4,3,6,7,8]
[4,4,3,3,2] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [[[.,[[[[.,.],.],[.,.]],.]],.],.] => [2,3,5,4,6,1,7,8]
[4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1]
[4,3,3,2,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [.,[[[[[.,.],[.,[.,[.,.]]]],.],.],.]] => [2,6,5,4,3,7,8,9,1]
[3,3,3,3,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [[[[[[.,[.,.]],.],.],.],[.,.]],.] => [2,1,3,4,5,7,6,8]
[3,3,3,3,2,2] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [[[[[[.,.],.],[.,[.,.]]],.],.],.] => [1,2,5,4,3,6,7,8]
[2,2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.] => [6,5,4,3,2,1,7,8,9]
[9,8] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]] => [8,7,6,5,4,3,2,9,10,1]
[8,8,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.] => [7,6,5,4,3,2,1,9,8,10]
[7,7,3] => [1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [[[.,[.,[.,[.,[[[.,.],.],.]]]]],.],.] => [5,6,7,4,3,2,1,8,9]
[6,6,5] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [[[.,[[[.,[.,[.,.]]],.],.]],.],.] => [4,3,2,5,6,1,7,8]
[5,5,5,2] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [[[[[.,[.,[.,.]]],[.,.]],.],.],.] => [3,2,1,5,4,6,7,8]
[5,5,4,3] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [[[.,[[[.,[[.,.],.]],.],.]],.],.] => [3,4,2,5,6,1,7,8]
[5,4,4,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1]
[4,4,4,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [[[[[[[.,.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,7,6,8]
[4,4,4,3,2] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [[[[[.,[[.,.],.]],[.,.]],.],.],.] => [2,3,1,5,4,6,7,8]
[4,4,3,3,3] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [[[.,[[[[.,[.,.]],.],.],.]],.],.] => [3,2,4,5,6,1,7,8]
[3,3,3,3,3,2] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [[[[[[.,[.,.]],.],[.,.]],.],.],.] => [2,1,3,5,4,6,7,8]
[3,3,3,2,2,2,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.] => [1,6,5,4,3,2,7,8,9]
[3,2,2,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]] => [7,6,5,4,3,2,8,9,10,1]
[6,5,4,2,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]] => [4,3,6,5,7,2,9,8,10,1]
[6,5,4,3,3,2,1] => [1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => [.,[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],.]] => [5,4,6,3,8,7,9,2,11,10,12,1]
[4,4,4,4,3,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [[[[[[[.,.],[.,.]],.],.],.],[.,.]],.] => [1,3,2,4,5,6,8,7,9]
[5,4,4,4,3] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [.,[[[[[[[.,.],[.,.]],.],.],.],.],.]] => [2,4,3,5,6,7,8,9,1]
[4,4,4,4,2] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [[[[[[[.,.],.],.],[.,.]],.],.],.] => [1,2,3,5,4,6,7,8]
[2,2,2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.] => [7,6,5,4,3,2,1,8,9,10]
[3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [[[[[[.,[.,[.,.]]],.],.],.],.],.] => [3,2,1,4,5,6,7,8]
[3,3,3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.] => [5,4,3,2,1,6,7,8,9,10]
[3,3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9]
[4,3,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]] => [4,3,2,5,6,7,8,9,1]
[4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8]
[4,4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[[[[[[[.,[.,.]],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9]
[5,5,5,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[[[[[[.,[.,.]],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8]
[6,6,6,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [[[[[[[.,[.,[.,.]]],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9]
[6,6,6] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[.,[.,[.,[.,.]]]],.],.],.],.] => [4,3,2,1,5,6,7,8]
[7,6,6] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]] => [5,4,3,2,6,7,8,9,1]
[6,6,6,6,6] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.] => [2,1,3,4,5,6,7,8,9,10]
[5,5,5,5,5,5] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10]
[7,7,7,7] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.] => [4,3,2,1,5,6,7,8,9,10]
[7,7,7] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.] => [5,4,3,2,1,6,7,8,9]
[5,5,5,5,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9]
[9,9] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.] => [8,7,6,5,4,3,2,1,9,10]
[8,8,8] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.] => [6,5,4,3,2,1,7,8,9,10]
[4,4,4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.] => [3,2,1,4,5,6,7,8,9,10]
[6,5,5,5] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1]
[5,4,4,4,4] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1]
[4,4,4,4,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],[.,.]],.] => [1,2,3,4,5,6,8,7,9]
[5,5,5,5,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.] => [2,1,3,4,5,6,8,7,9]
Map
parallelogram polyomino
Description
Return the Dyck path corresponding to the partition interpreted as a parallogram polyomino.
The Ferrers diagram of an integer partition can be interpreted as a parallogram polyomino, such that each part corresponds to a column.
This map returns the corresponding Dyck path.
Map
to binary tree: up step, left tree, down step, right tree
Description
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
A Dyck path $D$ of semilength $n$ with $ n > 1$ may be uniquely decomposed into $1L0R$ for Dyck paths L,R of respective semilengths $n_1, n_2$ with $n_1 + n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
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.