Identifier
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Images
[1] => [1,0] => [.,.] => [1]
[2] => [1,0,1,0] => [[.,.],.] => [1,2]
[1,1] => [1,1,0,0] => [.,[.,.]] => [2,1]
[3] => [1,0,1,0,1,0] => [[[.,.],.],.] => [1,2,3]
[2,1] => [1,0,1,1,0,0] => [[.,.],[.,.]] => [3,1,2]
[1,1,1] => [1,1,0,1,0,0] => [.,[[.,.],.]] => [2,3,1]
[4] => [1,0,1,0,1,0,1,0] => [[[[.,.],.],.],.] => [1,2,3,4]
[3,1] => [1,0,1,0,1,1,0,0] => [[[.,.],.],[.,.]] => [4,1,2,3]
[2,2] => [1,1,1,0,0,0] => [.,[.,[.,.]]] => [3,2,1]
[2,1,1] => [1,0,1,1,0,1,0,0] => [[.,.],[[.,.],.]] => [3,4,1,2]
[1,1,1,1] => [1,1,0,1,0,1,0,0] => [.,[[[.,.],.],.]] => [2,3,4,1]
[5] => [1,0,1,0,1,0,1,0,1,0] => [[[[[.,.],.],.],.],.] => [1,2,3,4,5]
[4,1] => [1,0,1,0,1,0,1,1,0,0] => [[[[.,.],.],.],[.,.]] => [5,1,2,3,4]
[3,2] => [1,0,1,1,1,0,0,0] => [[.,.],[.,[.,.]]] => [4,3,1,2]
[3,1,1] => [1,0,1,0,1,1,0,1,0,0] => [[[.,.],.],[[.,.],.]] => [4,5,1,2,3]
[2,2,1] => [1,1,1,0,0,1,0,0] => [.,[[.,[.,.]],.]] => [3,2,4,1]
[2,1,1,1] => [1,0,1,1,0,1,0,1,0,0] => [[.,.],[[[.,.],.],.]] => [3,4,5,1,2]
[1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,0] => [.,[[[[.,.],.],.],.]] => [2,3,4,5,1]
[6] => [1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[.,.],.],.],.],.],.] => [1,2,3,4,5,6]
[5,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[.,.],.],.],.],[.,.]] => [6,1,2,3,4,5]
[4,2] => [1,0,1,0,1,1,1,0,0,0] => [[[.,.],.],[.,[.,.]]] => [5,4,1,2,3]
[4,1,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [[[[.,.],.],.],[[.,.],.]] => [5,6,1,2,3,4]
[3,3] => [1,1,1,0,1,0,0,0] => [.,[.,[[.,.],.]]] => [3,4,2,1]
[3,2,1] => [1,0,1,1,1,0,0,1,0,0] => [[.,.],[[.,[.,.]],.]] => [4,3,5,1,2]
[3,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [[[.,.],.],[[[.,.],.],.]] => [4,5,6,1,2,3]
[2,2,2] => [1,1,1,1,0,0,0,0] => [.,[.,[.,[.,.]]]] => [4,3,2,1]
[2,2,1,1] => [1,1,1,0,0,1,0,1,0,0] => [.,[[[.,[.,.]],.],.]] => [3,2,4,5,1]
[2,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,.],.],.],.]] => [3,4,5,6,1,2]
[1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1]
[7] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[.,.],.],.],.],.],.],.] => [1,2,3,4,5,6,7]
[6,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[.,.],.],.],.],.],[.,.]] => [7,1,2,3,4,5,6]
[5,2] => [1,0,1,0,1,0,1,1,1,0,0,0] => [[[[.,.],.],.],[.,[.,.]]] => [6,5,1,2,3,4]
[5,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[.,.],.],.],.],[[.,.],.]] => [6,7,1,2,3,4,5]
[4,3] => [1,0,1,1,1,0,1,0,0,0] => [[.,.],[.,[[.,.],.]]] => [4,5,3,1,2]
[4,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [[[.,.],.],[[.,[.,.]],.]] => [5,4,6,1,2,3]
[4,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[.,.],.],.]] => [5,6,7,1,2,3,4]
[3,3,1] => [1,1,1,0,1,0,0,1,0,0] => [.,[[.,[[.,.],.]],.]] => [3,4,2,5,1]
[3,2,2] => [1,0,1,1,1,1,0,0,0,0] => [[.,.],[.,[.,[.,.]]]] => [5,4,3,1,2]
[3,2,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,.]],.],.]] => [4,3,5,6,1,2]
[3,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[.,.],.],.],.]] => [4,5,6,7,1,2,3]
[2,2,2,1] => [1,1,1,1,0,0,0,1,0,0] => [.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1]
[2,2,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1]
[2,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[.,.],.],.],.],.]] => [3,4,5,6,7,1,2]
[1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,.],.],.],.],.],.]] => [2,3,4,5,6,7,1]
[8] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[.,.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8]
[7,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [8,1,2,3,4,5,6,7]
[6,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[.,.],.],.],.],[.,[.,.]]] => [7,6,1,2,3,4,5]
[6,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,.],.]] => [7,8,1,2,3,4,5,6]
[5,3] => [1,0,1,0,1,1,1,0,1,0,0,0] => [[[.,.],.],[.,[[.,.],.]]] => [5,6,4,1,2,3]
[5,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[[[.,.],.],.],[[.,[.,.]],.]] => [6,5,7,1,2,3,4]
[5,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[[.,.],.],.],.],[[[.,.],.],.]] => [6,7,8,1,2,3,4,5]
[4,4] => [1,1,1,0,1,0,1,0,0,0] => [.,[.,[[[.,.],.],.]]] => [3,4,5,2,1]
[4,3,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[.,.],.]],.]] => [4,5,3,6,1,2]
[4,2,2] => [1,0,1,0,1,1,1,1,0,0,0,0] => [[[.,.],.],[.,[.,[.,.]]]] => [6,5,4,1,2,3]
[4,2,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,[.,.]],.],.]] => [5,4,6,7,1,2,3]
[4,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[[.,.],.],.],.]] => [5,6,7,8,1,2,3,4]
[3,3,2] => [1,1,1,0,1,1,0,0,0,0] => [.,[.,[[.,.],[.,.]]]] => [5,3,4,2,1]
[3,3,1,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1]
[3,2,2,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,.]]],.]] => [5,4,3,6,1,2]
[3,2,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,[.,.]],.],.],.]] => [4,3,5,6,7,1,2]
[3,1,1,1,1,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[[.,.],.],.],.],.]] => [4,5,6,7,8,1,2,3]
[2,2,2,2] => [1,1,1,1,0,1,0,0,0,0] => [.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1]
[2,2,2,1,1] => [1,1,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1]
[2,2,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,.]],.],.],.],.]] => [3,2,4,5,6,7,1]
[2,1,1,1,1,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => [3,4,5,6,7,8,1,2]
[1,1,1,1,1,1,1,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,1]
[9] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9]
[8,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,.]] => [9,1,2,3,4,5,6,7,8]
[7,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[.,.]]] => [8,7,1,2,3,4,5,6]
[7,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[[.,.],.]] => [8,9,1,2,3,4,5,6,7]
[6,3] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[[.,.],.],.],[.,[[.,.],.]]] => [6,7,5,1,2,3,4]
[6,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[[[[.,.],.],.],.],[[.,[.,.]],.]] => [7,6,8,1,2,3,4,5]
[6,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[[.,.],.],.]] => [7,8,9,1,2,3,4,5,6]
[5,4] => [1,0,1,1,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[.,.],.],.]]] => [4,5,6,3,1,2]
[5,3,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[[.,.],.],[[.,[[.,.],.]],.]] => [5,6,4,7,1,2,3]
[5,2,2] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,.]]]] => [7,6,5,1,2,3,4]
[5,2,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[[.,.],.],.],[[[.,[.,.]],.],.]] => [6,5,7,8,1,2,3,4]
[5,1,1,1,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[[[[.,.],.],.],.],[[[[.,.],.],.],.]] => [6,7,8,9,1,2,3,4,5]
[4,4,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1]
[4,3,2] => [1,0,1,1,1,0,1,1,0,0,0,0] => [[.,.],[.,[[.,.],[.,.]]]] => [6,4,5,3,1,2]
[4,3,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[[.,.],.]],.],.]] => [4,5,3,6,7,1,2]
[4,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[.,.],.],[[.,[.,[.,.]]],.]] => [6,5,4,7,1,2,3]
[4,2,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[.,[.,.]],.],.],.]] => [5,4,6,7,8,1,2,3]
[4,1,1,1,1,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[[[.,.],.],.],.],.]] => [5,6,7,8,9,1,2,3,4]
[3,3,3] => [1,1,1,1,1,0,0,0,0,0] => [.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1]
[3,3,2,1] => [1,1,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,.]]],.]] => [5,3,4,2,6,1]
[3,3,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[.,.],.]],.],.],.]] => [3,4,2,5,6,7,1]
[3,2,2,2] => [1,0,1,1,1,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,.],.]]]] => [5,6,4,3,1,2]
[3,2,2,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,[.,.]]],.],.]] => [5,4,3,6,7,1,2]
[3,2,1,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => [4,3,5,6,7,8,1,2]
[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] => [[[.,.],.],[[[[[[.,.],.],.],.],.],.]] => [4,5,6,7,8,9,1,2,3]
[2,2,2,2,1] => [1,1,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1]
[2,2,2,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [4,3,2,5,6,7,1]
[2,2,1,1,1,1,1] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => [3,2,4,5,6,7,8,1]
[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] => [[.,.],[[[[[[[.,.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,1,2]
[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] => [.,[[[[[[[[.,.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,1]
[10] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10]
[9,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] => [10,1,2,3,4,5,6,7,8,9]
[8,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] => [9,8,1,2,3,4,5,6,7]
[8,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] => [9,10,1,2,3,4,5,6,7,8]
[7,3] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[[[[.,.],.],.],.],[.,[[.,.],.]]] => [7,8,6,1,2,3,4,5]
>>> Load all 332 entries. <<<
[7,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[[[[[.,.],.],.],.],.],[[.,[.,.]],.]] => [8,7,9,1,2,3,4,5,6]
[7,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] => [8,9,10,1,2,3,4,5,6,7]
[6,4] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[.,.],.],[.,[[[.,.],.],.]]] => [5,6,7,4,1,2,3]
[6,3,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[[[.,.],.],.],[[.,[[.,.],.]],.]] => [6,7,5,8,1,2,3,4]
[6,2,2] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,.]]]] => [8,7,6,1,2,3,4,5]
[6,2,1,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[[[[.,.],.],.],.],[[[.,[.,.]],.],.]] => [7,6,8,9,1,2,3,4,5]
[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] => [[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] => [7,8,9,10,1,2,3,4,5,6]
[5,5] => [1,1,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1]
[5,4,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[[.,.],.],.]],.]] => [4,5,6,3,7,1,2]
[5,3,2] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[[.,.],.],[.,[[.,.],[.,.]]]] => [7,5,6,4,1,2,3]
[5,3,1,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,[[.,.],.]],.],.]] => [5,6,4,7,8,1,2,3]
[5,2,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[[[.,.],.],.],[[.,[.,[.,.]]],.]] => [7,6,5,8,1,2,3,4]
[5,2,1,1,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[[[.,.],.],.],[[[[.,[.,.]],.],.],.]] => [6,5,7,8,9,1,2,3,4]
[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] => [[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] => [6,7,8,9,10,1,2,3,4,5]
[4,4,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[.,.],.],[.,.]]]] => [6,3,4,5,2,1]
[4,4,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[.,.],.],.]],.],.]] => [3,4,5,2,6,7,1]
[4,3,3] => [1,0,1,1,1,1,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,.]]]]] => [6,5,4,3,1,2]
[4,3,2,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[.,.]]],.]] => [6,4,5,3,7,1,2]
[4,3,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => [4,5,3,6,7,8,1,2]
[4,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[.,.],.],[.,[.,[[.,.],.]]]] => [6,7,5,4,1,2,3]
[4,2,2,1,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,[.,[.,.]]],.],.]] => [6,5,4,7,8,1,2,3]
[4,2,1,1,1,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[[.,.],.],[[[[[.,[.,.]],.],.],.],.]] => [5,4,6,7,8,9,1,2,3]
[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] => [[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] => [5,6,7,8,9,10,1,2,3,4]
[3,3,3,1] => [1,1,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1]
[3,3,2,2] => [1,1,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,.],.]]]] => [5,6,3,4,2,1]
[3,3,2,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[.,.]]],.],.]] => [5,3,4,2,6,7,1]
[3,3,1,1,1,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => [3,4,2,5,6,7,8,1]
[3,2,2,2,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[[.,.],.]]],.]] => [5,6,4,3,7,1,2]
[3,2,2,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => [5,4,3,6,7,8,1,2]
[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] => [[.,.],[[[[[[.,[.,.]],.],.],.],.],.]] => [4,3,5,6,7,8,9,1,2]
[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] => [[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] => [4,5,6,7,8,9,10,1,2,3]
[2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1]
[2,2,2,2,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[[.,.],.]]],.],.]] => [4,5,3,2,6,7,1]
[2,2,2,1,1,1,1] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [4,3,2,5,6,7,8,1]
[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] => [.,[[[[[[[.,[.,.]],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,1]
[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] => [[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] => [3,4,5,6,7,8,9,10,1,2]
[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] => [.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,1]
[11] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.] => [1,2,3,4,5,6,7,8,9,10,11]
[10,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] => [11,1,2,3,4,5,6,7,8,9,10]
[9,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] => [10,9,1,2,3,4,5,6,7,8]
[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] => [[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]] => [10,11,1,2,3,4,5,6,7,8,9]
[7,4] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[[[.,.],.],.],[.,[[[.,.],.],.]]] => [6,7,8,5,1,2,3,4]
[7,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] => [9,8,7,1,2,3,4,5,6]
[6,5] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[.,.],.],.],.]]] => [4,5,6,7,3,1,2]
[6,4,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[[.,.],.],[[.,[[[.,.],.],.]],.]] => [5,6,7,4,8,1,2,3]
[6,3,2] => [1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[[[.,.],.],.],[.,[[.,.],[.,.]]]] => [8,6,7,5,1,2,3,4]
[5,5,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[.,.],.],.],.]],.]] => [3,4,5,6,2,7,1]
[5,4,2] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[.,.],[.,[[[.,.],.],[.,.]]]] => [7,4,5,6,3,1,2]
[5,4,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[.,.],[[[.,[[[.,.],.],.]],.],.]] => [4,5,6,3,7,8,1,2]
[5,3,3] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,.]]]]] => [7,6,5,4,1,2,3]
[5,3,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[[.,.],.],[[.,[[.,.],[.,.]]],.]] => [7,5,6,4,8,1,2,3]
[5,2,2,2] => [1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[[[.,.],.],.],[.,[.,[[.,.],.]]]] => [7,8,6,5,1,2,3,4]
[4,4,3] => [1,1,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,.]]]]] => [6,5,3,4,2,1]
[4,4,2,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[.,.]]],.]] => [6,3,4,5,2,7,1]
[4,4,1,1,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => [3,4,5,2,6,7,8,1]
[4,3,3,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[.,.]]]],.]] => [6,5,4,3,7,1,2]
[4,3,2,2] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[.,.],[.,[[.,.],[[.,.],.]]]] => [6,7,4,5,3,1,2]
[4,3,2,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]] => [6,4,5,3,7,8,1,2]
[4,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[[.,.],.],[[.,[.,[[.,.],.]]],.]] => [6,7,5,4,8,1,2,3]
[3,3,3,2] => [1,1,1,1,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1]
[3,3,3,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => [5,4,3,2,6,7,1]
[3,3,2,2,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,.],.]]],.]] => [5,6,3,4,2,7,1]
[3,3,2,1,1,1] => [1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]] => [5,3,4,2,6,7,8,1]
[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] => [.,[[[[[[.,[[.,.],.]],.],.],.],.],.]] => [3,4,2,5,6,7,8,9,1]
[3,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[.,.],.],.]]]] => [5,6,7,4,3,1,2]
[3,2,2,2,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => [5,6,4,3,7,8,1,2]
[2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[.,.],.],.]]],.]] => [4,5,6,3,2,7,1]
[2,2,2,2,1,1,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[[.,.],.]]],.],.],.]] => [4,5,3,2,6,7,8,1]
[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] => [.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]] => [3,2,4,5,6,7,8,9,10,1]
[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] => [.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] => [2,3,4,5,6,7,8,9,10,11,1]
[8,2,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] => [10,9,8,1,2,3,4,5,6,7]
[7,5] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [[[.,.],.],[.,[[[[.,.],.],.],.]]] => [5,6,7,8,4,1,2,3]
[6,6] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[.,.],.],.],.],.]]] => [3,4,5,6,7,2,1]
[6,5,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => [4,5,6,7,3,8,1,2]
[6,4,2] => [1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[[.,.],.],[.,[[[.,.],.],[.,.]]]] => [8,5,6,7,4,1,2,3]
[6,4,1,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[[.,.],.],[[[.,[[[.,.],.],.]],.],.]] => [5,6,7,4,8,9,1,2,3]
[6,3,3] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,.]]]]] => [8,7,6,5,1,2,3,4]
[5,5,2] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],[.,.]]]] => [7,3,4,5,6,2,1]
[5,5,1,1] => [1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [.,[[[.,[[[[.,.],.],.],.]],.],.]] => [3,4,5,6,2,7,8,1]
[5,4,3] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[.,.],[.,[[.,.],[.,[.,.]]]]] => [7,6,4,5,3,1,2]
[5,4,2,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => [7,4,5,6,3,8,1,2]
[5,3,3,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[[.,.],.],[[.,[.,[.,[.,.]]]],.]] => [7,6,5,4,8,1,2,3]
[5,3,2,2] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[[.,.],.],[.,[[.,.],[[.,.],.]]]] => [7,8,5,6,4,1,2,3]
[4,4,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1]
[4,4,3,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,[.,.]]]],.]] => [6,5,3,4,2,7,1]
[4,4,2,2] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[[.,.],.],[[.,.],.]]]] => [6,7,3,4,5,2,1]
[4,4,2,1,1] => [1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[[.,.],.],[.,.]]],.],.]] => [6,3,4,5,2,7,8,1]
[4,3,3,2] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[.,.]],.]]]] => [6,5,7,4,3,1,2]
[4,3,3,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => [6,5,4,3,7,8,1,2]
[4,3,2,2,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => [6,7,4,5,3,8,1,2]
[4,2,2,2,2] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[[.,.],.],[.,[.,[[[.,.],.],.]]]] => [6,7,8,5,4,1,2,3]
[3,3,3,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1]
[3,3,3,2,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => [5,4,6,3,2,7,1]
[3,3,3,1,1,1] => [1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [.,[[[[.,[.,[.,[.,.]]]],.],.],.]] => [5,4,3,2,6,7,8,1]
[3,3,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[[.,.],.],.]]]] => [5,6,7,3,4,2,1]
[3,3,2,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[[.,.],.]]],.],.]] => [5,6,3,4,2,7,8,1]
[3,2,2,2,2,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => [5,6,7,4,3,8,1,2]
[2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[.,.],.],.],.]]]] => [4,5,6,7,3,2,1]
[2,2,2,2,2,1,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[[[.,.],.],.]]],.],.]] => [4,5,6,3,2,7,8,1]
[7,6] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => [4,5,6,7,8,3,1,2]
[7,4,2] => [1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [[[[.,.],.],.],[.,[[[.,.],.],[.,.]]]] => [9,6,7,8,5,1,2,3,4]
[7,3,3] => [1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] => [9,8,7,6,1,2,3,4,5]
[6,6,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[[.,.],.],.],.],.]],.]] => [3,4,5,6,7,2,8,1]
[6,5,2] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => [8,4,5,6,7,3,1,2]
[6,4,3] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[[.,.],.],[.,[[.,.],[.,[.,.]]]]] => [8,7,5,6,4,1,2,3]
[5,5,3] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => [7,6,3,4,5,2,1]
[5,5,2,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [.,[[.,[[[[.,.],.],.],[.,.]]],.]] => [7,3,4,5,6,2,8,1]
[5,4,4] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],.]]]]] => [6,7,5,4,3,1,2]
[5,4,3,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => [7,6,4,5,3,8,1,2]
[5,4,2,2] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => [7,8,4,5,6,3,1,2]
[5,3,3,2] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[[.,.],.],[.,[.,[[.,[.,.]],.]]]] => [7,6,8,5,4,1,2,3]
[4,4,4,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => [5,6,4,3,2,7,1]
[4,4,3,2] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => [6,5,7,3,4,2,1]
[4,4,3,1,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [.,[[[.,[[.,.],[.,[.,.]]]],.],.]] => [6,5,3,4,2,7,8,1]
[4,4,2,2,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[[.,.],.]]],.]] => [6,7,3,4,5,2,8,1]
[4,3,3,3] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,.]]]]]] => [7,6,5,4,3,1,2]
[4,3,3,2,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => [6,5,7,4,3,8,1,2]
[4,3,2,2,2] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => [6,7,8,4,5,3,1,2]
[3,3,3,3,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => [6,5,4,3,2,7,1]
[3,3,3,2,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => [5,4,6,7,3,2,1]
[3,3,3,2,1,1] => [1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[[.,[.,.]],.]]],.],.]] => [5,4,6,3,2,7,8,1]
[3,3,2,2,2,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[[.,.],.],.]]],.]] => [5,6,7,3,4,2,8,1]
[3,2,2,2,2,2] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => [5,6,7,8,4,3,1,2]
[2,2,2,2,2,2,1] => [1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[[.,.],.],.],.]]],.]] => [4,5,6,7,3,2,8,1]
[8,3,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] => [10,9,8,7,1,2,3,4,5,6]
[7,7] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],.],.]]] => [3,4,5,6,7,8,2,1]
[7,6,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [[.,.],[[.,[[[[[.,.],.],.],.],.]],.]] => [4,5,6,7,8,3,9,1,2]
[7,5,2] => [1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[[.,.],.],[.,[[[[.,.],.],.],[.,.]]]] => [9,5,6,7,8,4,1,2,3]
[6,6,2] => [1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[[.,.],.],.],.],[.,.]]]] => [8,3,4,5,6,7,2,1]
[6,5,3] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => [8,7,4,5,6,3,1,2]
[6,4,4] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[[.,.],.]]]]] => [7,8,6,5,4,1,2,3]
[5,5,4] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => [6,7,5,3,4,2,1]
[5,5,3,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [.,[[.,[[[.,.],.],[.,[.,.]]]],.]] => [7,6,3,4,5,2,8,1]
[5,5,2,2] => [1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [.,[.,[[[[.,.],.],.],[[.,.],.]]]] => [7,8,3,4,5,6,2,1]
[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] => [.,[[[[[.,[[[[.,.],.],.],.]],.],.],.],.]] => [3,4,5,6,2,7,8,9,10,1]
[5,4,4,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => [6,7,5,4,3,8,1,2]
[5,4,3,2] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => [7,6,8,4,5,3,1,2]
[5,3,3,3] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] => [8,7,6,5,4,1,2,3]
[4,4,4,2] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => [5,6,4,7,3,2,1]
[4,4,4,1,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,[[.,.],.]]]],.],.]] => [5,6,4,3,2,7,8,1]
[4,4,3,3] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => [7,6,5,3,4,2,1]
[4,4,3,2,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[[.,.],[[.,[.,.]],.]]],.]] => [6,5,7,3,4,2,8,1]
[4,4,2,2,2] => [1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [.,[.,[[[.,.],.],[[[.,.],.],.]]]] => [6,7,8,3,4,5,2,1]
[4,3,3,3,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => [7,6,5,4,3,8,1,2]
[4,3,3,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => [6,5,7,8,4,3,1,2]
[3,3,3,3,2] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => [6,5,4,7,3,2,1]
[3,3,3,3,1,1] => [1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [.,[[[.,[.,[.,[.,[.,.]]]]],.],.]] => [6,5,4,3,2,7,8,1]
[3,3,3,2,2,1] => [1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[[.,[.,.]],.],.]]],.]] => [5,4,6,7,3,2,8,1]
[3,3,2,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[[[.,.],.],.],.]]]] => [5,6,7,8,3,4,2,1]
[2,2,2,2,2,2,2] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[[.,.],.],.],.],.]]]] => [4,5,6,7,8,3,2,1]
[8,7] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]] => [4,5,6,7,8,9,3,1,2]
[7,7,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,2,9,1]
[6,6,3] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [.,[.,[[[[.,.],.],.],[.,[.,.]]]]] => [8,7,3,4,5,6,2,1]
[6,5,4] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => [7,8,6,4,5,3,1,2]
[6,3,3,3] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [9,8,7,6,5,1,2,3,4]
[5,5,5] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => [5,6,7,4,3,2,1]
[5,5,4,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,[[.,.],.]]]],.]] => [6,7,5,3,4,2,8,1]
[5,5,3,2] => [1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [.,[.,[[[.,.],.],[[.,[.,.]],.]]]] => [7,6,8,3,4,5,2,1]
[5,4,4,2] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => [6,7,5,8,4,3,1,2]
[5,4,3,3] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => [8,7,6,4,5,3,1,2]
[4,4,4,3] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => [7,5,6,4,3,2,1]
[4,4,4,2,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,[[.,.],.]],.]]],.]] => [5,6,4,7,3,2,8,1]
[4,4,3,3,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[[.,.],[.,[.,[.,.]]]]],.]] => [7,6,5,3,4,2,8,1]
[4,4,3,2,2] => [1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[[.,[.,.]],.],.]]]] => [6,5,7,8,3,4,2,1]
[4,3,3,3,2] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => [7,6,5,8,4,3,1,2]
[3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => [6,7,5,4,3,2,1]
[3,3,3,3,2,1] => [1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [.,[[.,[.,[[.,[.,[.,.]]],.]]],.]] => [6,5,4,7,3,2,8,1]
[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] => [.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]] => [6,5,4,3,2,7,8,9,1]
[3,3,3,2,2,2] => [1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[[.,[.,.]],.],.],.]]]] => [5,4,6,7,8,3,2,1]
[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] => [[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]] => [5,6,7,8,9,4,3,1,2]
[8,8] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,2,1]
[7,7,2] => [1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]] => [9,3,4,5,6,7,8,2,1]
[7,3,3,3] => [1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] => [10,9,8,7,6,1,2,3,4,5]
[6,6,4] => [1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [.,[.,[[[.,.],.],[.,[[.,.],.]]]]] => [7,8,6,3,4,5,2,1]
[6,5,5] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => [6,7,8,5,4,3,1,2]
[5,5,5,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[[[.,.],.],.]]]],.]] => [5,6,7,4,3,2,8,1]
[5,5,4,2] => [1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,[[.,.],.]],.]]]] => [6,7,5,8,3,4,2,1]
[5,5,3,3] => [1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] => [8,7,6,3,4,5,2,1]
[5,4,4,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => [8,6,7,5,4,3,1,2]
[4,4,4,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => [7,6,5,4,3,2,1]
[4,4,4,3,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[[.,.],[.,.]]]]],.]] => [7,5,6,4,3,2,8,1]
[4,4,4,2,2] => [1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,[[.,.],.]],.],.]]]] => [5,6,4,7,8,3,2,1]
[4,4,3,3,2] => [1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [.,[.,[[.,.],[[.,[.,[.,.]]],.]]]] => [7,6,5,8,3,4,2,1]
[4,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => [7,8,6,5,4,3,1,2]
[4,3,3,2,2,2] => [1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [[.,.],[.,[.,[[[[.,[.,.]],.],.],.]]]] => [6,5,7,8,9,4,3,1,2]
[3,3,3,3,3,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[[.,.],.]]]]],.]] => [6,7,5,4,3,2,8,1]
[3,3,3,3,2,2] => [1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [.,[.,[.,[[[.,[.,[.,.]]],.],.]]]] => [6,5,4,7,8,3,2,1]
[3,3,2,2,2,2,2] => [1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] => [5,6,7,8,9,3,4,2,1]
[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] => [.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [4,5,6,7,8,9,3,2,1]
[9,8] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]] => [4,5,6,7,8,9,10,3,1,2]
[8,8,1] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [.,[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]] => [3,4,5,6,7,8,9,2,10,1]
[6,6,5] => [1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [.,[.,[[.,.],[.,[[[.,.],.],.]]]]] => [6,7,8,5,3,4,2,1]
[5,5,5,2] => [1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[[[.,.],.],.]],.]]]] => [5,6,7,4,8,3,2,1]
[5,5,4,3] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] => [8,6,7,5,3,4,2,1]
[5,4,4,4] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => [8,7,6,5,4,3,1,2]
[4,4,4,4,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]] => [7,6,5,4,3,2,8,1]
[4,4,4,3,2] => [1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[[.,.],[.,.]]],.]]]] => [7,5,6,4,8,3,2,1]
[4,4,3,3,3] => [1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] => [7,8,6,5,3,4,2,1]
[3,3,3,3,3,2] => [1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[[.,.],.]]],.]]]] => [6,7,5,4,8,3,2,1]
[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] => [.,[.,[.,[[[[[.,[.,.]],.],.],.],.]]]] => [5,4,6,7,8,9,3,2,1]
[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] => [[.,.],[.,[.,[[[[[[.,.],.],.],.],.],.]]]] => [5,6,7,8,9,10,4,3,1,2]
[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] => [[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] => [7,8,6,9,4,5,3,10,1,2]
[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] => [[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]] => [9,10,7,8,6,11,4,5,3,12,1,2]
[4,4,4,4,3,1] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]] => [7,6,8,5,4,3,2,9,1]
[5,4,4,4,3] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]] => [8,7,9,6,5,4,3,1,2]
[4,4,4,4,2] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]] => [7,6,5,4,8,3,2,1]
[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] => [.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] => [4,5,6,7,8,9,10,3,2,1]
[3,3,3,3,3,3] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [6,7,8,5,4,3,2,1]
[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] => [.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] => [6,7,8,9,10,5,4,3,2,1]
[3,3,3,3,3,3,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]] => [6,7,8,5,4,3,2,9,1]
[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] => [.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] => [6,7,8,9,5,4,3,2,1]
[4,3,3,3,3,3] => [1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]] => [7,8,9,6,5,4,3,1,2]
[4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [8,7,6,5,4,3,2,1]
[4,4,4,3,3,3] => [1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] => [7,8,9,5,6,4,3,2,1]
[4,4,4,4,4,4] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] => [8,9,7,6,5,4,3,2,1]
[5,5,5,5] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [7,8,6,5,4,3,2,1]
[6,6,6,6] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] => [7,8,9,6,5,4,3,2,1]
[6,6,6] => [1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[.,.],.],.],.]]]]] => [5,6,7,8,4,3,2,1]
[7,6,6] => [1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]] => [6,7,8,9,5,4,3,1,2]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] => [9,10,8,7,6,5,4,3,2,1]
[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] => [.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] => [10,9,8,7,6,5,4,3,2,1]
[7,7,7,7] => [1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] => [7,8,9,10,6,5,4,3,2,1]
[7,7,7] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] => [5,6,7,8,9,4,3,2,1]
[5,5,5,5,5] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] => [9,8,7,6,5,4,3,2,1]
[9,9] => [1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] => [3,4,5,6,7,8,9,10,2,1]
[8,8,8] => [1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] => [5,6,7,8,9,10,4,3,2,1]
[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] => [.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] => [8,9,10,7,6,5,4,3,2,1]
[6,5,5,5] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] => [8,9,7,6,5,4,3,1,2]
[5,4,4,4,4] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] => [9,8,7,6,5,4,3,1,2]
[4,4,4,4,4,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]] => [8,7,6,5,4,3,2,9,1]
[5,5,5,5,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]] => [7,8,6,5,4,3,2,9,1]
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: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ 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.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.
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.