Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
[.,.] => [1] => [.,.]
[.,[.,.]] => [2,1] => [[.,.],.]
[[.,.],.] => [1,2] => [.,[.,.]]
[.,[.,[.,.]]] => [3,2,1] => [[[.,.],.],.]
[.,[[.,.],.]] => [2,3,1] => [[.,.],[.,.]]
[[.,.],[.,.]] => [1,3,2] => [.,[[.,.],.]]
[[.,[.,.]],.] => [2,1,3] => [[.,.],[.,.]]
[[[.,.],.],.] => [1,2,3] => [.,[.,[.,.]]]
[.,[.,[.,[.,.]]]] => [4,3,2,1] => [[[[.,.],.],.],.]
[.,[.,[[.,.],.]]] => [3,4,2,1] => [[[.,.],.],[.,.]]
[.,[[.,.],[.,.]]] => [2,4,3,1] => [[.,.],[[.,.],.]]
[.,[[.,[.,.]],.]] => [3,2,4,1] => [[[.,.],.],[.,.]]
[.,[[[.,.],.],.]] => [2,3,4,1] => [[.,.],[.,[.,.]]]
[[.,.],[.,[.,.]]] => [1,4,3,2] => [.,[[[.,.],.],.]]
[[.,.],[[.,.],.]] => [1,3,4,2] => [.,[[.,.],[.,.]]]
[[.,[.,.]],[.,.]] => [2,1,4,3] => [[.,.],[[.,.],.]]
[[[.,.],.],[.,.]] => [1,2,4,3] => [.,[.,[[.,.],.]]]
[[.,[.,[.,.]]],.] => [3,2,1,4] => [[[.,.],.],[.,.]]
[[.,[[.,.],.]],.] => [2,3,1,4] => [[.,.],[.,[.,.]]]
[[[.,.],[.,.]],.] => [1,3,2,4] => [.,[[.,.],[.,.]]]
[[[.,[.,.]],.],.] => [2,1,3,4] => [[.,.],[.,[.,.]]]
[[[[.,.],.],.],.] => [1,2,3,4] => [.,[.,[.,[.,.]]]]
[.,[.,[.,[.,[.,.]]]]] => [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
[.,[.,[.,[[.,.],.]]]] => [4,5,3,2,1] => [[[[.,.],.],.],[.,.]]
[.,[.,[[.,.],[.,.]]]] => [3,5,4,2,1] => [[[.,.],.],[[.,.],.]]
[.,[.,[[.,[.,.]],.]]] => [4,3,5,2,1] => [[[[.,.],.],.],[.,.]]
[.,[.,[[[.,.],.],.]]] => [3,4,5,2,1] => [[[.,.],.],[.,[.,.]]]
[.,[[.,.],[.,[.,.]]]] => [2,5,4,3,1] => [[.,.],[[[.,.],.],.]]
[.,[[.,.],[[.,.],.]]] => [2,4,5,3,1] => [[.,.],[[.,.],[.,.]]]
[.,[[.,[.,.]],[.,.]]] => [3,2,5,4,1] => [[[.,.],.],[[.,.],.]]
[.,[[[.,.],.],[.,.]]] => [2,3,5,4,1] => [[.,.],[.,[[.,.],.]]]
[.,[[.,[.,[.,.]]],.]] => [4,3,2,5,1] => [[[[.,.],.],.],[.,.]]
[.,[[.,[[.,.],.]],.]] => [3,4,2,5,1] => [[[.,.],.],[.,[.,.]]]
[.,[[[.,.],[.,.]],.]] => [2,4,3,5,1] => [[.,.],[[.,.],[.,.]]]
[.,[[[.,[.,.]],.],.]] => [3,2,4,5,1] => [[[.,.],.],[.,[.,.]]]
[.,[[[[.,.],.],.],.]] => [2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]]
[[.,.],[.,[.,[.,.]]]] => [1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
[[.,.],[.,[[.,.],.]]] => [1,4,5,3,2] => [.,[[[.,.],.],[.,.]]]
[[.,.],[[.,.],[.,.]]] => [1,3,5,4,2] => [.,[[.,.],[[.,.],.]]]
[[.,.],[[.,[.,.]],.]] => [1,4,3,5,2] => [.,[[[.,.],.],[.,.]]]
[[.,.],[[[.,.],.],.]] => [1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
[[.,[.,.]],[.,[.,.]]] => [2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
[[.,[.,.]],[[.,.],.]] => [2,1,4,5,3] => [[.,.],[[.,.],[.,.]]]
[[[.,.],.],[.,[.,.]]] => [1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
[[[.,.],.],[[.,.],.]] => [1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]]
[[.,[.,[.,.]]],[.,.]] => [3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
[[.,[[.,.],.]],[.,.]] => [2,3,1,5,4] => [[.,.],[.,[[.,.],.]]]
[[[.,.],[.,.]],[.,.]] => [1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
[[[.,[.,.]],.],[.,.]] => [2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
[[[[.,.],.],.],[.,.]] => [1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
[[.,[.,[.,[.,.]]]],.] => [4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
[[.,[.,[[.,.],.]]],.] => [3,4,2,1,5] => [[[.,.],.],[.,[.,.]]]
[[.,[[.,.],[.,.]]],.] => [2,4,3,1,5] => [[.,.],[[.,.],[.,.]]]
[[.,[[.,[.,.]],.]],.] => [3,2,4,1,5] => [[[.,.],.],[.,[.,.]]]
[[.,[[[.,.],.],.]],.] => [2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]]
[[[.,.],[.,[.,.]]],.] => [1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
[[[.,.],[[.,.],.]],.] => [1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]]
[[[.,[.,.]],[.,.]],.] => [2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
[[[[.,.],.],[.,.]],.] => [1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
[[[.,[.,[.,.]]],.],.] => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
[[[.,[[.,.],.]],.],.] => [2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]]
[[[[.,.],[.,.]],.],.] => [1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
[[[[.,[.,.]],.],.],.] => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
[[[[[.,.],.],.],.],.] => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
[.,[.,[.,[.,[.,[.,.]]]]]] => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
[.,[.,[.,[.,[[.,.],.]]]]] => [5,6,4,3,2,1] => [[[[[.,.],.],.],.],[.,.]]
[.,[.,[.,[[.,.],[.,.]]]]] => [4,6,5,3,2,1] => [[[[.,.],.],.],[[.,.],.]]
[.,[.,[.,[[.,[.,.]],.]]]] => [5,4,6,3,2,1] => [[[[[.,.],.],.],.],[.,.]]
[.,[.,[.,[[[.,.],.],.]]]] => [4,5,6,3,2,1] => [[[[.,.],.],.],[.,[.,.]]]
[.,[.,[[.,.],[.,[.,.]]]]] => [3,6,5,4,2,1] => [[[.,.],.],[[[.,.],.],.]]
[.,[.,[[.,.],[[.,.],.]]]] => [3,5,6,4,2,1] => [[[.,.],.],[[.,.],[.,.]]]
[.,[.,[[.,[.,.]],[.,.]]]] => [4,3,6,5,2,1] => [[[[.,.],.],.],[[.,.],.]]
[.,[.,[[[.,.],.],[.,.]]]] => [3,4,6,5,2,1] => [[[.,.],.],[.,[[.,.],.]]]
[.,[.,[[.,[.,[.,.]]],.]]] => [5,4,3,6,2,1] => [[[[[.,.],.],.],.],[.,.]]
[.,[.,[[.,[[.,.],.]],.]]] => [4,5,3,6,2,1] => [[[[.,.],.],.],[.,[.,.]]]
[.,[.,[[[.,.],[.,.]],.]]] => [3,5,4,6,2,1] => [[[.,.],.],[[.,.],[.,.]]]
[.,[.,[[[.,[.,.]],.],.]]] => [4,3,5,6,2,1] => [[[[.,.],.],.],[.,[.,.]]]
[.,[.,[[[[.,.],.],.],.]]] => [3,4,5,6,2,1] => [[[.,.],.],[.,[.,[.,.]]]]
[.,[[.,.],[.,[.,[.,.]]]]] => [2,6,5,4,3,1] => [[.,.],[[[[.,.],.],.],.]]
[.,[[.,.],[.,[[.,.],.]]]] => [2,5,6,4,3,1] => [[.,.],[[[.,.],.],[.,.]]]
[.,[[.,.],[[.,.],[.,.]]]] => [2,4,6,5,3,1] => [[.,.],[[.,.],[[.,.],.]]]
[.,[[.,.],[[.,[.,.]],.]]] => [2,5,4,6,3,1] => [[.,.],[[[.,.],.],[.,.]]]
[.,[[.,.],[[[.,.],.],.]]] => [2,4,5,6,3,1] => [[.,.],[[.,.],[.,[.,.]]]]
[.,[[.,[.,.]],[.,[.,.]]]] => [3,2,6,5,4,1] => [[[.,.],.],[[[.,.],.],.]]
[.,[[.,[.,.]],[[.,.],.]]] => [3,2,5,6,4,1] => [[[.,.],.],[[.,.],[.,.]]]
[.,[[[.,.],.],[.,[.,.]]]] => [2,3,6,5,4,1] => [[.,.],[.,[[[.,.],.],.]]]
[.,[[[.,.],.],[[.,.],.]]] => [2,3,5,6,4,1] => [[.,.],[.,[[.,.],[.,.]]]]
[.,[[.,[.,[.,.]]],[.,.]]] => [4,3,2,6,5,1] => [[[[.,.],.],.],[[.,.],.]]
[.,[[.,[[.,.],.]],[.,.]]] => [3,4,2,6,5,1] => [[[.,.],.],[.,[[.,.],.]]]
[.,[[[.,.],[.,.]],[.,.]]] => [2,4,3,6,5,1] => [[.,.],[[.,.],[[.,.],.]]]
[.,[[[.,[.,.]],.],[.,.]]] => [3,2,4,6,5,1] => [[[.,.],.],[.,[[.,.],.]]]
[.,[[[[.,.],.],.],[.,.]]] => [2,3,4,6,5,1] => [[.,.],[.,[.,[[.,.],.]]]]
[.,[[.,[.,[.,[.,.]]]],.]] => [5,4,3,2,6,1] => [[[[[.,.],.],.],.],[.,.]]
[.,[[.,[.,[[.,.],.]]],.]] => [4,5,3,2,6,1] => [[[[.,.],.],.],[.,[.,.]]]
[.,[[.,[[.,.],[.,.]]],.]] => [3,5,4,2,6,1] => [[[.,.],.],[[.,.],[.,.]]]
[.,[[.,[[.,[.,.]],.]],.]] => [4,3,5,2,6,1] => [[[[.,.],.],.],[.,[.,.]]]
[.,[[.,[[[.,.],.],.]],.]] => [3,4,5,2,6,1] => [[[.,.],.],[.,[.,[.,.]]]]
[.,[[[.,.],[.,[.,.]]],.]] => [2,5,4,3,6,1] => [[.,.],[[[.,.],.],[.,.]]]
[.,[[[.,.],[[.,.],.]],.]] => [2,4,5,3,6,1] => [[.,.],[[.,.],[.,[.,.]]]]
[.,[[[.,[.,.]],[.,.]],.]] => [3,2,5,4,6,1] => [[[.,.],.],[[.,.],[.,.]]]
[.,[[[[.,.],.],[.,.]],.]] => [2,3,5,4,6,1] => [[.,.],[.,[[.,.],[.,.]]]]
>>> Load all 1947 entries. <<<
[.,[[[.,[.,[.,.]]],.],.]] => [4,3,2,5,6,1] => [[[[.,.],.],.],[.,[.,.]]]
[.,[[[.,[[.,.],.]],.],.]] => [3,4,2,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]]
[.,[[[[.,.],[.,.]],.],.]] => [2,4,3,5,6,1] => [[.,.],[[.,.],[.,[.,.]]]]
[.,[[[[.,[.,.]],.],.],.]] => [3,2,4,5,6,1] => [[[.,.],.],[.,[.,[.,.]]]]
[.,[[[[[.,.],.],.],.],.]] => [2,3,4,5,6,1] => [[.,.],[.,[.,[.,[.,.]]]]]
[[.,.],[.,[.,[.,[.,.]]]]] => [1,6,5,4,3,2] => [.,[[[[[.,.],.],.],.],.]]
[[.,.],[.,[.,[[.,.],.]]]] => [1,5,6,4,3,2] => [.,[[[[.,.],.],.],[.,.]]]
[[.,.],[.,[[.,.],[.,.]]]] => [1,4,6,5,3,2] => [.,[[[.,.],.],[[.,.],.]]]
[[.,.],[.,[[.,[.,.]],.]]] => [1,5,4,6,3,2] => [.,[[[[.,.],.],.],[.,.]]]
[[.,.],[.,[[[.,.],.],.]]] => [1,4,5,6,3,2] => [.,[[[.,.],.],[.,[.,.]]]]
[[.,.],[[.,.],[.,[.,.]]]] => [1,3,6,5,4,2] => [.,[[.,.],[[[.,.],.],.]]]
[[.,.],[[.,.],[[.,.],.]]] => [1,3,5,6,4,2] => [.,[[.,.],[[.,.],[.,.]]]]
[[.,.],[[.,[.,.]],[.,.]]] => [1,4,3,6,5,2] => [.,[[[.,.],.],[[.,.],.]]]
[[.,.],[[[.,.],.],[.,.]]] => [1,3,4,6,5,2] => [.,[[.,.],[.,[[.,.],.]]]]
[[.,.],[[.,[.,[.,.]]],.]] => [1,5,4,3,6,2] => [.,[[[[.,.],.],.],[.,.]]]
[[.,.],[[.,[[.,.],.]],.]] => [1,4,5,3,6,2] => [.,[[[.,.],.],[.,[.,.]]]]
[[.,.],[[[.,.],[.,.]],.]] => [1,3,5,4,6,2] => [.,[[.,.],[[.,.],[.,.]]]]
[[.,.],[[[.,[.,.]],.],.]] => [1,4,3,5,6,2] => [.,[[[.,.],.],[.,[.,.]]]]
[[.,.],[[[[.,.],.],.],.]] => [1,3,4,5,6,2] => [.,[[.,.],[.,[.,[.,.]]]]]
[[.,[.,.]],[.,[.,[.,.]]]] => [2,1,6,5,4,3] => [[.,.],[[[[.,.],.],.],.]]
[[.,[.,.]],[.,[[.,.],.]]] => [2,1,5,6,4,3] => [[.,.],[[[.,.],.],[.,.]]]
[[.,[.,.]],[[.,.],[.,.]]] => [2,1,4,6,5,3] => [[.,.],[[.,.],[[.,.],.]]]
[[.,[.,.]],[[.,[.,.]],.]] => [2,1,5,4,6,3] => [[.,.],[[[.,.],.],[.,.]]]
[[.,[.,.]],[[[.,.],.],.]] => [2,1,4,5,6,3] => [[.,.],[[.,.],[.,[.,.]]]]
[[[.,.],.],[.,[.,[.,.]]]] => [1,2,6,5,4,3] => [.,[.,[[[[.,.],.],.],.]]]
[[[.,.],.],[.,[[.,.],.]]] => [1,2,5,6,4,3] => [.,[.,[[[.,.],.],[.,.]]]]
[[[.,.],.],[[.,.],[.,.]]] => [1,2,4,6,5,3] => [.,[.,[[.,.],[[.,.],.]]]]
[[[.,.],.],[[.,[.,.]],.]] => [1,2,5,4,6,3] => [.,[.,[[[.,.],.],[.,.]]]]
[[[.,.],.],[[[.,.],.],.]] => [1,2,4,5,6,3] => [.,[.,[[.,.],[.,[.,.]]]]]
[[.,[.,[.,.]]],[.,[.,.]]] => [3,2,1,6,5,4] => [[[.,.],.],[[[.,.],.],.]]
[[.,[.,[.,.]]],[[.,.],.]] => [3,2,1,5,6,4] => [[[.,.],.],[[.,.],[.,.]]]
[[.,[[.,.],.]],[.,[.,.]]] => [2,3,1,6,5,4] => [[.,.],[.,[[[.,.],.],.]]]
[[.,[[.,.],.]],[[.,.],.]] => [2,3,1,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]]
[[[.,.],[.,.]],[.,[.,.]]] => [1,3,2,6,5,4] => [.,[[.,.],[[[.,.],.],.]]]
[[[.,.],[.,.]],[[.,.],.]] => [1,3,2,5,6,4] => [.,[[.,.],[[.,.],[.,.]]]]
[[[.,[.,.]],.],[.,[.,.]]] => [2,1,3,6,5,4] => [[.,.],[.,[[[.,.],.],.]]]
[[[.,[.,.]],.],[[.,.],.]] => [2,1,3,5,6,4] => [[.,.],[.,[[.,.],[.,.]]]]
[[[[.,.],.],.],[.,[.,.]]] => [1,2,3,6,5,4] => [.,[.,[.,[[[.,.],.],.]]]]
[[[[.,.],.],.],[[.,.],.]] => [1,2,3,5,6,4] => [.,[.,[.,[[.,.],[.,.]]]]]
[[.,[.,[.,[.,.]]]],[.,.]] => [4,3,2,1,6,5] => [[[[.,.],.],.],[[.,.],.]]
[[.,[.,[[.,.],.]]],[.,.]] => [3,4,2,1,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[[.,[[.,.],[.,.]]],[.,.]] => [2,4,3,1,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[[.,[[.,[.,.]],.]],[.,.]] => [3,2,4,1,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[[.,[[[.,.],.],.]],[.,.]] => [2,3,4,1,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[[[.,.],[.,[.,.]]],[.,.]] => [1,4,3,2,6,5] => [.,[[[.,.],.],[[.,.],.]]]
[[[.,.],[[.,.],.]],[.,.]] => [1,3,4,2,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
[[[.,[.,.]],[.,.]],[.,.]] => [2,1,4,3,6,5] => [[.,.],[[.,.],[[.,.],.]]]
[[[[.,.],.],[.,.]],[.,.]] => [1,2,4,3,6,5] => [.,[.,[[.,.],[[.,.],.]]]]
[[[.,[.,[.,.]]],.],[.,.]] => [3,2,1,4,6,5] => [[[.,.],.],[.,[[.,.],.]]]
[[[.,[[.,.],.]],.],[.,.]] => [2,3,1,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[[[[.,.],[.,.]],.],[.,.]] => [1,3,2,4,6,5] => [.,[[.,.],[.,[[.,.],.]]]]
[[[[.,[.,.]],.],.],[.,.]] => [2,1,3,4,6,5] => [[.,.],[.,[.,[[.,.],.]]]]
[[[[[.,.],.],.],.],[.,.]] => [1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
[[.,[.,[.,[.,[.,.]]]]],.] => [5,4,3,2,1,6] => [[[[[.,.],.],.],.],[.,.]]
[[.,[.,[.,[[.,.],.]]]],.] => [4,5,3,2,1,6] => [[[[.,.],.],.],[.,[.,.]]]
[[.,[.,[[.,.],[.,.]]]],.] => [3,5,4,2,1,6] => [[[.,.],.],[[.,.],[.,.]]]
[[.,[.,[[.,[.,.]],.]]],.] => [4,3,5,2,1,6] => [[[[.,.],.],.],[.,[.,.]]]
[[.,[.,[[[.,.],.],.]]],.] => [3,4,5,2,1,6] => [[[.,.],.],[.,[.,[.,.]]]]
[[.,[[.,.],[.,[.,.]]]],.] => [2,5,4,3,1,6] => [[.,.],[[[.,.],.],[.,.]]]
[[.,[[.,.],[[.,.],.]]],.] => [2,4,5,3,1,6] => [[.,.],[[.,.],[.,[.,.]]]]
[[.,[[.,[.,.]],[.,.]]],.] => [3,2,5,4,1,6] => [[[.,.],.],[[.,.],[.,.]]]
[[.,[[[.,.],.],[.,.]]],.] => [2,3,5,4,1,6] => [[.,.],[.,[[.,.],[.,.]]]]
[[.,[[.,[.,[.,.]]],.]],.] => [4,3,2,5,1,6] => [[[[.,.],.],.],[.,[.,.]]]
[[.,[[.,[[.,.],.]],.]],.] => [3,4,2,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]]
[[.,[[[.,.],[.,.]],.]],.] => [2,4,3,5,1,6] => [[.,.],[[.,.],[.,[.,.]]]]
[[.,[[[.,[.,.]],.],.]],.] => [3,2,4,5,1,6] => [[[.,.],.],[.,[.,[.,.]]]]
[[.,[[[[.,.],.],.],.]],.] => [2,3,4,5,1,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[[[.,.],[.,[.,[.,.]]]],.] => [1,5,4,3,2,6] => [.,[[[[.,.],.],.],[.,.]]]
[[[.,.],[.,[[.,.],.]]],.] => [1,4,5,3,2,6] => [.,[[[.,.],.],[.,[.,.]]]]
[[[.,.],[[.,.],[.,.]]],.] => [1,3,5,4,2,6] => [.,[[.,.],[[.,.],[.,.]]]]
[[[.,.],[[.,[.,.]],.]],.] => [1,4,3,5,2,6] => [.,[[[.,.],.],[.,[.,.]]]]
[[[.,.],[[[.,.],.],.]],.] => [1,3,4,5,2,6] => [.,[[.,.],[.,[.,[.,.]]]]]
[[[.,[.,.]],[.,[.,.]]],.] => [2,1,5,4,3,6] => [[.,.],[[[.,.],.],[.,.]]]
[[[.,[.,.]],[[.,.],.]],.] => [2,1,4,5,3,6] => [[.,.],[[.,.],[.,[.,.]]]]
[[[[.,.],.],[.,[.,.]]],.] => [1,2,5,4,3,6] => [.,[.,[[[.,.],.],[.,.]]]]
[[[[.,.],.],[[.,.],.]],.] => [1,2,4,5,3,6] => [.,[.,[[.,.],[.,[.,.]]]]]
[[[.,[.,[.,.]]],[.,.]],.] => [3,2,1,5,4,6] => [[[.,.],.],[[.,.],[.,.]]]
[[[.,[[.,.],.]],[.,.]],.] => [2,3,1,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[[[[.,.],[.,.]],[.,.]],.] => [1,3,2,5,4,6] => [.,[[.,.],[[.,.],[.,.]]]]
[[[[.,[.,.]],.],[.,.]],.] => [2,1,3,5,4,6] => [[.,.],[.,[[.,.],[.,.]]]]
[[[[[.,.],.],.],[.,.]],.] => [1,2,3,5,4,6] => [.,[.,[.,[[.,.],[.,.]]]]]
[[[.,[.,[.,[.,.]]]],.],.] => [4,3,2,1,5,6] => [[[[.,.],.],.],[.,[.,.]]]
[[[.,[.,[[.,.],.]]],.],.] => [3,4,2,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[[[.,[[.,.],[.,.]]],.],.] => [2,4,3,1,5,6] => [[.,.],[[.,.],[.,[.,.]]]]
[[[.,[[.,[.,.]],.]],.],.] => [3,2,4,1,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
[[[.,[[[.,.],.],.]],.],.] => [2,3,4,1,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
[[[[.,.],[.,[.,.]]],.],.] => [1,4,3,2,5,6] => [.,[[[.,.],.],[.,[.,.]]]]
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[[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.],.] => [6,7,5,4,3,2,1,8,9,10,11] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.],.] => [6,7,5,4,3,2,1,8,9,10] => [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[[[.,[[.,[.,[.,[[.,.],.]]]],.]],.],.] => [5,6,4,3,2,7,1,8,9] => [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[[[.,.],.],[[[.,[[[.,.],.],.]],.],.]] => [1,2,5,6,7,4,8,9,3] => [.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.] => [6,7,5,4,3,2,1,8,9] => [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]] => [5,4,3,2,1,8,9,7,6] => [[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]] => [7,6,5,4,3,2,1,9,10,8] => [[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]
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.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
searching the database
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