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Identifier

Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations

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]

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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.

Properties

injective, graded

Sage code

def mapping(elt):
    return elt.to_312_avoiding_permutation()

Weight

Created

Jan 19, 2020 at 07:29 by FindStatCrew

Updated

Jan 19, 2020 at 07:29 by Martin Rubey