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Identifier

Mp00010: Binary trees —to ordered tree: left child = left brother⟶ Ordered trees

Images

[.,.] => [[]]

[.,[.,.]] => [[[]]]

[[.,.],.] => [[],[]]

[.,[.,[.,.]]] => [[[[]]]]

[.,[[.,.],.]] => [[[],[]]]

[[.,.],[.,.]] => [[],[[]]]

[[.,[.,.]],.] => [[[]],[]]

[[[.,.],.],.] => [[],[],[]]

[.,[.,[.,[.,.]]]] => [[[[[]]]]]

[.,[.,[[.,.],.]]] => [[[[],[]]]]

[.,[[.,.],[.,.]]] => [[[],[[]]]]

[.,[[.,[.,.]],.]] => [[[[]],[]]]

[.,[[[.,.],.],.]] => [[[],[],[]]]

[[.,.],[.,[.,.]]] => [[],[[[]]]]

[[.,.],[[.,.],.]] => [[],[[],[]]]

[[.,[.,.]],[.,.]] => [[[]],[[]]]

[[[.,.],.],[.,.]] => [[],[],[[]]]

[[.,[.,[.,.]]],.] => [[[[]]],[]]

[[.,[[.,.],.]],.] => [[[],[]],[]]

[[[.,.],[.,.]],.] => [[],[[]],[]]

[[[.,[.,.]],.],.] => [[[]],[],[]]

[[[[.,.],.],.],.] => [[],[],[],[]]

[.,[.,[.,[.,[.,.]]]]] => [[[[[[]]]]]]

[.,[.,[.,[[.,.],.]]]] => [[[[[],[]]]]]

[.,[.,[[.,.],[.,.]]]] => [[[[],[[]]]]]

[.,[.,[[.,[.,.]],.]]] => [[[[[]],[]]]]

[.,[.,[[[.,.],.],.]]] => [[[[],[],[]]]]

[.,[[.,.],[.,[.,.]]]] => [[[],[[[]]]]]

[.,[[.,.],[[.,.],.]]] => [[[],[[],[]]]]

[.,[[.,[.,.]],[.,.]]] => [[[[]],[[]]]]

[.,[[[.,.],.],[.,.]]] => [[[],[],[[]]]]

[.,[[.,[.,[.,.]]],.]] => [[[[[]]],[]]]

[.,[[.,[[.,.],.]],.]] => [[[[],[]],[]]]

[.,[[[.,.],[.,.]],.]] => [[[],[[]],[]]]

[.,[[[.,[.,.]],.],.]] => [[[[]],[],[]]]

[.,[[[[.,.],.],.],.]] => [[[],[],[],[]]]

[[.,.],[.,[.,[.,.]]]] => [[],[[[[]]]]]

[[.,.],[.,[[.,.],.]]] => [[],[[[],[]]]]

[[.,.],[[.,.],[.,.]]] => [[],[[],[[]]]]

[[.,.],[[.,[.,.]],.]] => [[],[[[]],[]]]

[[.,.],[[[.,.],.],.]] => [[],[[],[],[]]]

[[.,[.,.]],[.,[.,.]]] => [[[]],[[[]]]]

[[.,[.,.]],[[.,.],.]] => [[[]],[[],[]]]

[[[.,.],.],[.,[.,.]]] => [[],[],[[[]]]]

[[[.,.],.],[[.,.],.]] => [[],[],[[],[]]]

[[.,[.,[.,.]]],[.,.]] => [[[[]]],[[]]]

[[.,[[.,.],.]],[.,.]] => [[[],[]],[[]]]

[[[.,.],[.,.]],[.,.]] => [[],[[]],[[]]]

[[[.,[.,.]],.],[.,.]] => [[[]],[],[[]]]

[[[[.,.],.],.],[.,.]] => [[],[],[],[[]]]

[[.,[.,[.,[.,.]]]],.] => [[[[[]]]],[]]

[[.,[.,[[.,.],.]]],.] => [[[[],[]]],[]]

[[.,[[.,.],[.,.]]],.] => [[[],[[]]],[]]

[[.,[[.,[.,.]],.]],.] => [[[[]],[]],[]]

[[.,[[[.,.],.],.]],.] => [[[],[],[]],[]]

[[[.,.],[.,[.,.]]],.] => [[],[[[]]],[]]

[[[.,.],[[.,.],.]],.] => [[],[[],[]],[]]

[[[.,[.,.]],[.,.]],.] => [[[]],[[]],[]]

[[[[.,.],.],[.,.]],.] => [[],[],[[]],[]]

[[[.,[.,[.,.]]],.],.] => [[[[]]],[],[]]

[[[.,[[.,.],.]],.],.] => [[[],[]],[],[]]

[[[[.,.],[.,.]],.],.] => [[],[[]],[],[]]

[[[[.,[.,.]],.],.],.] => [[[]],[],[],[]]

[[[[[.,.],.],.],.],.] => [[],[],[],[],[]]

[.,[.,[.,[.,[.,[.,.]]]]]] => [[[[[[[]]]]]]]

[.,[.,[.,[.,[[.,.],.]]]]] => [[[[[[],[]]]]]]

[.,[.,[.,[[.,.],[.,.]]]]] => [[[[[],[[]]]]]]

[.,[.,[.,[[.,[.,.]],.]]]] => [[[[[[]],[]]]]]

[.,[.,[.,[[[.,.],.],.]]]] => [[[[[],[],[]]]]]

[.,[.,[[.,.],[.,[.,.]]]]] => [[[[],[[[]]]]]]

[.,[.,[[.,.],[[.,.],.]]]] => [[[[],[[],[]]]]]

[.,[.,[[.,[.,.]],[.,.]]]] => [[[[[]],[[]]]]]

[.,[.,[[[.,.],.],[.,.]]]] => [[[[],[],[[]]]]]

[.,[.,[[.,[.,[.,.]]],.]]] => [[[[[[]]],[]]]]

[.,[.,[[.,[[.,.],.]],.]]] => [[[[[],[]],[]]]]

[.,[.,[[[.,.],[.,.]],.]]] => [[[[],[[]],[]]]]

[.,[.,[[[.,[.,.]],.],.]]] => [[[[[]],[],[]]]]

[.,[.,[[[[.,.],.],.],.]]] => [[[[],[],[],[]]]]

[.,[[.,.],[.,[.,[.,.]]]]] => [[[],[[[[]]]]]]

[.,[[.,.],[.,[[.,.],.]]]] => [[[],[[[],[]]]]]

[.,[[.,.],[[.,.],[.,.]]]] => [[[],[[],[[]]]]]

[.,[[.,.],[[.,[.,.]],.]]] => [[[],[[[]],[]]]]

[.,[[.,.],[[[.,.],.],.]]] => [[[],[[],[],[]]]]

[.,[[.,[.,.]],[.,[.,.]]]] => [[[[]],[[[]]]]]

[.,[[.,[.,.]],[[.,.],.]]] => [[[[]],[[],[]]]]

[.,[[[.,.],.],[.,[.,.]]]] => [[[],[],[[[]]]]]

[.,[[[.,.],.],[[.,.],.]]] => [[[],[],[[],[]]]]

[.,[[.,[.,[.,.]]],[.,.]]] => [[[[[]]],[[]]]]

[.,[[.,[[.,.],.]],[.,.]]] => [[[[],[]],[[]]]]

[.,[[[.,.],[.,.]],[.,.]]] => [[[],[[]],[[]]]]

[.,[[[.,[.,.]],.],[.,.]]] => [[[[]],[],[[]]]]

[.,[[[[.,.],.],.],[.,.]]] => [[[],[],[],[[]]]]

[.,[[.,[.,[.,[.,.]]]],.]] => [[[[[[]]]],[]]]

[.,[[.,[.,[[.,.],.]]],.]] => [[[[[],[]]],[]]]

[.,[[.,[[.,.],[.,.]]],.]] => [[[[],[[]]],[]]]

[.,[[.,[[.,[.,.]],.]],.]] => [[[[[]],[]],[]]]

[.,[[.,[[[.,.],.],.]],.]] => [[[[],[],[]],[]]]

[.,[[[.,.],[.,[.,.]]],.]] => [[[],[[[]]],[]]]

[.,[[[.,.],[[.,.],.]],.]] => [[[],[[],[]],[]]]

[.,[[[.,[.,.]],[.,.]],.]] => [[[[]],[[]],[]]]

[.,[[[[.,.],.],[.,.]],.]] => [[[],[],[[]],[]]]

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Description

Return an ordered tree of size $n+1$ by the following recursive rule:

if $x$ is the left child of $y$, $x$ becomes the left brother of $y$,
if $x$ is the right child of $y$, $x$ becomes the last child of $y$.

Properties

bijective, graded

Sage code

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

Weight

Created

Jan 01, 2018 at 00:00 by FindStatCrew

Updated

Jan 06, 2020 at 14:05 by Martin Rubey