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Identifier

Mp00015: Binary trees —to ordered tree: right child = right 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 right child of $y$ , $x$ becomes the right brother of $y$ ,
if $x$ is the left child of $y$ , $x$ becomes the first child of $y$ .

Properties

bijective, graded

Sage code

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

Weight

Created

Jan 19, 2020 at 07:29 by FindStatCrew

Updated

Jan 19, 2020 at 07:29 by Martin Rubey