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Identifier

Mp00050: Ordered trees —to binary tree: right brother = right child⟶ Binary trees

Images

[] => .

[[]] => [.,.]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

Return a binary tree of size $n-1$ (where $n$ is the size of an ordered tree $t$) obtained from $t$ by the following recursive rule:
- if $x$ is the right brother of $y$ in $t$, then $x$ becomes the right child of $y$;
- if $x$ is the first child of $y$ in $t$, then $x$ becomes the left child of $y$,
and removing the root of $t$.

Properties

bijective, graded

Sage code

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

Weight

Created

Jan 26, 2020 at 12:31 by FindStatCrew

Updated

Jan 26, 2020 at 12:31 by Martin Rubey