- FindStat

Identifier

Mp00050: Ordered trees —to binary tree: right brother = right child⟶ Binary trees
Mp00010: Binary trees —to ordered tree: left child = left brother⟶ Ordered trees

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 2229 entries. <<<

Map

to binary tree: right brother = right child

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 $t$.

Map

to ordered tree: left child = left brother

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 $y$.