- FindStat

Identifier

Mp00049: Ordered trees —to binary tree: left brother = left child⟶ Binary trees
Mp00015: Binary trees —to ordered tree: right child = right brother⟶ Ordered trees

Images

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 2229 entries. <<<

Map

to binary tree: left brother = left child

Description

Return a binary tree of size

$n-1$ (where

$n$ is the size of

$t$ , and where

$t$ is an ordered tree) by the following recursive rule:
- if

$x$ is the left brother of

$y$ in

$t$ , then

$x$ becomes the left child of

$y$ ;
- if

$x$ is the last child of

$y$ in

$t$ , then

$x$ becomes the right child of

$y$ ,
and removing the root of

$t$ .

Map

to ordered tree: right child = right brother

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 $y$ .