- FindStat

Identifier

Mp00050: Ordered trees —to binary tree: right brother = right child⟶ Binary trees
Mp00008: Binary trees —to complete tree⟶ Ordered trees
St000397: Ordered trees ⟶ ℤ

Values

[[]] => [.,.] => [[],[]] => 2

[[],[]] => [.,[.,.]] => [[],[[],[]]] => 2

[[[]]] => [[.,.],.] => [[[],[]],[]] => 2

[[],[],[]] => [.,[.,[.,.]]] => [[],[[],[[],[]]]] => 2

[[],[[]]] => [.,[[.,.],.]] => [[],[[[],[]],[]]] => 2

[[[]],[]] => [[.,.],[.,.]] => [[[],[]],[[],[]]] => 3

[[[],[]]] => [[.,[.,.]],.] => [[[],[[],[]]],[]] => 2

[[[[]]]] => [[[.,.],.],.] => [[[[],[]],[]],[]] => 2

[[],[],[],[]] => [.,[.,[.,[.,.]]]] => [[],[[],[[],[[],[]]]]] => 2

[[],[],[[]]] => [.,[.,[[.,.],.]]] => [[],[[],[[[],[]],[]]]] => 2

[[],[[]],[]] => [.,[[.,.],[.,.]]] => [[],[[[],[]],[[],[]]]] => 3

[[],[[],[]]] => [.,[[.,[.,.]],.]] => [[],[[[],[[],[]]],[]]] => 2

[[],[[[]]]] => [.,[[[.,.],.],.]] => [[],[[[[],[]],[]],[]]] => 2

[[[]],[],[]] => [[.,.],[.,[.,.]]] => [[[],[]],[[],[[],[]]]] => 3

[[[]],[[]]] => [[.,.],[[.,.],.]] => [[[],[]],[[[],[]],[]]] => 3

[[[],[]],[]] => [[.,[.,.]],[.,.]] => [[[],[[],[]]],[[],[]]] => 3

[[[[]]],[]] => [[[.,.],.],[.,.]] => [[[[],[]],[]],[[],[]]] => 3

[[[],[],[]]] => [[.,[.,[.,.]]],.] => [[[],[[],[[],[]]]],[]] => 2

[[[],[[]]]] => [[.,[[.,.],.]],.] => [[[],[[[],[]],[]]],[]] => 2

[[[[]],[]]] => [[[.,.],[.,.]],.] => [[[[],[]],[[],[]]],[]] => 3

[[[[],[]]]] => [[[.,[.,.]],.],.] => [[[[],[[],[]]],[]],[]] => 2

[[[[[]]]]] => [[[[.,.],.],.],.] => [[[[[],[]],[]],[]],[]] => 2

[[],[],[],[],[]] => [.,[.,[.,[.,[.,.]]]]] => [[],[[],[[],[[],[[],[]]]]]] => 2

[[],[],[],[[]]] => [.,[.,[.,[[.,.],.]]]] => [[],[[],[[],[[[],[]],[]]]]] => 2

[[],[],[[]],[]] => [.,[.,[[.,.],[.,.]]]] => [[],[[],[[[],[]],[[],[]]]]] => 3

[[],[],[[],[]]] => [.,[.,[[.,[.,.]],.]]] => [[],[[],[[[],[[],[]]],[]]]] => 2

[[],[],[[[]]]] => [.,[.,[[[.,.],.],.]]] => [[],[[],[[[[],[]],[]],[]]]] => 2

[[],[[]],[],[]] => [.,[[.,.],[.,[.,.]]]] => [[],[[[],[]],[[],[[],[]]]]] => 3

[[],[[]],[[]]] => [.,[[.,.],[[.,.],.]]] => [[],[[[],[]],[[[],[]],[]]]] => 3

[[],[[],[]],[]] => [.,[[.,[.,.]],[.,.]]] => [[],[[[],[[],[]]],[[],[]]]] => 3

[[],[[[]]],[]] => [.,[[[.,.],.],[.,.]]] => [[],[[[[],[]],[]],[[],[]]]] => 3

[[],[[],[],[]]] => [.,[[.,[.,[.,.]]],.]] => [[],[[[],[[],[[],[]]]],[]]] => 2

[[],[[],[[]]]] => [.,[[.,[[.,.],.]],.]] => [[],[[[],[[[],[]],[]]],[]]] => 2

[[],[[[]],[]]] => [.,[[[.,.],[.,.]],.]] => [[],[[[[],[]],[[],[]]],[]]] => 3

[[],[[[],[]]]] => [.,[[[.,[.,.]],.],.]] => [[],[[[[],[[],[]]],[]],[]]] => 2

[[],[[[[]]]]] => [.,[[[[.,.],.],.],.]] => [[],[[[[[],[]],[]],[]],[]]] => 2

[[[]],[],[],[]] => [[.,.],[.,[.,[.,.]]]] => [[[],[]],[[],[[],[[],[]]]]] => 3

[[[]],[],[[]]] => [[.,.],[.,[[.,.],.]]] => [[[],[]],[[],[[[],[]],[]]]] => 3

[[[]],[[]],[]] => [[.,.],[[.,.],[.,.]]] => [[[],[]],[[[],[]],[[],[]]]] => 3

[[[]],[[],[]]] => [[.,.],[[.,[.,.]],.]] => [[[],[]],[[[],[[],[]]],[]]] => 3

[[[]],[[[]]]] => [[.,.],[[[.,.],.],.]] => [[[],[]],[[[[],[]],[]],[]]] => 3

[[[],[]],[],[]] => [[.,[.,.]],[.,[.,.]]] => [[[],[[],[]]],[[],[[],[]]]] => 3

[[[[]]],[],[]] => [[[.,.],.],[.,[.,.]]] => [[[[],[]],[]],[[],[[],[]]]] => 3

[[[],[]],[[]]] => [[.,[.,.]],[[.,.],.]] => [[[],[[],[]]],[[[],[]],[]]] => 3

[[[[]]],[[]]] => [[[.,.],.],[[.,.],.]] => [[[[],[]],[]],[[[],[]],[]]] => 3

[[[],[],[]],[]] => [[.,[.,[.,.]]],[.,.]] => [[[],[[],[[],[]]]],[[],[]]] => 3

[[[],[[]]],[]] => [[.,[[.,.],.]],[.,.]] => [[[],[[[],[]],[]]],[[],[]]] => 3

[[[[]],[]],[]] => [[[.,.],[.,.]],[.,.]] => [[[[],[]],[[],[]]],[[],[]]] => 3

[[[[],[]]],[]] => [[[.,[.,.]],.],[.,.]] => [[[[],[[],[]]],[]],[[],[]]] => 3

[[[[[]]]],[]] => [[[[.,.],.],.],[.,.]] => [[[[[],[]],[]],[]],[[],[]]] => 3

[[[],[],[],[]]] => [[.,[.,[.,[.,.]]]],.] => [[[],[[],[[],[[],[]]]]],[]] => 2

[[[],[],[[]]]] => [[.,[.,[[.,.],.]]],.] => [[[],[[],[[[],[]],[]]]],[]] => 2

[[[],[[]],[]]] => [[.,[[.,.],[.,.]]],.] => [[[],[[[],[]],[[],[]]]],[]] => 3

[[[],[[],[]]]] => [[.,[[.,[.,.]],.]],.] => [[[],[[[],[[],[]]],[]]],[]] => 2

[[[],[[[]]]]] => [[.,[[[.,.],.],.]],.] => [[[],[[[[],[]],[]],[]]],[]] => 2

[[[[]],[],[]]] => [[[.,.],[.,[.,.]]],.] => [[[[],[]],[[],[[],[]]]],[]] => 3

[[[[]],[[]]]] => [[[.,.],[[.,.],.]],.] => [[[[],[]],[[[],[]],[]]],[]] => 3

[[[[],[]],[]]] => [[[.,[.,.]],[.,.]],.] => [[[[],[[],[]]],[[],[]]],[]] => 3

[[[[[]]],[]]] => [[[[.,.],.],[.,.]],.] => [[[[[],[]],[]],[[],[]]],[]] => 3

[[[[],[],[]]]] => [[[.,[.,[.,.]]],.],.] => [[[[],[[],[[],[]]]],[]],[]] => 2

[[[[],[[]]]]] => [[[.,[[.,.],.]],.],.] => [[[[],[[[],[]],[]]],[]],[]] => 2

[[[[[]],[]]]] => [[[[.,.],[.,.]],.],.] => [[[[[],[]],[[],[]]],[]],[]] => 3

[[[[[],[]]]]] => [[[[.,[.,.]],.],.],.] => [[[[[],[[],[]]],[]],[]],[]] => 2

[[[[[[]]]]]] => [[[[[.,.],.],.],.],.] => [[[[[[],[]],[]],[]],[]],[]] => 2

[[],[],[],[],[],[]] => [.,[.,[.,[.,[.,[.,.]]]]]] => [[],[[],[[],[[],[[],[[],[]]]]]]] => 2

[[],[],[],[],[[]]] => [.,[.,[.,[.,[[.,.],.]]]]] => [[],[[],[[],[[],[[[],[]],[]]]]]] => 2

[[],[],[],[[]],[]] => [.,[.,[.,[[.,.],[.,.]]]]] => [[],[[],[[],[[[],[]],[[],[]]]]]] => 3

[[],[],[],[[],[]]] => [.,[.,[.,[[.,[.,.]],.]]]] => [[],[[],[[],[[[],[[],[]]],[]]]]] => 2

[[],[],[],[[[]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [[],[[],[[],[[[[],[]],[]],[]]]]] => 2

[[],[],[[]],[],[]] => [.,[.,[[.,.],[.,[.,.]]]]] => [[],[[],[[[],[]],[[],[[],[]]]]]] => 3

[[],[],[[]],[[]]] => [.,[.,[[.,.],[[.,.],.]]]] => [[],[[],[[[],[]],[[[],[]],[]]]]] => 3

[[],[],[[],[]],[]] => [.,[.,[[.,[.,.]],[.,.]]]] => [[],[[],[[[],[[],[]]],[[],[]]]]] => 3

[[],[],[[[]]],[]] => [.,[.,[[[.,.],.],[.,.]]]] => [[],[[],[[[[],[]],[]],[[],[]]]]] => 3

[[],[],[[],[],[]]] => [.,[.,[[.,[.,[.,.]]],.]]] => [[],[[],[[[],[[],[[],[]]]],[]]]] => 2

[[],[],[[],[[]]]] => [.,[.,[[.,[[.,.],.]],.]]] => [[],[[],[[[],[[[],[]],[]]],[]]]] => 2

[[],[],[[[]],[]]] => [.,[.,[[[.,.],[.,.]],.]]] => [[],[[],[[[[],[]],[[],[]]],[]]]] => 3

[[],[],[[[],[]]]] => [.,[.,[[[.,[.,.]],.],.]]] => [[],[[],[[[[],[[],[]]],[]],[]]]] => 2

[[],[],[[[[]]]]] => [.,[.,[[[[.,.],.],.],.]]] => [[],[[],[[[[[],[]],[]],[]],[]]]] => 2

[[],[[]],[],[],[]] => [.,[[.,.],[.,[.,[.,.]]]]] => [[],[[[],[]],[[],[[],[[],[]]]]]] => 3

[[],[[]],[],[[]]] => [.,[[.,.],[.,[[.,.],.]]]] => [[],[[[],[]],[[],[[[],[]],[]]]]] => 3

[[],[[]],[[]],[]] => [.,[[.,.],[[.,.],[.,.]]]] => [[],[[[],[]],[[[],[]],[[],[]]]]] => 3

[[],[[]],[[],[]]] => [.,[[.,.],[[.,[.,.]],.]]] => [[],[[[],[]],[[[],[[],[]]],[]]]] => 3

[[],[[]],[[[]]]] => [.,[[.,.],[[[.,.],.],.]]] => [[],[[[],[]],[[[[],[]],[]],[]]]] => 3

[[],[[],[]],[],[]] => [.,[[.,[.,.]],[.,[.,.]]]] => [[],[[[],[[],[]]],[[],[[],[]]]]] => 3

[[],[[[]]],[],[]] => [.,[[[.,.],.],[.,[.,.]]]] => [[],[[[[],[]],[]],[[],[[],[]]]]] => 3

[[],[[],[]],[[]]] => [.,[[.,[.,.]],[[.,.],.]]] => [[],[[[],[[],[]]],[[[],[]],[]]]] => 3

[[],[[[]]],[[]]] => [.,[[[.,.],.],[[.,.],.]]] => [[],[[[[],[]],[]],[[[],[]],[]]]] => 3

[[],[[],[],[]],[]] => [.,[[.,[.,[.,.]]],[.,.]]] => [[],[[[],[[],[[],[]]]],[[],[]]]] => 3

[[],[[],[[]]],[]] => [.,[[.,[[.,.],.]],[.,.]]] => [[],[[[],[[[],[]],[]]],[[],[]]]] => 3

[[],[[[]],[]],[]] => [.,[[[.,.],[.,.]],[.,.]]] => [[],[[[[],[]],[[],[]]],[[],[]]]] => 3

[[],[[[],[]]],[]] => [.,[[[.,[.,.]],.],[.,.]]] => [[],[[[[],[[],[]]],[]],[[],[]]]] => 3

[[],[[[[]]]],[]] => [.,[[[[.,.],.],.],[.,.]]] => [[],[[[[[],[]],[]],[]],[[],[]]]] => 3

[[],[[],[],[],[]]] => [.,[[.,[.,[.,[.,.]]]],.]] => [[],[[[],[[],[[],[[],[]]]]],[]]] => 2

[[],[[],[],[[]]]] => [.,[[.,[.,[[.,.],.]]],.]] => [[],[[[],[[],[[[],[]],[]]]],[]]] => 2

[[],[[],[[]],[]]] => [.,[[.,[[.,.],[.,.]]],.]] => [[],[[[],[[[],[]],[[],[]]]],[]]] => 3

[[],[[],[[],[]]]] => [.,[[.,[[.,[.,.]],.]],.]] => [[],[[[],[[[],[[],[]]],[]]],[]]] => 2

[[],[[],[[[]]]]] => [.,[[.,[[[.,.],.],.]],.]] => [[],[[[],[[[[],[]],[]],[]]],[]]] => 2

[[],[[[]],[],[]]] => [.,[[[.,.],[.,[.,.]]],.]] => [[],[[[[],[]],[[],[[],[]]]],[]]] => 3

[[],[[[]],[[]]]] => [.,[[[.,.],[[.,.],.]],.]] => [[],[[[[],[]],[[[],[]],[]]],[]]] => 3

[[],[[[],[]],[]]] => [.,[[[.,[.,.]],[.,.]],.]] => [[],[[[[],[[],[]]],[[],[]]],[]]] => 3

[[],[[[[]]],[]]] => [.,[[[[.,.],.],[.,.]],.]] => [[],[[[[[],[]],[]],[[],[]]],[]]] => 3

>>> Load all 196 entries. <<<

[[],[[[],[],[]]]] => [.,[[[.,[.,[.,.]]],.],.]] => [[],[[[[],[[],[[],[]]]],[]],[]]] => 2

[[],[[[],[[]]]]] => [.,[[[.,[[.,.],.]],.],.]] => [[],[[[[],[[[],[]],[]]],[]],[]]] => 2

[[],[[[[]],[]]]] => [.,[[[[.,.],[.,.]],.],.]] => [[],[[[[[],[]],[[],[]]],[]],[]]] => 3

[[],[[[[],[]]]]] => [.,[[[[.,[.,.]],.],.],.]] => [[],[[[[[],[[],[]]],[]],[]],[]]] => 2

[[],[[[[[]]]]]] => [.,[[[[[.,.],.],.],.],.]] => [[],[[[[[[],[]],[]],[]],[]],[]]] => 2

[[[]],[],[],[],[]] => [[.,.],[.,[.,[.,[.,.]]]]] => [[[],[]],[[],[[],[[],[[],[]]]]]] => 3

[[[]],[],[],[[]]] => [[.,.],[.,[.,[[.,.],.]]]] => [[[],[]],[[],[[],[[[],[]],[]]]]] => 3

[[[]],[],[[]],[]] => [[.,.],[.,[[.,.],[.,.]]]] => [[[],[]],[[],[[[],[]],[[],[]]]]] => 3

[[[]],[],[[],[]]] => [[.,.],[.,[[.,[.,.]],.]]] => [[[],[]],[[],[[[],[[],[]]],[]]]] => 3

[[[]],[],[[[]]]] => [[.,.],[.,[[[.,.],.],.]]] => [[[],[]],[[],[[[[],[]],[]],[]]]] => 3

[[[]],[[]],[],[]] => [[.,.],[[.,.],[.,[.,.]]]] => [[[],[]],[[[],[]],[[],[[],[]]]]] => 3

[[[]],[[]],[[]]] => [[.,.],[[.,.],[[.,.],.]]] => [[[],[]],[[[],[]],[[[],[]],[]]]] => 3

[[[]],[[],[]],[]] => [[.,.],[[.,[.,.]],[.,.]]] => [[[],[]],[[[],[[],[]]],[[],[]]]] => 3

[[[]],[[[]]],[]] => [[.,.],[[[.,.],.],[.,.]]] => [[[],[]],[[[[],[]],[]],[[],[]]]] => 3

[[[]],[[],[],[]]] => [[.,.],[[.,[.,[.,.]]],.]] => [[[],[]],[[[],[[],[[],[]]]],[]]] => 3

[[[]],[[],[[]]]] => [[.,.],[[.,[[.,.],.]],.]] => [[[],[]],[[[],[[[],[]],[]]],[]]] => 3

[[[]],[[[]],[]]] => [[.,.],[[[.,.],[.,.]],.]] => [[[],[]],[[[[],[]],[[],[]]],[]]] => 3

[[[]],[[[],[]]]] => [[.,.],[[[.,[.,.]],.],.]] => [[[],[]],[[[[],[[],[]]],[]],[]]] => 3

[[[]],[[[[]]]]] => [[.,.],[[[[.,.],.],.],.]] => [[[],[]],[[[[[],[]],[]],[]],[]]] => 3

[[[],[]],[],[],[]] => [[.,[.,.]],[.,[.,[.,.]]]] => [[[],[[],[]]],[[],[[],[[],[]]]]] => 3

[[[[]]],[],[],[]] => [[[.,.],.],[.,[.,[.,.]]]] => [[[[],[]],[]],[[],[[],[[],[]]]]] => 3

[[[],[]],[],[[]]] => [[.,[.,.]],[.,[[.,.],.]]] => [[[],[[],[]]],[[],[[[],[]],[]]]] => 3

[[[[]]],[],[[]]] => [[[.,.],.],[.,[[.,.],.]]] => [[[[],[]],[]],[[],[[[],[]],[]]]] => 3

[[[],[]],[[]],[]] => [[.,[.,.]],[[.,.],[.,.]]] => [[[],[[],[]]],[[[],[]],[[],[]]]] => 3

[[[[]]],[[]],[]] => [[[.,.],.],[[.,.],[.,.]]] => [[[[],[]],[]],[[[],[]],[[],[]]]] => 3

[[[],[]],[[],[]]] => [[.,[.,.]],[[.,[.,.]],.]] => [[[],[[],[]]],[[[],[[],[]]],[]]] => 3

[[[],[]],[[[]]]] => [[.,[.,.]],[[[.,.],.],.]] => [[[],[[],[]]],[[[[],[]],[]],[]]] => 3

[[[[]]],[[],[]]] => [[[.,.],.],[[.,[.,.]],.]] => [[[[],[]],[]],[[[],[[],[]]],[]]] => 3

[[[[]]],[[[]]]] => [[[.,.],.],[[[.,.],.],.]] => [[[[],[]],[]],[[[[],[]],[]],[]]] => 3

[[[],[],[]],[],[]] => [[.,[.,[.,.]]],[.,[.,.]]] => [[[],[[],[[],[]]]],[[],[[],[]]]] => 3

[[[],[[]]],[],[]] => [[.,[[.,.],.]],[.,[.,.]]] => [[[],[[[],[]],[]]],[[],[[],[]]]] => 3

[[[[]],[]],[],[]] => [[[.,.],[.,.]],[.,[.,.]]] => [[[[],[]],[[],[]]],[[],[[],[]]]] => 3

[[[[],[]]],[],[]] => [[[.,[.,.]],.],[.,[.,.]]] => [[[[],[[],[]]],[]],[[],[[],[]]]] => 3

[[[[[]]]],[],[]] => [[[[.,.],.],.],[.,[.,.]]] => [[[[[],[]],[]],[]],[[],[[],[]]]] => 3

[[[],[],[]],[[]]] => [[.,[.,[.,.]]],[[.,.],.]] => [[[],[[],[[],[]]]],[[[],[]],[]]] => 3

[[[],[[]]],[[]]] => [[.,[[.,.],.]],[[.,.],.]] => [[[],[[[],[]],[]]],[[[],[]],[]]] => 3

[[[[]],[]],[[]]] => [[[.,.],[.,.]],[[.,.],.]] => [[[[],[]],[[],[]]],[[[],[]],[]]] => 3

[[[[],[]]],[[]]] => [[[.,[.,.]],.],[[.,.],.]] => [[[[],[[],[]]],[]],[[[],[]],[]]] => 3

[[[[[]]]],[[]]] => [[[[.,.],.],.],[[.,.],.]] => [[[[[],[]],[]],[]],[[[],[]],[]]] => 3

[[[],[],[],[]],[]] => [[.,[.,[.,[.,.]]]],[.,.]] => [[[],[[],[[],[[],[]]]]],[[],[]]] => 3

[[[],[],[[]]],[]] => [[.,[.,[[.,.],.]]],[.,.]] => [[[],[[],[[[],[]],[]]]],[[],[]]] => 3

[[[],[[]],[]],[]] => [[.,[[.,.],[.,.]]],[.,.]] => [[[],[[[],[]],[[],[]]]],[[],[]]] => 3

[[[],[[],[]]],[]] => [[.,[[.,[.,.]],.]],[.,.]] => [[[],[[[],[[],[]]],[]]],[[],[]]] => 3

[[[],[[[]]]],[]] => [[.,[[[.,.],.],.]],[.,.]] => [[[],[[[[],[]],[]],[]]],[[],[]]] => 3

[[[[]],[],[]],[]] => [[[.,.],[.,[.,.]]],[.,.]] => [[[[],[]],[[],[[],[]]]],[[],[]]] => 3

[[[[]],[[]]],[]] => [[[.,.],[[.,.],.]],[.,.]] => [[[[],[]],[[[],[]],[]]],[[],[]]] => 3

[[[[],[]],[]],[]] => [[[.,[.,.]],[.,.]],[.,.]] => [[[[],[[],[]]],[[],[]]],[[],[]]] => 3

[[[[[]]],[]],[]] => [[[[.,.],.],[.,.]],[.,.]] => [[[[[],[]],[]],[[],[]]],[[],[]]] => 3

[[[[],[],[]]],[]] => [[[.,[.,[.,.]]],.],[.,.]] => [[[[],[[],[[],[]]]],[]],[[],[]]] => 3

[[[[],[[]]]],[]] => [[[.,[[.,.],.]],.],[.,.]] => [[[[],[[[],[]],[]]],[]],[[],[]]] => 3

[[[[[]],[]]],[]] => [[[[.,.],[.,.]],.],[.,.]] => [[[[[],[]],[[],[]]],[]],[[],[]]] => 3

[[[[[],[]]]],[]] => [[[[.,[.,.]],.],.],[.,.]] => [[[[[],[[],[]]],[]],[]],[[],[]]] => 3

[[[[[[]]]]],[]] => [[[[[.,.],.],.],.],[.,.]] => [[[[[[],[]],[]],[]],[]],[[],[]]] => 3

[[[],[],[],[],[]]] => [[.,[.,[.,[.,[.,.]]]]],.] => [[[],[[],[[],[[],[[],[]]]]]],[]] => 2

[[[],[],[],[[]]]] => [[.,[.,[.,[[.,.],.]]]],.] => [[[],[[],[[],[[[],[]],[]]]]],[]] => 2

[[[],[],[[]],[]]] => [[.,[.,[[.,.],[.,.]]]],.] => [[[],[[],[[[],[]],[[],[]]]]],[]] => 3

[[[],[],[[],[]]]] => [[.,[.,[[.,[.,.]],.]]],.] => [[[],[[],[[[],[[],[]]],[]]]],[]] => 2

[[[],[],[[[]]]]] => [[.,[.,[[[.,.],.],.]]],.] => [[[],[[],[[[[],[]],[]],[]]]],[]] => 2

[[[],[[]],[],[]]] => [[.,[[.,.],[.,[.,.]]]],.] => [[[],[[[],[]],[[],[[],[]]]]],[]] => 3

[[[],[[]],[[]]]] => [[.,[[.,.],[[.,.],.]]],.] => [[[],[[[],[]],[[[],[]],[]]]],[]] => 3

[[[],[[],[]],[]]] => [[.,[[.,[.,.]],[.,.]]],.] => [[[],[[[],[[],[]]],[[],[]]]],[]] => 3

[[[],[[[]]],[]]] => [[.,[[[.,.],.],[.,.]]],.] => [[[],[[[[],[]],[]],[[],[]]]],[]] => 3

[[[],[[],[],[]]]] => [[.,[[.,[.,[.,.]]],.]],.] => [[[],[[[],[[],[[],[]]]],[]]],[]] => 2

[[[],[[],[[]]]]] => [[.,[[.,[[.,.],.]],.]],.] => [[[],[[[],[[[],[]],[]]],[]]],[]] => 2

[[[],[[[]],[]]]] => [[.,[[[.,.],[.,.]],.]],.] => [[[],[[[[],[]],[[],[]]],[]]],[]] => 3

[[[],[[[],[]]]]] => [[.,[[[.,[.,.]],.],.]],.] => [[[],[[[[],[[],[]]],[]],[]]],[]] => 2

[[[],[[[[]]]]]] => [[.,[[[[.,.],.],.],.]],.] => [[[],[[[[[],[]],[]],[]],[]]],[]] => 2

[[[[]],[],[],[]]] => [[[.,.],[.,[.,[.,.]]]],.] => [[[[],[]],[[],[[],[[],[]]]]],[]] => 3

[[[[]],[],[[]]]] => [[[.,.],[.,[[.,.],.]]],.] => [[[[],[]],[[],[[[],[]],[]]]],[]] => 3

[[[[]],[[]],[]]] => [[[.,.],[[.,.],[.,.]]],.] => [[[[],[]],[[[],[]],[[],[]]]],[]] => 3

[[[[]],[[],[]]]] => [[[.,.],[[.,[.,.]],.]],.] => [[[[],[]],[[[],[[],[]]],[]]],[]] => 3

[[[[]],[[[]]]]] => [[[.,.],[[[.,.],.],.]],.] => [[[[],[]],[[[[],[]],[]],[]]],[]] => 3

[[[[],[]],[],[]]] => [[[.,[.,.]],[.,[.,.]]],.] => [[[[],[[],[]]],[[],[[],[]]]],[]] => 3

[[[[[]]],[],[]]] => [[[[.,.],.],[.,[.,.]]],.] => [[[[[],[]],[]],[[],[[],[]]]],[]] => 3

[[[[],[]],[[]]]] => [[[.,[.,.]],[[.,.],.]],.] => [[[[],[[],[]]],[[[],[]],[]]],[]] => 3

[[[[[]]],[[]]]] => [[[[.,.],.],[[.,.],.]],.] => [[[[[],[]],[]],[[[],[]],[]]],[]] => 3

[[[[],[],[]],[]]] => [[[.,[.,[.,.]]],[.,.]],.] => [[[[],[[],[[],[]]]],[[],[]]],[]] => 3

[[[[],[[]]],[]]] => [[[.,[[.,.],.]],[.,.]],.] => [[[[],[[[],[]],[]]],[[],[]]],[]] => 3

[[[[[]],[]],[]]] => [[[[.,.],[.,.]],[.,.]],.] => [[[[[],[]],[[],[]]],[[],[]]],[]] => 3

[[[[[],[]]],[]]] => [[[[.,[.,.]],.],[.,.]],.] => [[[[[],[[],[]]],[]],[[],[]]],[]] => 3

[[[[[[]]]],[]]] => [[[[[.,.],.],.],[.,.]],.] => [[[[[[],[]],[]],[]],[[],[]]],[]] => 3

[[[[],[],[],[]]]] => [[[.,[.,[.,[.,.]]]],.],.] => [[[[],[[],[[],[[],[]]]]],[]],[]] => 2

[[[[],[],[[]]]]] => [[[.,[.,[[.,.],.]]],.],.] => [[[[],[[],[[[],[]],[]]]],[]],[]] => 2

[[[[],[[]],[]]]] => [[[.,[[.,.],[.,.]]],.],.] => [[[[],[[[],[]],[[],[]]]],[]],[]] => 3

[[[[],[[],[]]]]] => [[[.,[[.,[.,.]],.]],.],.] => [[[[],[[[],[[],[]]],[]]],[]],[]] => 2

[[[[],[[[]]]]]] => [[[.,[[[.,.],.],.]],.],.] => [[[[],[[[[],[]],[]],[]]],[]],[]] => 2

[[[[[]],[],[]]]] => [[[[.,.],[.,[.,.]]],.],.] => [[[[[],[]],[[],[[],[]]]],[]],[]] => 3

[[[[[]],[[]]]]] => [[[[.,.],[[.,.],.]],.],.] => [[[[[],[]],[[[],[]],[]]],[]],[]] => 3

[[[[[],[]],[]]]] => [[[[.,[.,.]],[.,.]],.],.] => [[[[[],[[],[]]],[[],[]]],[]],[]] => 3

[[[[[[]]],[]]]] => [[[[[.,.],.],[.,.]],.],.] => [[[[[[],[]],[]],[[],[]]],[]],[]] => 3

[[[[[],[],[]]]]] => [[[[.,[.,[.,.]]],.],.],.] => [[[[[],[[],[[],[]]]],[]],[]],[]] => 2

[[[[[],[[]]]]]] => [[[[.,[[.,.],.]],.],.],.] => [[[[[],[[[],[]],[]]],[]],[]],[]] => 2

[[[[[[]],[]]]]] => [[[[[.,.],[.,.]],.],.],.] => [[[[[[],[]],[[],[]]],[]],[]],[]] => 3

[[[[[[],[]]]]]] => [[[[[.,[.,.]],.],.],.],.] => [[[[[[],[[],[]]],[]],[]],[]],[]] => 2

[[[[[[[]]]]]]] => [[[[[[.,.],.],.],.],.],.] => [[[[[[[],[]],[]],[]],[]],[]],[]] => 2

search for individual values

searching the database for the individual values of this statistic

/ search for generating function

searching the database for statistics with the same generating function

click to show known generating functions

Description

The Strahler number of a rooted tree.

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 complete tree

Description

Return the same tree seen as an ordered tree. By default, leaves are transformed into actual nodes.