- FindStat

edit this map or download as text // json

Identifier

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

Images

[] => .

[[]] => [.,.]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 2230 entries. <<<

click to show experimental identities (only identities of compositions of up to three maps are shown)

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 $t$.

Properties

bijective, graded

Sage code

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

Weight

Created

Jan 19, 2020 at 07:28 by FindStatCrew

Updated

Jan 19, 2020 at 07:28 by Martin Rubey