Identifier
Images
=>
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[[[],[[[],[[[],[[[],[[[],[[],[]]],[[],[]]]],[]]],[]]],[]]],[]]=>[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.]]],.]]],.]]],.]
[[],[[[[],[[[],[[[],[[[],[]],[[],[]]]],[]]],[]]],[]],[[],[]]]]=>[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]],.]]],.]],[[.,.],.]]]
[[],[[[],[[[[],[[[],[[[],[]],[[],[]]]],[]]],[]],[[],[]]]],[]]]=>[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]],.]],[[.,.],.]]]],.]]
[[],[[[],[[[],[[[[],[[[],[]],[[],[]]]],[]],[[],[]]]],[]]],[]]]=>[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]],[[.,.],.]]]],.]]],.]]
[[],[[[],[[[],[[[],[[[[],[]],[[],[]]],[[],[]]]],[]]],[]]],[]]]=>[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]]],.]]],.]]],.]]
[[],[[[],[[[],[[[],[[[],[[[],[]],[[],[]]]],[]]],[]]],[]]],[]]]=>[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]],.]]],.]]],.]]
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 $t$.
- 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()
Created
Jan 19, 2020 at 07:28 by FindStatCrew
Updated
Jan 19, 2020 at 07:28 by Martin Rubey
searching the database
Sorry, this map was not found in the database.