edit this map or download as text // json
Identifier
Mp00049: Ordered trees —to binary tree: left brother = left child⟶ Binary trees
Images
=>
Cc0021;cc-rep-0Cc0010;cc-rep-1
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[[[],[[[],[]],[]]],[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[]]]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],[[.,[[.,.],.]],.]]] [[[],[[[],[[[],[]],[]]],[[[],[]],[[[],[[[],[]],[]]],[]]]]],[]]=>[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]]]],.] [[[],[[[],[]],[]]],[[[],[[[],[]],[[[],[[[],[]],[]]],[]]]],[]]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]]],.]] [[[],[[[],[]],[]]],[[[],[]],[[[],[[[],[[[],[]],[]]],[]]],[]]]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]],.]]] [[[],[[[],[]],[]]],[[[],[]],[[[],[[[],[]],[]]],[[[],[]],[]]]]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]]]] [[[],[[[],[[[],[]],[]]],[[[],[]],[[[],[]],[[[],[]],[]]]]]],[]]=>[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]]]],.] 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[[[],[[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[[[],[]],[]]]],[]]=>[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],.]]],[[.,[[.,.],.]],.]]]],.] [[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[[[],[[[],[]],[]]],[]]]=>[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],.]]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] [[[],[[[],[[[],[]],[[[],[]],[]]]],[]]],[[[],[]],[[[],[]],[]]]]=>[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],.]]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]] [[[],[[[],[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[]]]],[]]],[]]=>[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],[[.,[[.,.],.]],.]]]],.]]],.] [[[],[[[],[[[],[]],[[[],[]],[]]]],[[[],[]],[]]]],[[[],[]],[]]]=>[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],[[.,[[.,.],.]],.]]]],[[.,[[.,.],.]],.]] [[[],[[[],[[[],[]],[[[],[]],[]]]],[[[],[[[],[]],[]]],[]]]],[]]=>[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]]],.] 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[[[],[[[],[[[],[[],[]]],[[[],[[[],[]],[[],[]]]],[]]]],[]]],[]]=>[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]]]],.]]],.] [[[[],[[[[],[[[],[[],[]]],[[],[]]]],[]],[[],[]]]],[]],[[],[]]]=>[[.,[[.,[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.]],[[.,.],.]]]],.]],[[.,.],.]] [[[],[[[[],[[[],[[],[]]],[[[],[]],[[],[]]]]],[]],[[],[]]]],[]]=>[[.,[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]]]],.]],[[.,.],.]]]],.] [[[],[[[[[],[[[],[[],[]]],[[],[]]]],[]],[[],[]]],[[],[]]]],[]]=>[[.,[[.,.],[[.,[[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.]],[[.,.],.]]],[[.,.],.]]]],.] [[],[[[[[[],[[[],[]],[[],[]]]],[]],[[],[]]],[[],[]]],[[],[]]]]=>[[.,.],[[.,[[.,[[.,[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]],[[.,.],.]]],[[.,.],.]]],[[.,.],.]]] [[],[[[[[],[[[],[]],[[],[]]]],[]],[[],[]]],[[[],[]],[[],[]]]]]=>[[.,.],[[.,[[.,[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]]] 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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 $t$.
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