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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[[],[[],[[[[],[]],[[],[]]],[]]]]=>[[.,.],[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]] [[],[[],[[[[],[[],[]]],[]],[]]]]=>[[.,.],[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]] [[],[[],[[[[[],[]],[]],[]],[]]]]=>[[.,.],[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]] [[],[[[],[]],[[],[[],[[],[]]]]]]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]] [[],[[[],[]],[[],[[[],[]],[]]]]]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]] [[],[[[],[]],[[[],[]],[[],[]]]]]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]] [[],[[[],[]],[[[],[[],[]]],[]]]]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]] [[],[[[],[]],[[[[],[]],[]],[]]]]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]] [[],[[[],[[],[]]],[[],[[],[]]]]]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]] [[],[[[],[[],[]]],[[[],[]],[]]]]=>[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]] [[],[[[[],[]],[]],[[],[[],[]]]]]=>[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]] [[],[[[[],[]],[]],[[[],[]],[]]]]=>[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]] [[],[[[],[[],[[],[]]]],[[],[]]]]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]] [[],[[[],[[[],[]],[]]],[[],[]]]]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]] [[],[[[[],[]],[[],[]]],[[],[]]]]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]] [[],[[[[],[[],[]]],[]],[[],[]]]]=>[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]] [[],[[[[[],[]],[]],[]],[[],[]]]]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]] [[],[[[],[[],[[],[[],[]]]]],[]]]=>[[.,.],[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]] [[],[[[],[[],[[[],[]],[]]]],[]]]=>[[.,.],[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]] [[],[[[],[[[],[]],[[],[]]]],[]]]=>[[.,.],[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]] [[],[[[],[[[],[[],[]]],[]]],[]]]=>[[.,.],[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]] [[],[[[],[[[[],[]],[]],[]]],[]]]=>[[.,.],[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]] [[],[[[[],[]],[[],[[],[]]]],[]]]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]] [[],[[[[],[]],[[[],[]],[]]],[]]]=>[[.,.],[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]] [[],[[[[],[[],[]]],[[],[]]],[]]]=>[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]] [[],[[[[[],[]],[]],[[],[]]],[]]]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]] [[],[[[[],[[],[[],[]]]],[]],[]]]=>[[.,.],[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]] [[],[[[[],[[[],[]],[]]],[]],[]]]=>[[.,.],[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]] [[],[[[[[],[]],[[],[]]],[]],[]]]=>[[.,.],[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]] [[],[[[[[],[[],[]]],[]],[]],[]]]=>[[.,.],[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]] [[],[[[[[[],[]],[]],[]],[]],[]]]=>[[.,.],[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]] [[[],[]],[[],[[],[[],[[],[]]]]]]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] [[[],[]],[[],[[],[[[],[]],[]]]]]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]] [[[],[]],[[],[[[],[]],[[],[]]]]]=>[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]] [[[],[]],[[],[[[],[[],[]]],[]]]]=>[[.,[[.,.],.]],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]] [[[],[]],[[],[[[[],[]],[]],[]]]]=>[[.,[[.,.],.]],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]] [[[],[]],[[[],[]],[[],[[],[]]]]]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]] [[[],[]],[[[],[]],[[[],[]],[]]]]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]] [[[],[]],[[[],[[],[]]],[[],[]]]]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]] [[[],[]],[[[[],[]],[]],[[],[]]]]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]] [[[],[]],[[[],[[],[[],[]]]],[]]]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]] [[[],[]],[[[],[[[],[]],[]]],[]]]=>[[.,[[.,.],.]],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]] [[[],[]],[[[[],[]],[[],[]]],[]]]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]] [[[],[]],[[[[],[[],[]]],[]],[]]]=>[[.,[[.,.],.]],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]] [[[],[]],[[[[[],[]],[]],[]],[]]]=>[[.,[[.,.],.]],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]] [[[],[[],[]]],[[],[[],[[],[]]]]]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],[[.,.],.]]]] [[[],[[],[]]],[[],[[[],[]],[]]]]=>[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,[[.,.],.]],.]]] [[[],[[],[]]],[[[],[]],[[],[]]]]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],[[.,.],.]]] [[[],[[],[]]],[[[],[[],[]]],[]]]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],[[.,.],.]]],.]] [[[],[[],[]]],[[[[],[]],[]],[]]]=>[[.,[[.,.],[[.,.],.]]],[[.,[[.,[[.,.],.]],.]],.]] [[[[],[]],[]],[[],[[],[[],[]]]]]=>[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],[[.,.],.]]]] [[[[],[]],[]],[[],[[[],[]],[]]]]=>[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,[[.,.],.]],.]]] [[[[],[]],[]],[[[],[]],[[],[]]]]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],[[.,.],.]]] [[[[],[]],[]],[[[],[[],[]]],[]]]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],[[.,.],.]]],.]] [[[[],[]],[]],[[[[],[]],[]],[]]]=>[[.,[[.,[[.,.],.]],.]],[[.,[[.,[[.,.],.]],.]],.]] [[[],[[],[[],[]]]],[[],[[],[]]]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],[[.,.],.]]] [[[],[[],[[],[]]]],[[[],[]],[]]]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,[[.,.],.]],.]] [[[],[[[],[]],[]]],[[],[[],[]]]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],[[.,.],.]]] [[[],[[[],[]],[]]],[[[],[]],[]]]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,[[.,.],.]],.]] [[[[],[]],[[],[]]],[[],[[],[]]]]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],[[.,.],.]]] [[[[],[]],[[],[]]],[[[],[]],[]]]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,[[.,.],.]],.]] [[[[],[[],[]]],[]],[[],[[],[]]]]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],[[.,.],.]]] [[[[],[[],[]]],[]],[[[],[]],[]]]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,[[.,.],.]],.]] [[[[[],[]],[]],[]],[[],[[],[]]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],[[.,.],.]]] [[[[[],[]],[]],[]],[[[],[]],[]]]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,[[.,.],.]],.]] [[[],[[],[[],[[],[]]]]],[[],[]]]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],[[.,.],.]] [[[],[[],[[[],[]],[]]]],[[],[]]]=>[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],[[.,.],.]] [[[],[[[],[]],[[],[]]]],[[],[]]]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],[[.,.],.]] [[[],[[[],[[],[]]],[]]],[[],[]]]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],[[.,.],.]] [[[],[[[[],[]],[]],[]]],[[],[]]]=>[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],[[.,.],.]] [[[[],[]],[[],[[],[]]]],[[],[]]]=>[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],[[.,.],.]] [[[[],[]],[[[],[]],[]]],[[],[]]]=>[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],[[.,.],.]] [[[[],[[],[]]],[[],[]]],[[],[]]]=>[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],[[.,.],.]] [[[[[],[]],[]],[[],[]]],[[],[]]]=>[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],[[.,.],.]] [[[[],[[],[[],[]]]],[]],[[],[]]]=>[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],[[.,.],.]] [[[[],[[[],[]],[]]],[]],[[],[]]]=>[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],[[.,.],.]] [[[[[],[]],[[],[]]],[]],[[],[]]]=>[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],[[.,.],.]] [[[[[],[[],[]]],[]],[]],[[],[]]]=>[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],[[.,.],.]] [[[[[[],[]],[]],[]],[]],[[],[]]]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],[[.,.],.]] [[[],[[],[[],[[],[[],[]]]]]],[]]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]],.] [[[],[[],[[],[[[],[]],[]]]]],[]]=>[[.,[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]],.] [[[],[[],[[[],[]],[[],[]]]]],[]]=>[[.,[[.,.],[[.,.],[[.,[[.,.],.]],[[.,.],.]]]]],.] [[[],[[],[[[],[[],[]]],[]]]],[]]=>[[.,[[.,.],[[.,.],[[.,[[.,.],[[.,.],.]]],.]]]],.] [[[],[[],[[[[],[]],[]],[]]]],[]]=>[[.,[[.,.],[[.,.],[[.,[[.,[[.,.],.]],.]],.]]]],.] [[[],[[[],[]],[[],[[],[]]]]],[]]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]],.] [[[],[[[],[]],[[[],[]],[]]]],[]]=>[[.,[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]],.] [[[],[[[],[[],[]]],[[],[]]]],[]]=>[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],[[.,.],.]]]],.] [[[],[[[[],[]],[]],[[],[]]]],[]]=>[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],[[.,.],.]]]],.] [[[],[[[],[[],[[],[]]]],[]]],[]]=>[[.,[[.,.],[[.,[[.,.],[[.,.],[[.,.],.]]]],.]]],.] [[[],[[[],[[[],[]],[]]],[]]],[]]=>[[.,[[.,.],[[.,[[.,.],[[.,[[.,.],.]],.]]],.]]],.] [[[],[[[[],[]],[[],[]]],[]]],[]]=>[[.,[[.,.],[[.,[[.,[[.,.],.]],[[.,.],.]]],.]]],.] [[[],[[[[],[[],[]]],[]],[]]],[]]=>[[.,[[.,.],[[.,[[.,[[.,.],[[.,.],.]]],.]],.]]],.] [[[],[[[[[],[]],[]],[]],[]]],[]]=>[[.,[[.,.],[[.,[[.,[[.,[[.,.],.]],.]],.]],.]]],.] [[[[],[]],[[],[[],[[],[]]]]],[]]=>[[.,[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]],.] [[[[],[]],[[],[[[],[]],[]]]],[]]=>[[.,[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]],.] [[[[],[]],[[[],[]],[[],[]]]],[]]=>[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]],.] [[[[],[]],[[[],[[],[]]],[]]],[]]=>[[.,[[.,[[.,.],.]],[[.,[[.,.],[[.,.],.]]],.]]],.] [[[[],[]],[[[[],[]],[]],[]]],[]]=>[[.,[[.,[[.,.],.]],[[.,[[.,[[.,.],.]],.]],.]]],.] [[[[],[[],[]]],[[],[[],[]]]],[]]=>[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]],.] [[[[],[[],[]]],[[[],[]],[]]],[]]=>[[.,[[.,[[.,.],[[.,.],.]]],[[.,[[.,.],.]],.]]],.] [[[[[],[]],[]],[[],[[],[]]]],[]]=>[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],[[.,.],.]]]],.] [[[[[],[]],[]],[[[],[]],[]]],[]]=>[[.,[[.,[[.,[[.,.],.]],.]],[[.,[[.,.],.]],.]]],.] [[[[],[[],[[],[]]]],[[],[]]],[]]=>[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]],.] [[[[],[[[],[]],[]]],[[],[]]],[]]=>[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],[[.,.],.]]],.] [[[[[],[]],[[],[]]],[[],[]]],[]]=>[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],[[.,.],.]]],.] [[[[[],[[],[]]],[]],[[],[]]],[]]=>[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],[[.,.],.]]],.] [[[[[[],[]],[]],[]],[[],[]]],[]]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],[[.,.],.]]],.] [[[[],[[],[[],[[],[]]]]],[]],[]]=>[[.,[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]],.] [[[[],[[],[[[],[]],[]]]],[]],[]]=>[[.,[[.,[[.,.],[[.,.],[[.,[[.,.],.]],.]]]],.]],.] [[[[],[[[],[]],[[],[]]]],[]],[]]=>[[.,[[.,[[.,.],[[.,[[.,.],.]],[[.,.],.]]]],.]],.] [[[[],[[[],[[],[]]],[]]],[]],[]]=>[[.,[[.,[[.,.],[[.,[[.,.],[[.,.],.]]],.]]],.]],.] [[[[],[[[[],[]],[]],[]]],[]],[]]=>[[.,[[.,[[.,.],[[.,[[.,[[.,.],.]],.]],.]]],.]],.] [[[[[],[]],[[],[[],[]]]],[]],[]]=>[[.,[[.,[[.,[[.,.],.]],[[.,.],[[.,.],.]]]],.]],.] [[[[[],[]],[[[],[]],[]]],[]],[]]=>[[.,[[.,[[.,[[.,.],.]],[[.,[[.,.],.]],.]]],.]],.] [[[[[],[[],[]]],[[],[]]],[]],[]]=>[[.,[[.,[[.,[[.,.],[[.,.],.]]],[[.,.],.]]],.]],.] [[[[[[],[]],[]],[[],[]]],[]],[]]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],[[.,.],.]]],.]],.] [[[[[],[[],[[],[]]]],[]],[]],[]]=>[[.,[[.,[[.,[[.,.],[[.,.],[[.,.],.]]]],.]],.]],.] [[[[[],[[[],[]],[]]],[]],[]],[]]=>[[.,[[.,[[.,[[.,.],[[.,[[.,.],.]],.]]],.]],.]],.] [[[[[[],[]],[[],[]]],[]],[]],[]]=>[[.,[[.,[[.,[[.,[[.,.],.]],[[.,.],.]]],.]],.]],.] [[[[[[],[[],[]]],[]],[]],[]],[]]=>[[.,[[.,[[.,[[.,[[.,.],[[.,.],.]]],.]],.]],.]],.] [[[[[[[],[]],[]],[]],[]],[]],[]]=>[[.,[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]],.]
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
26
Created
Jan 19, 2020 at 07:28 by FindStatCrew
Updated
Jan 19, 2020 at 07:28 by Martin Rubey