edit this map or download as text // json
Identifier
Mp00050: Ordered trees —to binary tree: right brother = right 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 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 $t$.
Properties
bijective, graded
Sage code
def mapping(elt):
    return elt.to_binary_tree_right_branch()
Weight
26
Created
Jan 26, 2020 at 12:31 by FindStatCrew
Updated
Jan 26, 2020 at 12:31 by Martin Rubey