edit this map or download as text // json
Identifier
Mp00010: Binary trees —to ordered tree: left child = left brother⟶ Ordered trees
Images
=>
Cc0010;cc-rep-0Cc0021;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 an ordered tree of size $n+1$ by the following recursive rule:
  • if $x$ is the left child of $y$, $x$ becomes the left brother of $y$,
  • if $x$ is the right child of $y$, $x$ becomes the last child of $y$.
Properties
bijective, graded
Sage code
def mapping(elt):
    return elt.to_ordered_tree_left_branch()
Weight
26
Created
Jan 01, 2018 at 00:00 by FindStatCrew
Updated
Jan 06, 2020 at 14:05 by Martin Rubey