- FindStat

Identifier
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Mp00015: Binary trees —to ordered tree: right child = right brother⟶ Ordered trees
Images
=>
            
              Cc0010;cc-rep-0Cc0010;cc-rep-1Cc0021;cc-rep-2
            

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[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[[[[[[]],[]]],[[]]]]
[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[[[[[],[[]]]],[[]]]]
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[[.,[.,[.,[.,[.,.]]]]],[[[[.,.],.],.],.]]=>[[.,[.,[.,[.,.]]]],[[[[[.,.],.],.],.],.]]=>[[[],[],[],[]],[[[[[]]]]]]
[[[[[.,.],.],.],.],[[.,.],[.,[.,.]]]]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[]]],[]],[],[],[],[]]
[[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[[[]]]],[]],[],[],[]]
[[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[[[[[[[]]]]],[]],[],[]]
[[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[[[.,.],.],.]]]=>[[],[[[[[]]]]],[[[]]]]
[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]=>[[],[[[[[[[]]]]]]],[],[]]
[[[.,.],[.,[.,.]]],[[.,.],[[.,.],[.,.]]]]=>[[[[.,.],[.,.]],[.,.]],[[[.,.],.],[.,.]]]=>[[[[[]],[]],[]],[[[]]],[]]
[[[.,.],[.,.]],[[.,.],[[.,[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],.]],[.,.]],[[.,.],[.,.]]]=>[[[[[]],[[]]],[]],[[]],[]]
[[[[[[.,.],.],.],.],[.,.]],[[.,.],.]]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]=>[[[],[]],[[]],[],[],[],[]]
[[.,.],[[[[[[.,.],.],.],[.,.]],.],.]]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]]=>[[[],[],[[]],[],[],[]],[]]
[.,[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]]=>[[[[.,[.,[[[[.,.],.],.],.]]],.],.],.]=>[[[[[],[],[[[[]]]]]]]]
[[[[[.,.],[.,.]],[[.,.],[.,.]]],.],.]=>[.,[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]]=>[[],[],[[[]],[]],[[]],[]]
[[[[.,[[.,[.,.]],[.,.]]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[[.,.],[[.,.],.]],.]]]]=>[[],[[]],[[]],[[[]],[[]]]]
[[.,[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]],.]=>[.,[[[.,.],[[[.,[[.,.],.]],[.,.]],.]],.]]=>[[],[[[]],[[[],[[]]],[]]]]
[[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],[.,[.,.]]],.]]=>[[],[[[[[[]]]]],[],[]]]
[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]=>[[[[[[[]]]]],[],[],[]]]
[[.,[[.,[[[[[.,.],.],.],.],.]],.]],.]=>[.,[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]]=>[[],[[],[[],[],[],[],[]]]]
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[[[[[[.,.],.],.],.],[[.,.],[.,.]]],.]=>[.,[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]]=>[[],[[[]],[]],[],[],[],[]]
[[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]=>[[],[],[],[],[],[],[],[],[[[]]]]
[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]=>[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.]=>[[[[[[],[],[[[]]]]]]]]
[[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[[[]],[],[],[],[],[[[]]]]
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[[[]],[],[],[],[],[],[[[]]]]
[[[.,[.,.]],[[[[[.,.],.],.],.],.]],.]=>[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]=>[[],[[],[],[],[],[]],[[]]]
[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]=>[[[[[[.,.],[[[.,.],.],.]],.],.],.],.]=>[[[[[[[]],[[[]]]]]]]]
[[[[[[.,[.,[[[.,.],.],.]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]]]=>[[],[],[],[],[],[[[],[],[]]]]
[.,[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]]=>[[[[.,.],[[.,.],.]],[[.,.],[.,.]]],.]=>[[[[[]],[[]]],[[]],[]]]
[[[.,[[[.,[[.,.],[.,.]]],.],[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],[.,[[[.,.],[.,.]],.]]],.]]]=>[[[]],[[]],[[[]],[],[[[]],[]]]]
[[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]=>[[],[[[[[[[]]]]],[]]]]
[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]=>[[],[[[[[[[[]]]],[]]]]]]
[[.,[[.,.],[[.,[[.,.],.]],[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],[[.,[.,.]],.]],[.,.]],.]]=>[[[]],[[[[]],[[],[]]],[]]]
          
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.
Map
to ordered tree: right child = right brother
Description
Return an ordered tree of size $n+1$ by the following recursive rule:
if $x$ is the right child of $y$, $x$ becomes the right brother of $y$,
if $x$ is the left child of $y$, $x$ becomes the first child of $y$.