- FindStat

Identifier
Mp00010: Binary trees —to ordered tree: left child = left brother⟶ Ordered trees
Mp00050: Ordered trees —to binary tree: right brother = right child⟶ Binary trees
Images
=>
            
              Cc0010;cc-rep-0Cc0021;cc-rep-1Cc0010;cc-rep-2
            

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[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[[[]],[[]],[[]],[],[]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
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[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[[[[],[],[]]],[],[],[]]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
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[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[[[[]],[[]]],[],[],[]]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[[[],[],[[]]],[],[],[]]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[[[[[]]],[]],[],[],[]]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[[[[],[]],[]],[],[],[]]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[[[],[[]],[]],[],[],[]]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
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[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[[],[[[[]]]],[],[],[]]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[[],[[[],[]]],[],[],[]]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[[],[[],[[]]],[],[],[]]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[[],[[[]],[]],[],[],[]]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[[],[[],[],[]],[],[],[]]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[[[]],[[[]]],[],[],[]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[[[]],[[],[]],[],[],[]]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[[],[],[[[]]],[],[],[]]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[[],[],[[],[]],[],[],[]]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[[[[]]],[[]],[],[],[]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[[[],[]],[[]],[],[],[]]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[[],[[]],[[]],[],[],[]]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
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[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[[],[],[],[[]],[],[],[]]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[[[[[]]]],[],[],[],[]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[[[[],[]]],[],[],[],[]]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[[[],[[]]],[],[],[],[]]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[[[[]],[]],[],[],[],[]]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[[[],[],[]],[],[],[],[]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[[],[[[]]],[],[],[],[]]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[[],[[],[]],[],[],[],[]]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[]],[[]],[],[],[],[]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[[],[],[[]],[],[],[],[]]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[[[[]]],[],[],[],[],[]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[[[],[]],[],[],[],[],[]]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[[],[[]],[],[],[],[],[]]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[[[]],[],[],[],[],[],[]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[[],[],[],[],[],[],[],[]]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
          
Map
to ordered tree: left child = left brother
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 $y$.
Map
to binary tree: right brother = right child
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 $t$.