- FindStat

Identifier
Mp00015: Binary trees —to ordered tree: right child = right 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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[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[[[[[[],[]],[]],[]]]]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[[[[[[[]]],[]],[]]]]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[[[[[[],[],[]]],[]]]]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]
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[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[[[[[[[]],[]]],[]]]]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]
[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[[[[[[[],[]]]],[]]]]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]
[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[[[[[[[[]]]]],[]]]]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
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[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[[[[[],[[]],[],[]]]]]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]
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[[[[.,[[.,[.,[.,.]]],.]],.],.],.]=>[[[[[],[[],[],[]]]]]]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]
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[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[[[[[[]],[],[],[]]]]]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[[[[[.,.],[.,[[.,.],.]]],.],.],.]=>[[[[[[]],[],[[]]]]]]=>[[[[[.,.],[.,[[.,.],.]]],.],.],.]
[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[[[[[[]],[[]],[]]]]]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]
[[[[[.,.],[[.,[.,.]],.]],.],.],.]=>[[[[[[]],[[],[]]]]]]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]
[[[[[.,.],[[[.,.],.],.]],.],.],.]=>[[[[[[]],[[[]]]]]]]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]
[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[[[[[[],[]],[],[]]]]]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[[[[[.,[.,.]],[[.,.],.]],.],.],.]=>[[[[[[],[]],[[]]]]]]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]
[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[[[[[[[]]],[],[]]]]]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[[[[[[[]]],[[]]]]]]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]
[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[[[[[[],[],[]],[]]]]]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[[[[[[],[[]]],[]]]]]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[[[[[[[]],[]],[]]]]]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]
[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[[[[[[[],[]]],[]]]]]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[[[[[[[[]]]],[]]]]]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[[[[[[],[],[],[]]]]]]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[[[[[[],[],[[]]]]]]]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]
[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[[[[[[],[[]],[]]]]]]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[[[[[[],[[],[]]]]]]]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[[[[[[],[[[]]]]]]]]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[[[[[[[]],[],[]]]]]]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[[[[[[[]],[[]]]]]]]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[[[[[],[]],[]]]]]]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[[[[[[[[]]],[]]]]]]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[[[[[[[],[],[]]]]]]]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]
[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[[[[[[[],[[]]]]]]]]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[[[[[[[[]],[]]]]]]]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[[[[[[[[],[]]]]]]]]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[[[[[[[[[]]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[[[],[]],[]],[]],[]],[]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[[[[[[],[]],[]],[]],[]],[]],[]]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[[],[[[],[[[],[]],[]]],[]]]=>[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]]
[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[[],[[[[],[]],[[],[]]],[]]]=>[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]]
[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[[],[[[[],[[],[]]],[]],[]]]=>[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]]
[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[[],[[[[[],[]],[]],[]],[]]]=>[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]]
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[[[],[[[],[[],[]]],[]]],[]]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]]
[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[[[],[[[[],[]],[]],[]]],[]]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]
[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[[[],[]],[[[],[]],[]]],[]]=>[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]
[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[[[[],[[],[]]],[[],[]]],[]]=>[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]
[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[[[],[]],[]],[[],[]]],[]]=>[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]
[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]]=>[[],[[[],[[[[],[]],[]],[]]],[]]]=>[.,[[[.,[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]],.]]
[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]]=>[[],[[[[],[]],[[[],[]],[]]],[]]]=>[.,[[[[.,[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]],.]]
[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]]=>[[],[[[[],[[],[]]],[[],[]]],[]]]=>[.,[[[[.,[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]],.]]
[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]]=>[[],[[[[[],[]],[]],[[],[]]],[]]]=>[.,[[[[[.,[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]],.]]
[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]=>[[],[[[[],[[[],[]],[]]],[]],[]]]=>[.,[[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],[.,.]],.]]
[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]]=>[[],[[[[[],[]],[[],[]]],[]],[]]]=>[.,[[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],[.,.]],.]]
[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]]=>[[],[[[[[],[[],[]]],[]],[]],[]]]=>[.,[[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],[.,.]],.]]
[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]=>[[],[[[[[[],[]],[]],[]],[]],[]]]=>[.,[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]]
[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]=>[[[],[[[],[[],[]]],[]]],[[],[]]]=>[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[[.,[.,.]],.]]
[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]]=>[[[],[[[],[[[],[]],[]]],[]]],[]]=>[[.,[[[.,[[[.,[.,.]],[.,.]],.]],[.,.]],.]],[.,.]]
[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]]=>[[[],[[[[],[]],[[],[]]],[]]],[]]=>[[.,[[[[.,[.,.]],[[.,[.,.]],.]],[.,.]],.]],[.,.]]
[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]]=>[[[],[[[[],[[],[]]],[]],[]]],[]]=>[[.,[[[[.,[[.,[.,.]],.]],[.,.]],[.,.]],.]],[.,.]]
[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[[[],[[[[[],[]],[]],[]],[]]],[]]=>[[.,[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]],[.,.]]
[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]=>[[[[],[]],[[[[],[]],[]],[]]],[]]=>[[[.,[.,.]],[[[[.,[.,.]],[.,.]],[.,.]],.]],[.,.]]
[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[[[],[[],[]]],[[[],[]],[]]],[]]=>[[[.,[[.,[.,.]],.]],[[[.,[.,.]],[.,.]],.]],[.,.]]
[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]=>[[[[[],[]],[]],[[[],[]],[]]],[]]=>[[[[.,[.,.]],[.,.]],[[[.,[.,.]],[.,.]],.]],[.,.]]
[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[[[[],[[[],[]],[]]],[[],[]]],[]]=>[[[.,[[[.,[.,.]],[.,.]],.]],[[.,[.,.]],.]],[.,.]]
[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]=>[[[[[],[]],[[],[]]],[[],[]]],[]]=>[[[[.,[.,.]],[[.,[.,.]],.]],[[.,[.,.]],.]],[.,.]]
[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[[[],[[],[]]],[]],[[],[]]],[]]=>[[[[.,[[.,[.,.]],.]],[.,.]],[[.,[.,.]],.]],[.,.]]
[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]=>[[[[[[],[]],[]],[]],[[],[]]],[]]=>[[[[[.,[.,.]],[.,.]],[.,.]],[[.,[.,.]],.]],[.,.]]
[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]]=>[[[[],[[[],[[],[]]],[]]],[]],[]]=>[[[.,[[[.,[[.,[.,.]],.]],[.,.]],.]],[.,.]],[.,.]]
          
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 $y$.
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 $t$.