Identifier
Mp00015: Binary trees —to ordered tree: right child = right brother⟶ Ordered trees
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Mp00050: Ordered trees —to binary tree: right brother = right child⟶ Binary trees
Images
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Cc0010;cc-rep-0Cc0021;cc-rep-1Cc0021;cc-rep-2Cc0010;cc-rep-3
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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
left-right symmetry
Description
Return the left-right symmetrized tree of an ordered tree.
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 $t$.