Identifier
Mp00015: to ordered tree: right child = right brotherOrdered trees
Mp00048: left-right symmetryOrdered trees
Mp00049: to binary tree: left brother = left child
Images
=>
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: left brother = left child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of $t$, and where $t$ is an ordered tree) by the following recursive rule:
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.