Identifier
Mp00016: left-right symmetryBinary trees
Mp00015: to ordered tree: right child = right brother
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 $y$.