Identifier
Mp00019: Binary trees —right rotate⟶ Binary trees
Mp00010: Binary trees —to ordered tree: left child = left brother⟶ Ordered trees
Mp00048: Ordered trees —left-right symmetry⟶ Ordered trees
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-1Cc0021;cc-rep-2Cc0021;cc-rep-3
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[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[[],[[],[[],[]],[]],[]]=>[[],[[],[[],[]],[]],[]] [.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[[],[[[]],[[]],[]],[]]=>[[],[[],[[]],[[]]],[]] [.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[[],[[],[],[[]],[]],[]]=>[[],[[],[[]],[],[]],[]] [.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[[],[[[[]]],[],[]],[]]=>[[],[[],[],[[[]]]],[]] [.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[[],[[[],[]],[],[]],[]]=>[[],[[],[],[[],[]]],[]] [.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[[],[[],[[]],[],[]],[]]=>[[],[[],[],[[]],[]],[]] [.,[[.,.],[[[[.,[.,.]],.],.],.]]]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]=>[[],[[[]],[],[],[]],[]]=>[[],[[],[],[],[[]]],[]] [.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[[],[[],[],[],[],[]],[]]=>[[],[[],[],[],[],[]],[]] 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[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]=>[[[[]]],[[],[],[]],[]]=>[[],[[],[],[]],[[[]]]] [.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[[[],[]],[[[[]]]],[]]=>[[],[[[[]]]],[[],[]]] [.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[[[],[]],[[[],[]]],[]]=>[[],[[[],[]]],[[],[]]] [.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[[[],[]],[[],[[]]],[]]=>[[],[[[]],[]],[[],[]]] [.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]=>[[[],[]],[[[]],[]],[]]=>[[],[[],[[]]],[[],[]]] [.,[[.,[[.,.],.]],[[[.,.],.],.]]]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[[[],[]],[[],[],[]],[]]=>[[],[[],[],[]],[[],[]]] [.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[[],[[]],[[[[]]]],[]]=>[[],[[[[]]]],[[]],[]] [.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[[],[[]],[[[],[]]],[]]=>[[],[[[],[]]],[[]],[]] 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[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]=>[[],[[[]]],[[],[]],[]]=>[[],[[],[]],[[[]]],[]] [.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[[],[[],[]],[[[]]],[]]=>[[],[[[]]],[[],[]],[]] [.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[[],[[],[]],[[],[]],[]]=>[[],[[],[]],[[],[]],[]] [.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[[[]],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[[]]] [.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[[[]],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[[]]] [.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[[],[],[[]],[[[]]],[]]=>[[],[[[]]],[[]],[],[]] [.,[[[[.,.],.],[.,.]],[[.,.],.]]]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[[],[],[[]],[[],[]],[]]=>[[],[[],[]],[[]],[],[]] [.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[[[[]]],[],[[[]]],[]]=>[[],[[[]]],[],[[[]]]] 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[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[],[[[[[[[]]]]]]]]]=>[[[[[[[[[]]]]]]],[]]] [[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[],[[[[[[[[]]]]]]]]]=>[[[[[[[[[]]]]]]]],[]] [[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]=>[[[],[],[[[[[[]]]]]]]]=>[[[[[[[[]]]]]],[],[]]] [[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[[[[[[[[]]]]]]],[[]]]=>[[[]],[[[[[[[]]]]]]]] [[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[[[]],[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[],[[]]] [[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[[[[[[[[[]]]]]]]],[[]]]=>[[[]],[[[[[[[[]]]]]]]]] [[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[],[[[[[[]]]]]],[[]]]=>[[[]],[[[[[[]]]]]],[]] 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[[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[.,.]]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]]=>[[[],[[]],[[]],[[]],[[]]]]=>[[[[]],[[]],[[]],[[]],[]]] [[.,[[[.,.],[.,.]],[.,.]]],[[.,.],[.,.]]]=>[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]]=>[[[],[[]],[[]],[[],[[]]]]]=>[[[[[]],[]],[[]],[[]],[]]] [[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[.,.]]]=>[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]]=>[[[],[[]],[[],[[]],[[]]]]]=>[[[[[]],[[]],[]],[[]],[]]] [[.,[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]],[.,.]]=>[.,[[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]],[.,.]]]=>[[[],[[]],[[],[[]],[[]]],[[]]]]=>[[[[]],[[[]],[[]],[]],[[]],[]]] [[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]],[.,.]]=>[.,[[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]],[.,.]]]=>[[[],[[]],[[],[[]]],[[]],[[]]]]=>[[[[]],[[]],[[[]],[]],[[]],[]]] [[.,[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]]],[.,.]]=>[.,[[[[[.,.],[.,.]],[.,.]],[[.,.],[.,.]]],[.,.]]]=>[[[],[[]],[[]],[[],[[]]],[[]]]]=>[[[[]],[[[]],[]],[[]],[[]],[]]] [[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]],[.,.]]=>[.,[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]]=>[[[],[[]],[[]],[[]],[[]],[[]]]]=>[[[[]],[[]],[[]],[[]],[[]],[]]] [[.,[[[.,.],[.,.]],[[.,.],[.,.]]]],[[.,.],[.,.]]]=>[.,[[[[.,.],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]]=>[[[],[[]],[[],[[]]],[[],[[]]]]]=>[[[[[]],[]],[[[]],[]],[[]],[]]] [[.,[[[[.,.],[.,.]],[.,.]],[.,.]]],[[.,.],[.,.]]]=>[.,[[[[[.,.],[.,.]],[.,.]],[.,.]],[[.,.],[.,.]]]]=>[[[],[[]],[[]],[[]],[[],[[]]]]]=>[[[[[]],[]],[[]],[[]],[[]],[]]] [[.,[[[.,.],[.,.]],[.,.]]],[[[.,.],[.,.]],[.,.]]]=>[.,[[[[.,.],[.,.]],[.,.]],[[[.,.],[.,.]],[.,.]]]]=>[[[],[[]],[[]],[[],[[]],[[]]]]]=>[[[[[]],[[]],[]],[[]],[[]],[]]] [[.,[[.,.],[.,.]]],[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[.,[[[.,.],[.,.]],[[[[.,.],[.,.]],[.,.]],[.,.]]]]=>[[[],[[]],[[],[[]],[[]],[[]]]]]=>[[[[[]],[[]],[[]],[]],[[]],[]]] [[[.,[[.,.],[.,.]]],[[.,.],[.,.]]],[[.,.],[.,.]]]=>[[.,[[.,.],[.,.]]],[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[[[],[[]]],[[],[[]],[[],[[]]]]]=>[[[[[]],[]],[[]],[]],[[[]],[]]] [[[.,[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]],[.,.]]=>[[.,[.,.]],[[[[.,.],[.,.]],[[.,.],[.,.]]],[.,.]]]=>[[[]],[[],[[]],[[],[[]]],[[]]]]=>[[[[]],[[[]],[]],[[]],[]],[[]]] [[[[.,[.,.]],[.,.]],[[.,.],[.,.]]],[[.,.],[.,.]]]=>[[[.,[.,.]],[.,.]],[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[[[]],[[]],[[],[[]],[[],[[]]]]]=>[[[[[]],[]],[[]],[]],[[]],[[]]] [.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[[],[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[],[]] [[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[[[[[[.,[.,.]],.],.],.],.],[[.,.],.]]=>[[[]],[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[],[[]]] [.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[[],[],[],[],[],[[]],[],[]]=>[[],[],[[]],[],[],[],[],[]] [.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[[],[],[],[],[],[],[],[[]],[]]=>[[],[[]],[],[],[],[],[],[],[]] [.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]=>[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[[[],[],[],[],[],[]],[],[]]=>[[],[],[[],[],[],[],[],[]]] [[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[[[],[],[],[],[],[],[],[]]]=>[[[],[],[],[],[],[],[],[]]] [[[[[[[.,[[.,.],.]],.],.],.],.],.],.]=>[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[[[],[]],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[[],[]]] [[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[[[],[],[],[],[],[],[],[],[]]]=>[[[],[],[],[],[],[],[],[],[]]] [[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[[],[],[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[],[],[]] [[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[[],[],[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[],[],[]] [[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[[],[],[],[],[],[],[[]],[[]]]=>[[[]],[[]],[],[],[],[],[],[]] [[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[[],[],[],[],[],[],[],[[],[]]]=>[[[],[]],[],[],[],[],[],[],[]] [.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[[[[]]],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[[[]]]] [.,[[[[[.,[.,[.,[.,.]]]],.],.],.],.]]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[[[[[]]]],[],[],[],[],[]]=>[[],[],[],[],[],[[[[]]]]] [.,[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[[[[[[]]]]],[],[],[],[]]=>[[],[],[],[],[[[[[]]]]]] [.,[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[[[[[[[]]]]]],[],[],[]]=>[[],[],[],[[[[[[]]]]]]] [.,[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[[[[]]],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[[[]]]] [.,[[[[[[.,.],[.,[.,.]]],.],.],.],.]]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[[],[[[]]],[],[],[],[],[]]=>[[],[],[],[],[],[[[]]],[]] [.,[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[[[[[]]]],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[[[[]]]]] [.,[[[[[.,.],[.,[.,[.,.]]]],.],.],.]]=>[[[[[[.,.],[.,[.,[.,.]]]],.],.],.],.]=>[[],[[[[]]]],[],[],[],[]]=>[[],[],[],[],[[[[]]]],[]] [.,[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[[[[[[]]]]],[],[],[],[],[]]=>[[],[],[],[],[],[[[[[]]]]]] [.,[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]]=>[[[[[.,.],[.,[.,[.,[.,.]]]]],.],.],.]=>[[],[[[[[]]]]],[],[],[]]=>[[],[],[],[[[[[]]]]],[]] [.,[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[[[[[[[]]]]]],[],[],[],[]]=>[[],[],[],[],[[[[[[]]]]]]] [.,[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[[[[[[[[]]]]]]],[],[],[]]=>[[],[],[],[[[[[[[]]]]]]]] [[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[[],[],[],[],[],[],[],[],[],[[]]]=>[[[]],[],[],[],[],[],[],[],[],[]] [[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[],[[[[[[[[[]]]]]]]]]]=>[[[[[[[[[[]]]]]]]]],[]] [.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[[],[],[],[],[[]],[],[],[]]=>[[],[],[],[[]],[],[],[],[]] [[[[[[[.,.],.],.],.],.],[[[.,.],.],.]],.]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[[],[],[],[],[],[[],[],[],[]]]=>[[[],[],[],[]],[],[],[],[],[]] [.,[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[[],[],[],[[]],[],[],[],[],[]]=>[[],[],[],[],[],[[]],[],[],[]] [[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[[[[[[[[],[],[]]]]]]]]=>[[[[[[[[],[],[]]]]]]]] [[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[[[[[[[],[],[],[]]]]]]]=>[[[[[[[],[],[],[]]]]]]] [[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[[[[[[],[],[],[],[]]]]]]=>[[[[[[],[],[],[],[]]]]]] [[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[[[[[],[],[],[],[],[]]]]]=>[[[[[],[],[],[],[],[]]]]] [[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]=>[[[[[[[[[],[],[]]]]]]]]]=>[[[[[[[[[],[],[]]]]]]]]] [[.,.],[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]=>[[[[[[[[],[],[],[]]]]]]]]=>[[[[[[[[],[],[],[]]]]]]]] [[.,.],[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[[[[[[[],[],[],[],[]]]]]]]=>[[[[[[[],[],[],[],[]]]]]]] [[.,.],[.,[.,[[[[[[.,.],.],.],.],.],.]]]]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]=>[[[[[[],[],[],[],[],[]]]]]]=>[[[[[[],[],[],[],[],[]]]]]] [[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]=>[[[[[],[],[],[],[],[],[]]]]]=>[[[[[],[],[],[],[],[],[]]]]] [[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]=>[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]=>[[[],[[],[],[],[],[],[]]]]=>[[[[],[],[],[],[],[]],[]]] [[[.,.],[[[[[[.,.],.],.],.],.],.]],.]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[[],[[],[],[],[],[],[],[]]]=>[[[],[],[],[],[],[],[]],[]] [[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]=>[[[],[[[[[[],[]]]]]]]]=>[[[[[[[[],[]]]]]],[]]] [[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]=>[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]=>[[[],[[[[[[]],[]]]]]]]=>[[[[[[[],[[]]]]]],[]]] [[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[[],[],[],[],[],[],[[[[]]]]]=>[[[[[]]]],[],[],[],[],[],[]] [[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[],[],[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[],[],[]] [[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[],[],[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[],[],[]] [[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[],[],[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]],[],[]] [[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[],[],[],[],[],[[[[[]]]]]]=>[[[[[[]]]]],[],[],[],[],[]] [[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[],[],[],[],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[],[],[],[]] [[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[],[],[],[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]],[],[],[]] [[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[],[],[[[[[[[[]]]]]]]]]=>[[[[[[[[[]]]]]]]],[],[]] [[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[[[[[[[]]]]]],[[[]]]]=>[[[[]]],[[[[[[]]]]]]] [[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[[[[[[]]]]],[[[[]]]]]=>[[[[[]]]],[[[[[]]]]]] [[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[[[[[]]]],[[[[[]]]]]]=>[[[[[[]]]]],[[[[]]]]] [[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[]]],[[[[[[]]]]]]]=>[[[[[[[]]]]]],[[[]]]] [[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[]],[[[[[[[]]]]]]]]=>[[[[[[[[]]]]]]],[[]]] [[[[[.,.],[.,.]],[.,.]],.],[[.,.],[.,.]]]=>[[[[.,.],[.,.]],[.,.]],[.,[[.,.],[.,.]]]]=>[[],[[]],[[]],[[[],[[]]]]]=>[[[[[]],[]]],[[]],[[]],[]] [[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[[[[[[[[[[]],[]]]]]]]]]=>[[[[[[[[[],[[]]]]]]]]]] [.,[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[[],[[]],[],[],[],[],[],[],[]]=>[[],[],[],[],[],[],[],[[]],[]] [[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[[],[],[],[],[],[[[]],[]]]=>[[[],[[]]],[],[],[],[],[]] [[.,[[[[[[.,[.,.]],.],.],.],.],.]],.]=>[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[[[[]],[],[],[],[],[],[]]]=>[[[],[],[],[],[],[],[[]]]] [[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[[[[[[[[[]]]]]],[]]]]=>[[[[],[[[[[[]]]]]]]]] [[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]=>[[[],[],[],[],[],[],[[]]]]=>[[[[]],[],[],[],[],[],[]]] [[.,[[[[[[.,.],[.,.]],.],.],.],.]],.]=>[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[[[],[[]],[],[],[],[],[]]]=>[[[],[],[],[],[],[[]],[]]] [[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.],.]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[[[[[[[],[]]]]]],[[]]]=>[[[]],[[[[[[],[]]]]]]]
Map
right rotate
Description
Return the result of right rotation applied to a binary tree.
Right rotation on binary trees is defined as follows: Let $T$ be a binary tree such that the left child of the root of $T$ is a node. Let $C$ be the right child of the root of $T$, and let $A$ and $B$ be the left and right children of the left child of the root of $T$. (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the right rotation of $T$ is the binary tree in which the left child of the root is $A$, whereas the right child of the root is a node whose left and right children are $B$ and $C$.
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
left-right symmetry
Description
Return the left-right symmetrized tree of an ordered tree.