- FindStat

Identifier
Mp00019: Binary trees —right rotate⟶ Binary trees
Mp00010: Binary trees —to ordered tree: left child = left brother⟶ Ordered trees
Images
=>
            
              Cc0010;cc-rep-0Cc0010;cc-rep-1Cc0021;cc-rep-2
            

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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 $y$.