Identifier
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=>
Cc0010;cc-rep-0Cc0010;cc-rep-1
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[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]
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[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]
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[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]
[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]
[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]
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[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]
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[.,[[.,.],[[.,[[[.,.],.],.]],.]]]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]
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[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]
[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]
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[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
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[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]
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[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
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[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]
[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]
[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
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[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
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click to show experimental identities
(only identities of compositions of up to three maps are shown)
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 $C$.
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 $C$.
Properties
bijective, graded
Sage code
def mapping(elt): if not elt[0].is_empty(): return elt.right_rotate() return BinaryTree([elt[1], elt[0]])
Weight
26
Created
Jan 29, 2020 at 14:22 by FindStatCrew
Updated
Jan 29, 2020 at 14:22 by Martin Rubey
searching the database
Sorry, this map was not found in the database.