Identifier
Images
=>
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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[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
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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 left rotation applied to a binary tree.
Left rotation on binary trees is defined as follows: Let $T$ be a binary tree such that the right child of the root of $T$ is a node. Let $A$ be the left child of the root of $T$, and let $B$ and $C$ be the left and right children of the right child of the root of $T$. (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the left rotation of $T$ is the binary tree in which the right child of the root is $C$, whereas the left child of the root is a node whose left and right children are $A$ and $B$.
Left rotation on binary trees is defined as follows: Let $T$ be a binary tree such that the right child of the root of $T$ is a node. Let $A$ be the left child of the root of $T$, and let $B$ and $C$ be the left and right children of the right child of the root of $T$. (Keep in mind that nodes of trees are identified with the subtrees consisting of their descendants.) Then, the left rotation of $T$ is the binary tree in which the right child of the root is $C$, whereas the left child of the root is a node whose left and right children are $A$ and $B$.
Properties
bijective, graded
Sage code
def mapping(elt): if not elt[1].is_empty(): return elt.left_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.