edit this map or download as text // json
Identifier
Mp00019: Binary trees —right rotate⟶ Binary trees
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-1
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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 $C$.
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