edit this map or download as text // json
Identifier
Mp00009: Binary trees —left rotate⟶ Binary trees
Images
=>
Cc0010;cc-rep-0Cc0010;cc-rep-1
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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 $B$.
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