RightRotation from BinaryTree
Rotate the root to the right: the left child becomes the root, the root its right child.
FindStat's Mp00019. A tree whose root has no left child has nothing to rotate; FindStat then moves its right subtree to the left, as [A, .], and so do we. That makes it a bijection on every size, inverse to LeftRotation.
Called as CombinatorialMap(x, "RightRotation"). The head's page has its examples.
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Each element of BinaryTree at a size, and its image, applied in your browser; sizes past 6 are not offered.
Properties
Transport a statistic
Pick a statistic on BinaryTree. Its distribution over the images of BinaryTree at each size is computed, and compared with the 37 statistics on BinaryTree: those that share it are the ones the map sends it to, as far as the sizes computed show.
FindStat Mp00019
right rotate
Matched by value: our map agrees with FindStat's image on each of the 196 rows of size at most 6 we can read (0 unread; its table has 1200 rows).
BijectionGraded mapas FindStat records them, checked by FindStat's contributors.
| Object | Image |
|---|---|
[.,.] | [.,.] |
[.,[.,.]] | [[.,.],.] |
[[.,.],.] | [.,[.,.]] |
[.,[.,[.,.]]] | [[.,[.,.]],.] |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00019 has the rest.