Mirror from BinaryTree
The left-right symmetry of a binary tree: every node's two subtrees swapped.
FindStat's Mp00016, an involution. Conjugated by the Dyck-path bijection it is DecompositionReverse.
Called as CombinatorialMap(x, "Mirror"). The head's page has its examples.
Live
Explore
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.
Also from
The same name out of other carriers, each its own implementation: OrderedTree.
FindStat Mp00016
left-right symmetry
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 mapInvolutionas FindStat records them, checked by FindStat's contributors.
| Object | Image |
|---|---|
[.,.] | [.,.] |
[.,[.,.]] | [[.,.],.] |
[[.,.],.] | [.,[.,.]] |
[.,[.,[.,.]]] | [[[.,.],.],.] |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00016 has the rest.