BinaryTree from DyckPath
A Dyck path U A D B, cut at its first return, as the binary tree [φ⁻¹(A), φ⁻¹(B)].
Called as CombinatorialMap(x, "BinaryTree"). The head's page has its examples.
Live
Explore
Each element of DyckPath at a size, and its image, applied in your browser; sizes past 7 are not offered.
Properties
Transport a statistic
Pick a statistic on BinaryTree. Its distribution over the images of DyckPath at each size is computed, and compared with the 171 statistics on DyckPath: 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: BinaryTreeParentArray, OrderedTree.
FindStat Mp00034
to binary tree: up step, left tree, down step, right tree
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 |
|---|---|
[1,0] | [.,.] |
[1,0,1,0] | [.,[.,.]] |
[1,1,0,0] | [[.,.],.] |
[1,0,1,0,1,0] | [.,[.,[.,.]]] |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00034 has the rest.