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.
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Also from
The same name out of other carriers, each its own implementation: BinaryTreeParentArray.
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.
Return the binary tree corresponding to the Dyck path under the transformation up step - left tree - down step - right tree.
| 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.