BinarySearchTree from Permutation
The tree built by inserting σ(1), σ(2), ... into an empty binary search tree.
The sylvester congruence: two permutations land on the same tree exactly when they agree on which of any pair is inserted first. Built as its parent array (BinarySearchTreeParentArray), then read as a tree.
Called as CombinatorialMap(x, "BinarySearchTree"). The head's page has its examples.
Live
FindStat Mp00072
binary search tree: left to right
Matched by value: our map agrees with FindStat's image on each of the 873 rows of size at most 6 we can read (0 unread; its table has 1200 rows).
SurjectionGraded mapas FindStat records them, checked by FindStat's contributors.
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
| Object | Image |
|---|---|
[1] | [.,.] |
[1,2] | [.,[.,.]] |
[2,1] | [[.,.],.] |
[1,2,3] | [.,[.,[.,.]]] |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/Mp00072 has the rest.