Growing and Destroying Catalan-Stanley Trees
Stanley lists the class of Dyck paths where all returns to the axis are of odd length as one of the many objects enumerated by (shifted) Catalan numbers. By the standard bijection in this context, these special Dyck paths correspond to a class of rooted plane trees, so-called Catalan-Stanley trees....
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
2018-02-01
|
| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3964/pdf |
| Summary: | Stanley lists the class of Dyck paths where all returns to the axis are of
odd length as one of the many objects enumerated by (shifted) Catalan numbers.
By the standard bijection in this context, these special Dyck paths correspond
to a class of rooted plane trees, so-called Catalan-Stanley trees.
This paper investigates a deterministic growth procedure for these trees by
which any Catalan-Stanley tree can be grown from the tree of size one after
some number of rounds; a parameter that will be referred to as the age of the
tree. Asymptotic analyses are carried out for the age of a random
Catalan-Stanley tree of given size as well as for the "speed" of the growth
process by comparing the size of a given tree to the size of its ancestors. |
|---|---|
| ISSN: | 1365-8050 |