English

Deepest nodes in marked ordered trees

Combinatorics 2022-02-16 v2

Abstract

A variation of ordered trees, where each rightmost edge might be marked or not, if it does not lead to an endnode, is investigated. These marked ordered trees were introduced by E. Deutsch et al.\ to model skew Dyck paths. We study the number of deepest nodes in such trees. Explicit generating functions are established and the average number of deepest nodes, which approaches 53\frac53 when the number of nodes gets large. This is to be compared to standard ordered trees where the average number of deepest nodes approaches 22.

Keywords

Cite

@article{arxiv.2202.05455,
  title  = {Deepest nodes in marked ordered trees},
  author = {Helmut Prodinger},
  journal= {arXiv preprint arXiv:2202.05455},
  year   = {2022}
}

Comments

Look at the conclusion for an interesting challenge

R2 v1 2026-06-24T09:31:30.104Z