English

Protected Vertices in Motzkin trees

Combinatorics 2017-12-29 v1

Abstract

In this paper we find recurrence relations for the asymptotic probability a vertex is kk protected in all Motzkin trees. We use a similar technique to calculate the probabilities for balanced vertices of rank kk. From this we calculate upper and lower bounds for the probability a vertex is balanced and upper and lower bounds for the expected rank of balanced vertices.

Keywords

Cite

@article{arxiv.1712.09507,
  title  = {Protected Vertices in Motzkin trees},
  author = {Anthony Van Duzer},
  journal= {arXiv preprint arXiv:1712.09507},
  year   = {2017}
}

Comments

7 pages

R2 v1 2026-06-22T23:29:58.018Z