English

$k$-protected vertices in unlabeled rooted plane trees

Combinatorics 2016-06-30 v3

Abstract

We find a simple, closed formula for the proportion of vertices which are kk-protected in all unlabeled rooted plane trees on nn vertices. We also find that, as nn goes to infinity, the average rank of a random vertex in a tree of size nn approaches 0.727649, and the average rank of the root of a tree of size nn approaches 1.62297.

Keywords

Cite

@article{arxiv.1606.00083,
  title  = {$k$-protected vertices in unlabeled rooted plane trees},
  author = {Keith Copenhaver},
  journal= {arXiv preprint arXiv:1606.00083},
  year   = {2016}
}
R2 v1 2026-06-22T14:14:26.958Z