$k$-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 -protected in all unlabeled rooted plane trees on vertices. We also find that, as goes to infinity, the average rank of a random vertex in a tree of size approaches 0.727649, and the average rank of the root of a tree of size 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}
}