Balanced vertices in labeled rooted trees
Combinatorics
2017-09-15 v2
Abstract
In a rooted tree, we call a vertex {\em balanced} if it is at equal distance from all its descendant leaves. We count balanced vertices in three different tree varieties. For decreasing binary trees, we can prove that the probability that a vertex chosen uniformly at random from the set of all trees of a given size is balanced is monotone decreasing.
Keywords
Cite
@article{arxiv.1705.09688,
title = {Balanced vertices in labeled rooted trees},
author = {Miklos Bona},
journal= {arXiv preprint arXiv:1705.09688},
year = {2017}
}
Comments
16 pages, 3 figures