@Article{JMS-56-1,
author = {Yang , Lin and Yang , Shengliang},
title = {Protected Branches in Ordered Trees},
journal = {Journal of Mathematical Study},
year = {2022},
volume = {56},
number = {1},
pages = {1--17},
abstract = {<p style="text-align: justify;">In this paper, we consider the class of ordered trees and its two subclasses, bushes and planted trees, which consist of the ordered trees with root degree at least $2$ and with root degree $1$ respectively. In these three classes, we study the number of trees of size $n$ with $k$ protected (resp. unprotected) branches, and the total number of branches (resp. protected branches, unprotected branches) among all trees of size $n$. The explicit formulas as well as the generating functions are obtained. Furthermore, we find that, in each class, as $n$ goes to infinity, the proportion of protected&nbsp; branches among all branches in all trees of size $n$ approaches $ 1/3$.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v56n1.23.01},
url = {http://global-sci.org/intro/article_detail/jms/21217.html}
}