k-protected vertices in unlabeled rooted plane trees

2016/06/01 by Copenhaver, Keith
#05A15 #05A16 #05C05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1606.00083

Abstract

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

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