Protection numbers in simply generated trees and P\'olya trees
Combinatorics
2019-04-09 v1
Abstract
We determine the limit of the expected value and the variance of the protection number of the root in simply generated trees, in P\'olya trees, and in unlabelled non-plane binary trees, when the number of vertices tends to infinity. Moreover, we compute expectation and variance of the protection number of a randomly chosen vertex in all those tree classes. We obtain exact formulas as sum representations, where the obtained sums are rapidly converging and therefore allowing an efficient numerical computation of high accuracy. Most proofs are based on a singularity analysis of generating functions.
Keywords
Cite
@article{arxiv.1904.03519,
title = {Protection numbers in simply generated trees and P\'olya trees},
author = {Bernhard Gittenberger and Zbigniew Gołębiewski and Isabella Larcher and Małgorzata Sulkowska},
journal= {arXiv preprint arXiv:1904.03519},
year = {2019}
}