Fringe Analysis of Plane Trees Related to Cutting and Pruning
Combinatorics
2018-03-19 v1
Abstract
Rooted plane trees are reduced by four different operations on the fringe. The number of surviving nodes after reducing the tree repeatedly for a fixed number of times is asymptotically analyzed. The four different operations include cutting all or only the leftmost leaves or maximal paths. This generalizes the concept of pruning a tree. The results include exact expressions and asymptotic expansions for the expected value and the variance as well as central limit theorems.
Keywords
Cite
@article{arxiv.1704.01095,
title = {Fringe Analysis of Plane Trees Related to Cutting and Pruning},
author = {Benjamin Hackl and Clemens Heuberger and Sara Kropf and Helmut Prodinger},
journal= {arXiv preprint arXiv:1704.01095},
year = {2018}
}