Protection Number in Plane Trees
Combinatorics
2017-12-21 v1
Abstract
The protection number of a plane tree is the minimal distance of the root to a leaf; this definition carries over to an arbitrary node in a plane tree by considering the maximal subtree having this node as a root. We study the the protection number of a uniformly chosen random tree of size and also the protection number of a uniformly chosen node in a uniformly chosen random tree of size . The method is to apply singularity analysis to appropriate generating functions. Additional results are provided as well.
Keywords
Cite
@article{arxiv.1702.06816,
title = {Protection Number in Plane Trees},
author = {Clemens Heuberger and Helmut Prodinger},
journal= {arXiv preprint arXiv:1702.06816},
year = {2017}
}