English

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 nn and also the protection number of a uniformly chosen node in a uniformly chosen random tree of size nn. 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}
}
R2 v1 2026-06-22T18:25:19.938Z