Leaf-to-leaf distances in Catalan trees
Mathematical Physics
2019-02-22 v3 Combinatorics
math.MP
Abstract
We study the average leaf-to-leaf path lengths on ordered Catalan tree graphs with nodes and show that these are equivalent to the average length of paths starting from the root node. We give an explicit analytic formula for the average leaf-to-leaf path length as a function of separation of the leaves and study its asymptotic properties. At the heart of our method is a strategy based on an abstract graph representation of generating functions.
Cite
@article{arxiv.1502.07893,
title = {Leaf-to-leaf distances in Catalan trees},
author = {Andrew M. Goldsborough and Jonathan M. Fellows and Matthew Bates and S. Alex Rautu and George Rowlands and Rudolf A. Römer},
journal= {arXiv preprint arXiv:1502.07893},
year = {2019}
}
Comments
18 pages, 5 figures