Counting Rooted Trees: The Universal Law t(n) ~ C \rho^{-n} n^{-3/2}
Combinatorics
2007-05-23 v3
Abstract
Combinatorial classes T that are recursively defined using combinations of the standard multiset, sequence, directed cycle and cycle constructions, and their restrictions, have generating series T(z) with a positive radius of convergence; for most of these a simple test can be used to quickly show that the form of the asymptotics is the same as that for the class of rooted trees: C \rho^{-n} n^{-3/2} where \rho is the radius of convergence of T.
Keywords
Cite
@article{arxiv.math/0512432,
title = {Counting Rooted Trees: The Universal Law t(n) ~ C \rho^{-n} n^{-3/2}},
author = {Jason P. Bell and Stanley N. Burris and Karen A. Yeats},
journal= {arXiv preprint arXiv:math/0512432},
year = {2007}
}
Comments
53 pages, 5 figures, typos corrected, final version