English

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