Counting Rooted Trees: The Universal Law t(n) ~ C ρ^{-n} n^{-3/2}

Details Counting Rooted Trees: The Universal Law t(n) ~ C ρ^{-n} n^{-3/2} Counting Rooted Trees: The Universal Law t(n) ~ C ρ^{-n} n^{-3/2}

2005-12-19

arxiv.org/abs/math/0512432v3

The Electronic Journal of Combinatorics, 13 (2006), #R63

Mathematics

Combinatorics

53 pages, 5 figures, typos corrected, final version

Scientific paper

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.

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