Counting rooted trees: the universal law \(t(n)\sim C\rho^{-n} n^{-3/2}\)
The electronic journal of combinatorics, Tome 13 (2006)
Combinatorial classes ${\cal T}$ that are recursively defined using combinations of the standard multiset, sequence, directed cycle and cycle constructions, and their restrictions, have generating series ${\bf T}(z)$ 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 ${\bf T}$.
@article{10_37236_1089,
author = {Jason P. Bell and Stanley N. Burris and Karen A. Yeats},
title = {Counting rooted trees: the universal law \(t(n)\sim {C\rho^{-n}} n^{-3/2}\)},
journal = {The electronic journal of combinatorics},
year = {2006},
volume = {13},
doi = {10.37236/1089},
zbl = {1099.05023},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1089/}
}
TY - JOUR
AU - Jason P. Bell
AU - Stanley N. Burris
AU - Karen A. Yeats
TI - Counting rooted trees: the universal law \(t(n)\sim C\rho^{-n} n^{-3/2}\)
JO - The electronic journal of combinatorics
PY - 2006
VL - 13
UR - http://geodesic.mathdoc.fr/articles/10.37236/1089/
DO - 10.37236/1089
ID - 10_37236_1089
ER -
Jason P. Bell; Stanley N. Burris; Karen A. Yeats. Counting rooted trees: the universal law \(t(n)\sim C\rho^{-n} n^{-3/2}\). The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1089
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