Khinchin families, set constructions, partitions and exponentials
Combinatorics
2022-05-20 v1 Complex Variables
Probability
Abstract
In this paper, we give a simple criterion to verify that functions of the form are in the Hayman class when is a power series with nonnegative coefficients. Thus, using the Hayman and B\'aez-Duarte formulas, we obtain asymptotics for the coefficients of generating functions that arise in many examples of set construction in analytic combinatorics. This new criterion greatly simplifies that obtained previously by the authors.
Cite
@article{arxiv.2205.09577,
title = {Khinchin families, set constructions, partitions and exponentials},
author = {Alicia Cantón and José L. Fernández and Pablo Fernández and Víctor J. Maciá},
journal= {arXiv preprint arXiv:2205.09577},
year = {2022}
}