Khinchin families, set constructions, partitions and exponentials

2022/05/19 by Cantón, Alicia, Fernández, José L., Fernández, Pablo +1 · 1 citation
#11P82 #60F99 #Combinatorics (math.CO) #Complex Variables (math.CV) #FOS: Mathematics #Primary 30B10 #Probability (math.PR) #Secondary: 05A16

paper · doi:10.48550/arxiv.2205.09577

Abstract

In this paper, we give a simple criterion to verify that functions of the form e^g are in the Hayman class when g is a power series with nonnegative coefficients. Thus, using the Hayman and Báez-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.

Cited by

• Galton-Watson processes, simple varieties of trees and Khinchin families

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