Vol. 12, No. 7, 2019

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Asymptotic expansion of Warlimont functions on Wright semigroups

Marco Aldi and Hanqiu Tan

Vol. 12 (2019), No. 7, 1081–1098
Abstract

We calculate full asymptotic expansions of prime-independent multiplicative functions on additive arithmetic semigroups that satisfy a strong form of Knopfmacher’s axioms. When applied to the semigroup of unlabeled graphs, our method yields detailed asymptotic information on how graphs decompose into connected components. As a second class of examples, we discuss polynomials in several variables over a finite field.

Keywords
arithmetical semigroups, asymptotic enumeration, graph enumeration
Mathematical Subject Classification 2010
Primary: 05A16
Secondary: 05C30, 11T06
Milestones
Received: 8 July 2017
Revised: 8 January 2019
Accepted: 2 April 2019
Published: 12 October 2019

Communicated by Kenneth S. Berenhaut
Authors
Marco Aldi
Department of Mathematics and Applied Mathematics
Virginia Commonwealth University
Richmond, VA
United States
Hanqiu Tan
Virginia Commonwealth University
Richmond, VA
United States