Asymptotic expansion of Warlimont functions on Wright semigroups

Aldi, Marco; Tan, Hanqiu

doi:10.2140/involve.2019.12.1081

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-4184 (online)

ISSN 1944-4176 (print)

Author index

To appear

Other MSP journals

Asymptotic expansion of Warlimont functions on Wright semigroups

Marco Aldi and Hanqiu Tan

Vol. 12 (2019), No. 7, 1081–1098

DOI: 10.2140/involve.2019.12.1081

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

Vol. 12, No. 7, 2019