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Asymptotic
expansion of Warlimont functions on Wright semigroups
Marco Aldi and Hanqiu Tan
Vol. 12 (2019), No. 7, 1081–1098
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Abstract |
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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. |
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Keywords
arithmetical semigroups, asymptotic enumeration, graph
enumeration
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Mathematical Subject Classification 2010
Primary: 05A16
Secondary: 05C30, 11T06
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Milestones
Received: 8 July 2017
Revised: 8 January 2019
Accepted: 2 April 2019
Published: 12 October 2019
Communicated by Kenneth S. Berenhaut
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Authors |
| Marco Aldi | |
| Department of Mathematics and
Applied Mathematics Virginia Commonwealth University Richmond, VA United States |
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| Hanqiu Tan | |
| Virginia Commonwealth
University Richmond, VA United States |
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