On the asymptotic behavior of unions of sets of lengths in atomic monoids

Baginski, Paul; Chapman, Scott; Hine, Natalie; Paixão, João

doi:10.2140/involve.2008.1.101

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On the asymptotic behavior of unions of sets of lengths in atomic monoids

Paul Baginski, Scott Thomas Chapman, Natalie Hine and João Paixão

Vol. 1 (2008), No. 1, 101–110

DOI: 10.2140/involve.2008.1.101

Abstract

Let $M$ be a commutative cancellative atomic monoid. We use unions of sets of lengths in $M$ to construct the $V$ -Delta set of $M$ . We first derive some basic properties of $V$ -Delta sets and then show how they offer a method to investigate the asymptotic behavior of the sizes of unions of sets of lengths.

Keywords

nonunique factorization, elasticity of factorization, unions of sets of lengths

Mathematical Subject Classification 2000

Primary: 20M14

Secondary: 20D60, 11B75

Milestones

Received: 28 October 2007

Accepted: 29 October 2007

Published: 28 February 2008

Communicated by Kenneth S. Berenhaut

Authors

Paul Baginski
University of California at Berkeley Department of Mathematics Berkeley CA 94720-3840 United States

Scott Thomas Chapman
Trinity University Department of Mathematics One Trinity Place San Antonio, TX 78212-7200 United States

Natalie Hine
The College of New Jersey Mathematics and Statistics Department P.O. Box 7718 Ewing, NJ 08628-0718 United States

João Paixão
Virginia Tech Department of Mathematics 460 McBryde Blacksburg, VA 24061-0123 United States

Vol. 1, No. 1, 2008