Vol. 1, No. 1, 2008

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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

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.

nonunique factorization, elasticity of factorization, unions of sets of lengths
Mathematical Subject Classification 2000
Primary: 20M14
Secondary: 20D60, 11B75
Received: 28 October 2007
Accepted: 29 October 2007
Published: 28 February 2008

Communicated by Kenneth S. Berenhaut
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