#### 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
##### Abstract

Let $M$ be a commutative cancellative atomic monoid. We use unions of sets of lengths in $M$ to construct the $\mathsc{V}$-Delta set of $M$. We first derive some basic properties of $\mathsc{V}$-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