Delta Sets of Numerical Monoids Using Nonminimal Sets of Generators

Abstract

Several recent articles have studied the structure of the delta set of a numerical monoid. We continue this work with the assumption that the generating set S chosen for the numerical monoid M is not necessarily minimal. We show that for certain choices of S, the resulting delta set can be made (in terms of cardinality) arbitrarily large or small. We close with a close analysis of the case where M =⟨n ₁, n ₂, in ₁ + jn ₂⟩for non-negative i and j.

Key Words:

• Delta set
• Nonunique factorization
• Numerical monoid
• Numerical semigroup

2000 Mathematics Subject Classification:

• 20M14
• 20D60
• 11B75

ACKNOWLEDGMENTS

The second, third and fourth authors received support from the National Science Foundation under grant DMS-0648390. The authors wish to thank Desmond Torkornoo for discussions related to this work.

Dedicated to Professor William W. Smith on the occasion of his retirement from the faculty at the University of North Carolina at Chapel Hill.

Notes

Communicated by I. Swanson.