Delta Sets of Numerical Monoids Using Nonminimal Sets of Generators

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...

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Bibliographic Details
Published in:Communications in algebra 2010-07, Vol.38 (7), p.2622-2634
Main Authors: Chapman, S. T., Daigle, Jay, Hoyer, Rolf, Kaplan, Nathan
Format: Article
Language:English
Subjects:
Algebra
Delta set
Deltas
Generators
Monoids
Nonunique factorization
Numerical monoid
Numerical semigroup
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Summary: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.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927870903045165