Realizable sets of catenary degrees of numerical monoids
Published Web Locationhttps://arxiv.org/pdf/1705.04276.pdf
The catenary degree is an invariant that measures the distance between factorizations of elements within an atomic monoid. In this paper, we classify which finite subsets of Z≥0 occur as the set of catenary degrees of a numerical monoid (i.e., a co-finite, additive submonoid of Z≥0). In particular, we show that, with one exception, every finite subset of Z≥0 that can possibly occur as the set of catenary degrees of some atomic monoid is actually achieved by a numerical monoid.