Realizable sets of catenary degrees of numerical monoids

Abstract: 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 $\mathbb Z_{\ge 0}$ occur as the set of catenary degrees of a numerical monoid (i.e., a co-finite, additive submonoid of $\mathbb Z_{\ge 0}$). In particular, we show that, with one exception, every finite subset of $\mathbb Z_{\ge 0}$ that can possibly occur as the set of catenary degrees of some atomic monoid is actually achieved by a numerical monoid.