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## Realizable sets of catenary degrees of numerical monoids

## Published Web Location

https://arxiv.org/pdf/1705.04276.pdfNo data is associated with this publication.

## 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 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.