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arXiv · 1705.04276

Realizable sets of catenary degrees of numerical monoids

Christopher O'Neill·Roberto Pelayo
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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.

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Christopher O'Neill, Roberto Pelayo. 2017-05-11. Realizable sets of catenary degrees of numerical monoids. https://doi.org/10.1017/s0004972717000995

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