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REALISABLE SETS OF CATENARY DEGREES OF NUMERICAL MONOIDS
Published online by Cambridge University Press: 04 December 2017
Abstract
The catenary degree is an invariant that measures the distance between factorisations of elements within an atomic monoid. In this paper, we classify which finite subsets of $\mathbb{Z}_{\geq 0}$ occur as the set of catenary degrees of a numerical monoid (that is, a co-finite, additive submonoid of $\mathbb{Z}_{\geq 0}$). In particular, we show that, with one exception, every finite subset of $\mathbb{Z}_{\geq 0}$ 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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- Research Article
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- © 2017 Australian Mathematical Publishing Association Inc.
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