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REALISABLE SETS OF CATENARY DEGREES OF NUMERICAL MONOIDS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 97 / Issue 2 / April 2018
- Published online by Cambridge University Press:
- 04 December 2017, pp. 240-245
- Print publication:
- April 2018
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- Article
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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.
