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Realizable sets of catenary degrees of numerical monoids

  • Author(s): O'Neill, Christopher
  • Pelayo, Roberto
  • et al.

Published Web Location

https://arxiv.org/pdf/1705.04276.pdf
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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 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.

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