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arXiv · 1409.3425

On the set of elasticities in numerical monoids

Thomas Barron·Christopher O'Neill·Roberto Pelayo
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Abstract

In an atomic, cancellative, commutative monoid $S$, the elasticity of an element provides a coarse measure of its non-unique factorizations by comparing the largest and smallest values in its set of factorization lengths (called its length set). In this paper, we show that the set of length sets $\mathcal L(S)$ for any arithmetical numerical monoid $S$ can be completely recovered from its set of elasticities $R(S)$; therefore, $R(S)$ is as strong a factorization invariant as $\mathcal L(S)$ in this setting. For general numerical monoids, we describe the set of elasticities as a specific collection of monotone increasing sequences with a common limit point of $\max R(S)$.

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Thomas Barron, Christopher O'Neill, Roberto Pelayo. 2015-06-25. On the set of elasticities in numerical monoids. https://doi.org/10.1007/s00233-015-9740-2

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