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arXiv · 2007.09406

Approximating length-based invariants in atomic Puiseux monoids

Harold Polo
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Abstract

A numerical monoid is a cofinite additive submonoid of the nonnegative integers, while a Puiseux monoid is an additive submonoid of the nonnegative cone of the rational numbers. Using that a Puiseux monoid is an increasing union of copies of numerical monoids, we prove that some of the factorization invariants of these two classes of monoids are related through a limiting process. This allows us to extend results from numerical to Puiseux monoids. We illustrate the versatility of this technique by recovering various known results about Puiseux monoids.

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Harold Polo. 2021-12-02. Approximating length-based invariants in atomic Puiseux monoids. https://arxiv.org/abs/2007.09406

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