Approximating length-based invariants in atomic Puiseux monoids

H. Polo


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.


atomic Puiseux monoids, numerical monoids, approximation, factorization invariants, sets of lengths, elasticity, set of distances

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