Factorization invariants in numerical monoids

Abstract

Nonunique factorization in commutative monoids is often studied using factorization invariants, which assign to each monoid element a quantity determined by the factorization structure. For numerical monoids (co-finite, additive submonoids of the natural numbers), several factorization invariants have received much attention in the recent literature. In this survey article, we give an overview of the length set, elasticity, delta set, $\omega$-primality, and catenary degree invariants in the setting of numerical monoids. For each invariant, we present current major results in the literature and identify the primary open questions that remain.

References in corpus (7)

• The Realization Problem for Delta Sets of Numerical Semigroups
• On factorization invariants and Hilbert functions
• A Characterization of class groups via sets of lengths {II}
• A characterization of class groups via sets of lengths
• On the set of catenary degrees of finitely generated cancellative commutative monoids
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Cited by in corpus (5)

• On factorization invariants and Hilbert functions
• Minimal presentations of shifted numerical monoids
• Apéry sets of shifted numerical monoids
• Augmented Hilbert series of numerical semigroups
• On Atomic Density of Numerical Semigroup Algebras