77 research outputs found
Factorization invariants in numerical monoids
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,
-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
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