When the catenary degree agrees with the tame degree in numerical semigroups of embedding dimension three

García-Sánchez, Pedro A.; Viola, Caterina

doi:10.2140/involve.2015.8.677

Cited by 3 publications

(2 citation statements)

References 9 publications

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“…, ω(n k )} is the maximum ω-value obtained at an irreducible [10]. This connection has been explored in some of the recent literature, in part as a method of bounding ω(S) [10,28,29]. Recent investigations focusing on the ω-values of all non-unit elements in monoids have uncovered interesting asymptotic behavior.…”

Section: ω-Primalitymentioning

confidence: 99%

Factorization invariants in numerical monoids

O’Neill¹,

Pelayo²

2017

Algebraic and Geometric Methods in Discrete Mathematics

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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 N), 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, ω-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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Section: ω-Primalitymentioning

confidence: 99%

Factorization invariants in numerical monoids

O’Neill¹,

Pelayo²

2017

Algebraic and Geometric Methods in Discrete Mathematics

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“…For numerical semigroups with embedding dimension three, we also know when the catenary degree equals the tame degree [13], or when the tame degree and the ω-primality coincide [7]. In this manuscript we focus on the characterization of numerical semigroups with embedding dimension three for which the maximum of the Delta set plus two equals the catenary degree.…”

Section: Introductionmentioning

confidence: 99%