2022/12/16 by Tristram Bogart, Bogart, Tristram, Christopher O’Neill +3
Mathematics · #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Graph theory and applications #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2212.08285
openalex publication_date 2022/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A natural operation on numerical semigroups is taking a quotient by a positive integer. If \mathcal S is a quotient of a numerical semigroup with k generators, we call \mathcal S a k-quotient. We give a necessary condition for a given numerical semigroup \mathcal S to be a k-quotient, and present, for each k ≥ 3, the first known family of numerical semigroups that cannot be written as a k-quotient. We also examine the probability that a randomly selected numerical semigroup with k generators is a k-quotient.