When is a Numerical Semigroup A Quotient?

Abstract

A natural operation on numerical semigroups is taking a quotient by a positive integer. If S is a quotient of a numerical semigroup with k generators, we call S a k-quotient. We give a necessary condition for a given numerical semigroup 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.

Publisher

Cambridge University Press

Publication Date

2-1-2023

Publication Title

Bulletin of the Australian Mathematical Society

Department

Mathematics

Document Type

Article

DOI

https://dx.doi.org/10.1017/S0004972723000035

Keywords

Numerical semigroup, Embedding dimension, Quotient, Proportionally modular semigroup

Language

English

Format

text

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