When is a Numerical Semigroup A Quotient?
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.
Bogart, Tristram, Christopher O'Neill, and Kevin Woods. 2023. "When is a Numerical Semigroup a Quotient?" Bulletin of the Australian Mathematical Society, 1-10. DOI: 10.1017/S0004972723000035.
Cambridge University Press
Bulletin of the Australian Mathematical Society
Numerical semigroup, Embedding dimension, Quotient, Proportionally modular semigroup