Ratio-Covarieties of Numerical Semigroups Moreno Frías, María Ángeles Rosales González, José Carlos Numerical semigroup Frobenius number Genus In this work, we will introduce the concept of ratio-covariety, as a family R of numerical semigroups that has a minimum, denoted by min(R), is closed under intersection, and if S ∈ R and S ̸= min(R), then S\{r(S)} ∈ R, where r(S) denotes the ratio of S. The notion of ratiocovariety will allow us to: (1) describe an algorithmic procedure to compute R; (2) prove the existence of the smallest element of R that contains a set of positive integers; and (3) talk about the smallest ratio-covariety that contains a finite set of numerical semigroups. In addition, in this paper we will apply the previous results to the study of the ratio-covariety R(F,m) = {S | S is a numerical semigroup with Frobenius number F and multiplicity m}. 2024-05-28T08:55:02Z 2024-05-28T08:55:02Z 2024-03-14 journal article Moreno-Frías, M.A.; Rosales, J.C. Ratio-Covarieties of Numerical Semigroups. Axioms 2024, 13, 193. https://doi.org/10.3390/axioms13030193 https://hdl.handle.net/10481/92145 10.3390/axioms13030193 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional MDPI