%0 Journal Article 
%A Moreno Frías, María Ángeles
%A Rosales, José Carlos
%T Ratio-Covarieties of Numerical Semigroups
%D 2024
%U http://hdl.handle.net/10498/35378
%X 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}.
%K Numerical semigroup
%K ratio-covariety
%K Frobenius number
%K genus
%K ratio
%K algorithm
%~ Universidad de Cádiz