Ratio-Covarieties of Numerical Semigroups
Metadatos
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MDPI
Materia
Numerical semigroup Frobenius number Genus
Fecha
2024-03-14Referencia bibliográfica
Moreno-Frías, M.A.; Rosales, J.C. Ratio-Covarieties of Numerical Semigroups. Axioms 2024, 13, 193. https://doi.org/10.3390/axioms13030193
Resumen
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}.