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- Title
Ratio-Covarieties of Numerical Semigroups.
- Authors
Moreno-Frías, María Ángeles; Rosales, José Carlos
- Abstract
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 ratio-covariety 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 }.
- Subjects
RAMSEY numbers; INTEGERS
- Publication
Axioms (2075-1680), 2024, Vol 13, Issue 3, p193
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms13030193