2023/02/17 by M. A. Moreno-Frías, J. C. Rosales, Moreno-Frías, M. A. +1 · 1 citation
Computer Science · Decision Sciences · Mathematics · #11D07 #20M14 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Scheduling and Timetabling Solutions
paper · pdf · doi:10.48550/arxiv.2302.09121
openalex publication_date 2023/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Denote by \mathrm m(S) the multiplicity of a numerical semigroup S. A covariety is a nonempty family \mathscrC of numerical semigroups that fulfills the following conditions: there is the minimum of \mathscrC, the intersection of two elements of \mathscrC is again an element of \mathscrC and S\backslash \\mathrm m(S)\∈ \mathscrC for all S∈ \mathscrC such that S≠ min(\mathscrC). In this work we describe an algorithmic procedure to compute all the elements of \mathscrC. We prove that there exists the smallest element of \mathscrC containing a set of positive integers. We show that \mathscrA(F)=\S| S is a numerical semigroup with Frobenius number F\ is a covariety, and we particularize the previous results in this covariety. Finally, we will see that there is the smallest covariety containing a finite set of numerical semigroups.