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Turkish Journal of Mathematics

DOI

10.55730/1300-0098.3436

Abstract

A covariety is a nonempty family $C$ of numerical semigroups that satisfies a certain conditions. In this work we will show that if $F$ is a positive integer, then the set of Arf numerical semigroup with Frobenius number $F$, denoted by $(F)$, is a covatiety. The previous results will be used to give an algorithm which calculates the set $(F).$ Also we will see that if $X\subseteq S\backslash \Delta(F)$ for some $S\in (F),$ then there is the smallest element of $(F)$ containing $X.$

Keywords

Numerical semigroup, multiplicity, Frobenius number, covariety, Arf numerical semigroup, Arf-sequence, algorithm

First Page

1392

Last Page

1405

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