Arf numerical semigroups with high multiplicity via Gröbner basis

Abstract

In this paper, Arf numerical semigroups with high multiplicity are given. RF (Row Factorization)-matrices, Gröbner basis are presented by writing the ideals of numerical semigroup with RF-matrices. In addition, it is prove that if we have a minimal presentation (or a Gröbner basis of the ideal associated to the semigroup), then this will be a system of generators of the numerical semigroup.