Perfect numerical semigroups

Abstract

A numerical semigroup is perfect if it does not have isolated gaps. In this paper we will order the perfectnumerical semigroups with a fixed multiplicity. This ordering allows us to give an algorithm procedure to obtain them.We also study the perfect monoid, which is a subset of N that can be expressed as an intersection of perfect numericalsemigroups, and we present the perfect monoid generated by a subset of N. We give an algorithm to calculate it. Westudy the perfect closure of a numerical semigroup, as well as the perfect numerical semigroup with maximal embeddingdimension, in particular Arf and saturated numerical semigroups.