Fundamental Gaps in Numerical Semigroups with Respect to Their Multiplicity

Abstract

For a numerical semigroup, we introduce the concept of a fundamental gap with respect to the multiplicity of the semigroup. The semigroup is fully determined by its multiplicity and these gaps. We study the case when a set of non–negative integers is the set of fundamental gaps with respect to the multiplicity of a numerical semigroup. Numerical semigroups with maximum and minimum number of this kind of gaps are described.