Fundamental Gaps in Numerical Semigroups with Respect to Their Multiplicity

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. The authors would like to thank the referee for her/his comments and suggestions This paper is supported by the project BFM2000–1469