Fundamental Gaps in Numerical Semigroups with Respect to Their Multiplicity

Authors: Rosales, J.¹; García–Sánchez, P.²; García–García, J.³; Jiménez Madrid, J.⁴

Source: Acta Mathematica Sinica, Volume 20, Number 4, July 2004 , pp. 629-646(18)

Publisher: Springer

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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.

Keywords: Numerical semigroup; Gap; Multiplicity; Frobenius number; 20M14

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10114-003-0298-7

Affiliations: 1: Departamento de Álgebra, Universidad de Granada, E-18071, Granada, Spain, Email: jrosales@ugr.es 2: Departamento de Álgebra, Universidad de Granada, E-18071, Granada, Spain, Email: pedro@ugr.es 3: Departamento de Álgebra, Universidad de Granada, E-18071, Granada, Spain, Email: jigg@ugr.es 4: Instituto de Astrofísica de Andalucía (CSIC), 3004, 18080, Granada, Spain, Email: madrid@iaa.es

Publication date: 2004-07-01