Fundamental Gaps in Numerical Semigroups with Respect to Their Multiplicity

Fundamental Gaps in Numerical Semigroups with Respect to Their Multiplicity

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摘要 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. 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.

作者 J.C.ROSALES P.A.GARCíA-SANCHEZ J.I.GARCíA-GARCíA J.A.JIMENEZMADRID

机构地区 DepartamentodeAlgebra InstitutodeAstrofisicadeAndalucia(CSIC)

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2004年第4期629-646,共18页 数学学报（英文版）

基金 supported by the project BFM2000-1469

关键词 Numerical semigroup GAP MULTIPLICITY Frobenius number Numerical semigroup Gap Multiplicity Frobenius number

分类号 O152 [理学—基础数学]

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Acta Mathematica Sinica,English Series

2004年第4期

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Fundamental Gaps in Numerical Semigroups with Respect to Their Multiplicity

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