Proportionally Modular Diophantine Inequalities and Their Multiplicity

Let I be an interval of positive rational numbers. Then the set S （I） = T ∩ N, where T is the submonoid of （Q0＋, ＋） generated by T, is a numerical semigroup. These numerical semigroups are called proportionally modular and can be characterized as the set of integer solutions of a Diophantine inequal...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 26; no. 11; pp. 2059 - 2070
Main Authors Rosales, José Carlos, Branco, Manuel Batista, Vasco, Paulo
Format Journal Article
LanguageEnglish
Published Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.11.2010
Springer Nature B.V
Subjects
Inequalities
Inequality
Integers
Intervals
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Modular
丢番图不等式
多重性
有理数
模块化
特征相关
multiplicity
11D04
20M14
Diophantine inequality
Numerical semigroup
Frobenius number
11D75
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Summary:Let I be an interval of positive rational numbers. Then the set S （I） = T ∩ N, where T is the submonoid of （Q0＋, ＋） generated by T, is a numerical semigroup. These numerical semigroups are called proportionally modular and can be characterized as the set of integer solutions of a Diophantine inequality of the form ax rood b 〈 cx. In this paper we are interested in the study of the maximal intervals I subject to the condition that S （I） has a given multiplicity. We also characterize the numerical semigroups associated with these maximal intervals.
Bibliography:Numerical semigroup, Diophantine inequality, multiplicity, Frobenius number
O424
11-2039/O1
O156.7
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-010-7573-1