Arithmetic Varieties of Numerical Semigroups

In this paper we present the notion of arithmetic variety for numerical semigroups. We study various aspects related to these varieties such as the smallest arithmetic that contains a set of numerical semigroups and we exhibit the rooted tree associated with an arithmetic variety. This tree is not l...

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Bibliographic Details
Published inResultate der Mathematik Vol. 79; no. 4
Main Authors Branco, Manuel B., Ojeda, Ignacio, Rosales, José Carlos
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2024
Subjects
Mathematics
Mathematics and Statistics
multiplicity
20M07
varieties
depth
Numerical semigroup
Frobenius number
rooted tree
Primary 20M14
Secondary 05C05
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Summary:In this paper we present the notion of arithmetic variety for numerical semigroups. We study various aspects related to these varieties such as the smallest arithmetic that contains a set of numerical semigroups and we exhibit the rooted tree associated with an arithmetic variety. This tree is not locally finite; however, if the Frobenius number is fixed, the tree has finitely many nodes and algorithms can be developed. All algorithms provided in this article include their (non-debugged) implementation in GAP.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-024-02212-5