The tree of irreducible numerical semigroups with fixed Frobenius number

In this paper we present a procedure to build the set of irreducible numerical semigroups with a fixed Frobenius number. The construction gives us a rooted tree structure for this set. Furthermore, by using the notion of Kunz-coordinates vector we translate the problem of finding such a tree into th...

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Bibliographic Details
Published inForum mathematicum Vol. 25; no. 6; pp. 1249 - 1261
Main Authors Blanco, Victor, Rosales, José Carlos
Format Journal Article
LanguageEnglish
Published Berlin Walter de Gruyter GmbH 01.11.2013
Subjects
Frobenius number
irreducible numerical semigroup
Numerical semigroup
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Summary:In this paper we present a procedure to build the set of irreducible numerical semigroups with a fixed Frobenius number. The construction gives us a rooted tree structure for this set. Furthermore, by using the notion of Kunz-coordinates vector we translate the problem of finding such a tree into the problem of manipulating vectors with as many component as the Frobenius number.
ISSN:0933-7741
1435-5337
DOI:10.1515/form.2011.151