Numerical semigroups with embedding dimension three

Part of the Developments in Mathematics book series (DEVM, volume 20)


Herzog in [14] proves that for embedding dimension three numerical semigroups, the concepts of symmetric and complete intersection coincide. Hence with the help of Proposition 1.17 and what we know about embedding dimension two numerical semigroups, a formula for the Frobenius number and the genus of a symmetric numerical semigroup with embedding dimension three can easily be found. As for the pseudo-symmetric case, an expression for the Frobenius number of a numerical semigroup of embedding dimension three can be given in terms of the generators (and consequently also a formula for the genus in view of Corollary 3.5). This formula is presented by the authors in [82].


Complete Intersection Minimal Generator Numerical Semigroup Minimal System Unique Expression 
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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Algebra, Faculty of SciencesUniversity of Granada, Campus University FuentenuevaGranadaSpain

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