Constructing the set of complete intersection numerical semigroups with a given Frobenius number

2012/04/19 by Abdallah Assi, Assi, Abdallah, Pedro A. García-Sánchez +1
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.CO

paper · pdf · doi:10.48550/arxiv.1204.4258

13 pages Results improved, References added

openalex publication_date 2012/04/19 · arxiv created 2013/01/21 · arxiv updated 2013/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Delorme suggested that the set of all complete intersection numerical semigroups can be computed recursively. We have implemented this algorithm, and particularized it to several subfamilies of this class of numerical semigroups: free and telescopic numerical semigroups, and numerical semigroups associated to an irreducible plane curve singularity. The recursive nature of this procedure allows us to give bounds for the embedding dimension and for the minimal generators of a semigroup in any of these families.

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