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

TL;DR

This paper implements a recursive algorithm to construct all complete intersection numerical semigroups with a given Frobenius number, and applies it to specific subclasses, providing bounds for their invariants.

Contribution

It operationalizes Delorme's recursive method and specializes it to subfamilies, offering bounds on embedding dimension and minimal generators.

Findings

Algorithm successfully constructs complete intersection numerical semigroups.

Bounds for embedding dimension and minimal generators are established.

Application to subclasses like free, telescopic, and singularity-associated semigroups.

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.