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Arithmetic varieties of numerical semigroups

Commutative Algebra 2023-11-23 v1

Abstract

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 root three 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.

Keywords

Cite

@article{arxiv.2311.13500,
  title  = {Arithmetic varieties of numerical semigroups},
  author = {Manuel B. Branco and Ignacio Ojeda and José Carlos Rosales},
  journal= {arXiv preprint arXiv:2311.13500},
  year   = {2023}
}

Comments

15 pages

R2 v1 2026-06-28T13:28:44.576Z