# Characterization of Gaps and Elements of a Numerical Semigroup Using Groebner Bases

## TL;DR

This paper explores the use of Groebner bases to analyze numerical semigroups, providing systematic characterizations of their gaps and elements, combining survey and original research.

## Contribution

It offers a new systematic approach to characterize numerical semigroup elements using Groebner bases, advancing theoretical understanding.

## Key findings

- Characterization of semigroup elements via Groebner bases
- Systematic approach to gaps and elements of numerical semigroups
- Proved new results on semigroup structure

## Abstract

This article is partly a survey and partly a research paper. It tackles the use of Groebner bases for addressing problems of numerical semigroups, which is a topic that has been around for some years, but it does it in a systematic way which enables us to prove some results and a hopefully interesting characterization of the elements of a semigroup in terms of Groebner bases.