MÁRQUEZ CAMPOS , Guadalupe

En esta tesis trata básicamente, de en primer lugar establecer una relación entre bases de Groebner y semigrupos numéricos y en segundo lugar utilizar dicha relación para obtener diversas aplicaciones y resultados. La memoria consta de tres capítulos y un apéndice con una pequeña sección final con conclusiones y algunos problemas abiertos de...

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...

A simple way of computing the Apéry set of a numerical semigroup (or monoid) with respect to a generator, using Groebner bases, is presented, together with a generalization for affine semigroups. This computation allows us to calculate the type set and, henceforth, to check the Gorenstein condition which characterizes the symmetric numerical subgroups.

In this paper we use an elementary approach by using numerical semigroups (specifically, those with two generators) to give a formula for the number of integral points inside a right-angled triangle with rational vertices. This is the basic case for computing the number of integral points inside a rational (not necessarily convex) polygon.