The main purpose of this book is to introduce algebraic, combinatorial, and computational
methods to study monomial algebras and their presentation ideals, including Stanley …

Let K= Fq be a finite field with q elements and let X be a subset of a projective space Ps− 1,
over the field K, parameterized by Laurent monomials. Let I (X) be the vanishing ideal of X …

The closure of a discrete exponential family is described by a finite set of equations
corresponding to the circuits of an underlying oriented matroid. These equations are similar …

A model for statistical ranking is a family of probability distributions whose states are
orderings of a fixed finite set of items. We represent the orderings as maximal chains in a …

This paper investigates maximizers of the information divergence from an exponential family
\calE. It is shown that the rI-projection of a maximizer P to \calE is a convex combination of P …

Let K be a field and let X (resp. X∗) be a subset of a projective space Ps− 1 (resp. affine
space As), over the field K, parameterized by rational functions. Let I (X)(resp. I (X∗)) be the …

In this article, we study specializations of multigradings and apply them to the problem of the
computation of the arithmetical rank of a lattice ideal IL 𝒢⊂ K [x 1,…, xn]. The arithmetical …

In this thesis, we first study the problem of determining set theoretic complete intersection
(stci) projective monomial curves. We are also interested in finding the equations of the …

Presentamos aplicaciones del álgebra conmutativa a la teoría de códigos evaluación.
Mostramos como se pueden calcular los parámetros básicos de los códigos evaluación …

Los ideales tóricos son un tipo particular de ideales del anillo de polinomios que están
generados por diferencias de monomios (binomios), son primos y graduados. Su estudio es …