Rafael H. Villarreal

activity

20052026

most citedA note on Rees algebras and the MFMC property

46 citations · 49 across the 6 of their papers we have counts for

collaborators

7 papers

math.AC2026

Systems of parameters consisting of linear forms for monomial ideal quotients

Edwin A. Contreras, Enrique Reyes, Rafael H. Villarreal

Let $S = K [x_{1}, \dots, x_{n}]$ be a polynomial ring over a field $K$ and let $I$ be a monomial ideal of $S$ . We classify linear systems of parameters of $S / I$ over any field $K$ using l…

math.AC2026

Signature invariants of monomial ideals

Jovanny Ibarguen, Carlos E. Valencia, Rafael H. Villarreal

Let $I$ be a monomial ideal of a polynomial ring $R = K [x_{1}, \dots, x_{n}]$ over a field $K$ and let $sgn (I)$ be its signature ideal. If $I$ is not a principal ideal, we show that…

math.CO2025

Weighted Ehrhart functions

Enrique Reyes, Carlos E. Valencia, Rafael H. Villarreal

We give an algorithm to compute weighted Ehrhart functions of lattice polytopes for polynomial weights using Lagrange interpolation. We show how to compute generating functions of…

math.CO2024

Ehrhart Functions of Weighted Lattice Points

Jesus A. De Loera, Carlos E. Valencia, Rafael H. Villarreal +1

This paper studies three different ways to assign weights to the lattice points of a convex polytope and discusses the algebraic and combinatorial properties of the resulting weigh…

math.AC2024

The v-numbers and linear presentations of ideals of covers of graphs

Humberto Muñoz-George, Enrique Reyes, Rafael H. Villarreal

Let $G$ be a graph and let $J = I_{c} (G)$ be its ideal of covers. The aims of this work are to study the {\rm v}-number $v (J)$ of $J$ and to study when $J$ is linearly presented…

math.AC2006★ 3 cited

Blowup algebras of square-free monomial ideals and some links to combinatorial optimization problems

I. Gitler, E. Reyes, R. H. Villarreal

Let I=(x^{v_1},...,x^{v_q} be a square-free monomial ideal of a polynomial ring K[x_1,...,x_n] over an arbitrary field K and let A be the incidence matrix with column vectors {v_1}…

math.AC2005★ 46 cited

A note on Rees algebras and the MFMC property

I. Gitler, C. E. Valencia, R. H. Villarreal

We study irreducible representations of Rees cones and characterize the max-flow min-cut property of clutters in terms of the normality of Rees algebras and the integrality of cert…