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

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5 papers · 1 filter

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.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…