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Rafael H. Villarreal

Rafael H. Villarreal

Overview

Rafael H. Villarreal is affiliated with CINVESTAV in Mexico and has a research focus primarily in Mathematics and Computer Science. Their work spans multiple subfields including Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology, Artificial Intelligence, and Electrical and Electronic Engineering.

The principal topics covered in their research include:

  • Commutative Algebra and Its Applications
  • Polynomial and algebraic computation
  • Algebraic Geometry and Number Theory
  • Coding theory and cryptography
  • Rings, Modules, and Algebras
  • Graph theory and CDMA systems
  • Algebraic structures and combinatorial models

Rafael H. Villarreal's recent publications reveal a focus on the algebraic and combinatorial properties of ideals and graphs within commutative algebra. Selected papers include:

  • "Normally torsion-free edge ideals of weighted oriented graphs," 2023, Communications in Algebra
  • "Bounds for the minimum distance function," 2021, DOAJ (DOAJ: Directory of Open Access Journals)
  • "Unmixed and Cohen-Macaulay Weighted Oriented Kőnig Graphs," 2021, Studia Scientiarum Mathematicarum Hungarica
  • "Normality Criteria for Monomial Ideals," 2022, Results in Mathematics
  • "A duality theorem for the ic-resurgence of edge ideals," 2022, European Journal of Combinatorics

The scientist publishes frequently in venues such as:

  • arXiv (Cornell University)
  • Designs Codes and Cryptography
  • Analele Universităţii "Ovidius" Constanţa. Seria Matematică
  • DOAJ (DOAJ: Directory of Open Access Journals)
  • Communications in Algebra

Collaborations feature several frequent co-authors who have contributed to their body of work. These include:

  • Humberto Muñoz-George
  • Manuel González Sarabia
  • Maria Vaz Pinto
  • Gonzalo Grisalde
  • Enrique Reyes

Overall, Rafael H. Villarreal's research integrates algebraic methods with combinatorial models and computational techniques, producing work that intersects a range of mathematical disciplines and topics of contemporary interest.

Best Publications

  • On the Ideal Theory of Graphs

    A. Simis;Wolmer V. Vasconcelos;Rafael H. Villarreal

  • Cohen-macaulay graphs

    Rafael H. Villarreal

  • Edge Ideals: Algebraic and Combinatorial Properties

    Susan Morey;Rafael H. Villarreal

  • Rees algebras of edge ideals

    Rafael H. Villarreal

  • Shellable graphs and sequentially Cohen--Macaulay bipartite graphs

    Adam Van Tuyl;Rafael H. Villarreal

  • The Integral Closure of Subrings Associated to Graphs

    Aron Simis;Wolmer V Vasconcelos;Rafael H Villarreal

  • Ideals with sliding depth

    J. Herzog;W. V. Vasconcelos;R. Villarreal

  • Associated primes of powers of edge ideals

    José Martínez-Bernal;Susan Morey;Rafael H. Villarreal

  • Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields

    Carlos RenteríA-MáRquez;Aron Simis;Rafael H. Villarreal

  • Affine cartesian codes

    Hiram H. López;Carlos Rentería-Márquez;Rafael H. Villarreal

  • A Note on Rees Algebras and the MFMC Property

    Isidoro Gitler;Carlos E. Valencia;Rafael H. Villarreal

  • Ring graphs and complete intersection toric ideals

    Isidoro Gitler;Enrique Reyes;Rafael H. Villarreal

  • Minimum distance functions of graded ideals and Reed–Muller-type codes☆

    José Martínez-Bernal;Yuriko Pitones;Rafael H. Villarreal

  • Unmixed bipartite graphs

    Rafael H. Villarreal

  • The minimum distance of parameterized codes on projective tori

    Eliseo Sarmiento;Maria Vaz Pinto;Rafael H. Villarreal

  • Cohen–Macaulay, shellable and unmixed clutters with a perfect matching of König type

    Susan Morey;Enrique Reyes;Rafael H. Villarreal

  • Blowup Algebras of Square-Free Monomial Ideals and Some Links to Combinatorial Optimization Problems

    Isidoro Gitler;Enrique Reyes;Rafael H. Villarreal

  • Blowup algebras of ideals of vertex covers of bipartite graphs

    Isidoro Gitler;Enrique Reyes;Rafael H. Villarreal

  • Cohen-macaulay bipartite graphs

    Mario Estrada;Rafael H. Villarreal

  • Affine cartesian codes

    Hiram H. Lopez;Carlos Renteria;Rafael H. Villarreal

Frequent Co-Authors

Aron Simis
Aron Simis Federal University of Pernambuco
Wolmer V. Vasconcelos
Wolmer V. Vasconcelos Rutgers, The State University of New Jersey
Jürgen Herzog
Jürgen Herzog University of Duisburg-Essen
Winfried Bruns
Winfried Bruns Osnabrück University

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