Dr. Rafael Heraclio Villarreal Rodríguez

Departamento de Matemáticas
Centro de Investigación y de Estudios Avanzados del I.P.N.
Av. Instituto Politécnico Nacional 2508
Col. San Pedro Zacatenco, México DF., C.P. 07360
e-mail: vila [@] math.cinvestav.mx.

Areas of interest:

  • Commutative Algebra (Research Area)
  • Algebraic Geometry
  • Combinatorics and computational Algebra

Recent Papers:

  1. Regularity of the vanishing ideal over a parallel composition of paths (with A. Macchia, J. Neves and M. Vaz Pinto), J. Commut. Algebra, to appear.
  2. Generalized minimum distance functions and algebraic invariants of Geramita ideals (with S. M. Cooper, A. Seceleanu, S. O. Tohaneanu and M. Vaz Pinto), Adv. in Appl. Math. 112 (2020), 101940.
  3. On the generalized Hamming weights of certain Reed-Muller-type codes (with D. Jaramillo and M. Gonzalez-Sarabia), Analele Univ. Ovidius din Constanta, Math. Series, to appear.
  4. Generalized Hamming weights of projective Reed--Muller-type codes over graphs (with M. A. Valencia-Bucio and J. Martinez-Bernal), Discrete Math. 343 (2020), no. 1, 111639.
  5. Linear codes over signed graphs (with M. A. Valencia-Bucio and J. Martinez-Bernal), Des. Codes Cryptogr., to appear.

Monomial Algebras

Click here for the web page for the Second Edition of my book Monomial Algebras. This book brings together several areas of pure and applied mathematics, and shows how monomial algebras are related to polyhedral geometry, combinatorial optimization, and combinatorics of hypergraphs.

Interests and Current Activities

I am currently an Associate Editor of the Bulletin Mathematique, and was a member of the boards of Communications in Algebra, Boletin de la Sociedad Matematica Mexicana and Aportaciones Matematicas.