Dr. Rafael Heraclio Villarreal Rodríguez

Professor 3E
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. Evaluation codes and their basic parameters (with D. Jaramillo and M. Vaz Pinto), Des. Codes Cryptogr. 89 (2021), no. 2, 269-300.
  2. The v-number of edge ideals, (with D. Jaramillo), J. Combin. Theory Ser. A 177 (2021), 105310.
  3. The dual of an evaluation code, (with H. H. López and I. Soprunov), Des. Codes Cryptogr. 89 (2021), no. 7, 1367-1403.
  4. Bounds for the minimum distance function, (with L. Núñez-Betancourt and Y. Pitones), An. Stiint. Univ. Ovidius Constanta Ser. Mat. 29(3) (2021), 229-242.
  5. Unmixed and Cohen-Macaulay weighted oriented Konig graphs, (with Y. Pitones and E. Reyes), Studia Sci. Math. Hungar. 58 (2021), no. 3, 276-292.
  6. Induced matchings and the v-number of graded ideals, (with G. Grisalde and E. Reyes), Mathematics 9(2021), no. 22, Article number 2860.
  7. Rees algebras of filtrations of covering polyhedra and integral closure of powers of monomial ideals, (with G. Grisalde and A. Seceleanu), Res. Math. Sci. 9, 13 (2022).

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 Journal of Algebraic Combinatorics and Bulletin Mathematique, and was a member of the boards of Communications in Algebra, Boletin de la Sociedad Matematica Mexicana and Aportaciones Matematicas.