Dr. Rafael Heraclio Villarreal Rodríguez

BOOKS:

1. Monomial Algebras, Monographs and Textbooks in Pure and Applied Mathematics 238, Marcel Dekker, Inc., New York, 2001. Book

BOOK CHAPTERS:

1. Monomial Algebras and Polyhedral Geometry, in Handbook of Algebra, Vol. 3 (M. Hazewinkel Ed.), Elsevier, Amsterdam, 2003, pp. 257–314. Book Chapters

BOOK PROJECT:

1. Combinatorial Optimization Methods in Commutative Algebra. Incomplete very preliminary version of a book project. Download PDF

PAPERS:

  1. Ideals with sliding depth, (with J. Herzog and W. V. Vasconcelos), Nagoya Math. J. 99 (1985), 159–172.
  2. On Gorenstein ideals of codimension four, (with W. V. Vasconcelos), Proc. Amer. Math. Soc. 98 (1986), 205–210.
  3. Rees algebras and Koszul homology, J. Algebra 119 (1988), 83–104.
  4. Cohen–Macaulay graphs, Manuscripta Math. 66 (1990), 277–293.
  5. Koszul homology of Cohen–Macaulay rings with linear resolutions, (with C. Rentería), Proc. Amer. Math. Soc. 115 (1992), 51–58.
  6. Monomial algebras, Aportaciones Matemáticas, Investigación 6 (1992), 69–75.
  7. Critical binomials of monomial curves, (with A. Alcántar), Comm. Algebra 22 (1994), 3037–3052.
  8. On the ideal theory of graphs, (with A. Simis and W. V. Vasconcelos), J. Algebra, 167 (1994), 389–416.
  9. Rees algebras of edge ideals, Comm. Algebra 23 (1995), 3513–3524.
  10. A note on generators of least degree in Gorenstein ideals, (with M. Miller), Proc. Amer. Math. Soc. 124 (1996), 377–382.
  11. Normality of subrings generated by square free monomials, J. Pure & Applied Algebra 113 (1996), 91–106.
  12. Cohen–Macaulay bipartite graphs (with M. Estrada), Arch. Math. 68 (1997), 124–128.
  13. Degree bounds in monomial subrings (with W. Bruns and W. V. Vasconcelos), Illinois J. Math. 41 (1997), 341–353.
  14. The integral closure of subrings associated to graphs (with A. Simis and W. V. Vasconcelos), J. Algebra 199 (1998), 281–289.
  15. Generic Gaussian ideals (with A. Corso and W. Vasconcelos), J. Pure & Applied Algebra 125 (1998), 117-127.
  16. On the equations of the edge cone of a graph and some applications, Manuscripta Math. 97 (1998), 309–317.
  17. Rees algebras of complete bipartite graphs, Mat. Contemp. 16 (1999), 281–289.
  18. The second Betti number of an edge ideal, (with S. Eliahou), Aportaciones Matemáticas, Comunicaciones 25 (1999), 115–119.
  19. A note on affine toric varieties (with E. Reyes and L. Zárate), Linear Algebra Appl. 318 (2000), 173–179.
  20. On the normality of monomial ideals of mixed products (with G. Restuccia), Comm. Algebra 29(8) (2001), 3571–3580.
  21. On systems of binomials in the ideal of a toric variety (with S. Eliahou), Proc. Amer. Math. Soc. 130 (2002), 345–351.
  22. On the normality of Rees algebras associated to totally unimodular matrices (with V. Bonanzinga and C. Escobar), Results Math. 41, 3/4, (2002), 258–264.
  23. Gráficas con una cubierta maximal independiente y cotas para algunos invariantes (con C. Valencia), Morfismos 6(1) (2002), 57–71.
  24. Monomial ideals and the computation of multiplicities (with D. Delfino, A. Taylor, W. V. Vasconcelos and N. Weininger), in Commutative Rings Theory and Applications, Proceedings: Fez (M. Fontana et al., Eds.), Lecture Notes in Pure and Applied Math. 231, Marcel Dekker, New York, 2003, pp. 87–106. Download the PS file
  25. Constraints for the normality of monomial subrings and birationality (with A. Simis), Proc. Amer. Math. Soc. 131 (2003), 2043–2048.
  26. Canonical modules of certain edge subrings (with C. E. Valencia), European J. Combin. 24(5) (2003), 471–487.
  27. Relative volumes and minors in monomial subrings (with C. Escobar and J. Martínez-Bernal), Linear Algebra Appl. 374 (2003), 275–290.
  28. A note on the Rees algebra of a bipartite graph (with I. Gitler and C. E. Valencia), J. Pure & Applied Algebra, 201 (2005), 17-24. Download the PDF file.
  29. Normality of semigroups with some links to graph theory, Discrete Math., 302 (2005), 267-284.
  30. Blowup algebras of ideals of vertex covers of bipartite graphs (with I. Gitler and E. Reyes), Contemp. Math. 376 (2005), 273-279. Download the PS file.
  31. Complete intersections in affine monomial curves (with I. Bermejo, P. Gimenez and E. Reyes), Bol. Soc. Mat. Mexicana (3) 11 (2005), 191-203. Download the PDF file.
  32. Linear syzygies and birational combinatorics (with A. Simis), Results Math. 48 (2005), no. 3-4, 326-343. Download the PDF file.
  33. C. Escobar, R. H. Villarreal and Y. Yoshino, Torsion freeness and normality of blowup rings of monomial ideals, Commutative Algebra, Lect. Notes Pure Appl. Math. 244, Chapman & Hall/CRC, Boca Raton, FL, 2006, pp. 69-84. Download the PS file.
  34. Explicit representations of the edge cone of a graph (with C. E. Valencia), International Journal of Contemporary Mathematical Sciences, Vol. 1, 2006, no. 1-4, 53 - 66. Download the PDF file.
  35. A note on Rees algebras and the MFMC property (with I. Gitler and C. Valencia), Beiträge Algebra Geom. 48 (2007), No. 1, 141-150. Download the PDF file.
  36. Ring graphs and toric ideals, (with I. Gitler and E. Reyes), Electronic Notes in Discrete Mathematics 28C (2007), 393-400.
  37. Unmixed bipartite graphs, Rev. Colombiana Mat. 41(2)(2007), 393-395.
  38. Normalization of monomial ideals and Hilbert functions, Proc. Amer. Math. Soc. 136 (2008), 1933-1943.
  39. Rees algebras and polyhedral cones of ideals of vertex covers of perfect graphs, J. Algebraic Combin. 27(3) (2008), 293-305.
  40. Shellable graphs and sequentially Cohen-Macaulay bipartite graphs (with A. Van Tuyl), J. Combin. Theory Ser. A 115 (2008), no.5, 799-814.
  41. Rees cones and monomial rings of matroids, Linear Algebra Appl. 428 (2008), 2933-2940.
  42. Cohen-Macaulay, Shellable and unmixed clutters with a perfect matching of Koenig type (with S. Morey and E. Reyes), J. Pure Appl. Algebra 212(7) (2008), 1770-1786.
  43. Duality, a-invariants and canonical modules of rings arising from linear optimization problems (with J. P. Brennan and L. A. Dupont), Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 51 (2008), no. 4, 279-305.
  44. Blowup algebras of square-free monomial ideals and some links to combinatorial optimization problems (with I. Gitler and E. Reyes), Rocky Mountain J. Math. 39 (2009), no. 1, 71-102. Download the PDF file.
  45. Cohen-Macaulay admissible clutters (with H. T. Ha and S. Morey), J. Commut. Algebra 1 (2009), no. 3, 463-480. Download the PDF file.
  46. Cohen-Macaulay clutters with combinatorial optimization properties and parallelizations of normal edge ideals (with L. A. Dupont and E. Reyes), Sao Paulo J. Math. Sci. 3 (2009), no. 1, 61-75. Download the PDF file.
  47. Ring graphs and complete intersection toric ideals (with I. Gitler and E. Reyes), Discrete Math. 310 (2010), no. 3, 430-441. Download the PDF file.
  48. Edge ideals of clique clutters of comparability graphs and the normality of monomial ideals (with L. A. Dupont), Math. Scand. 106 (2010), no. 1, 88-98. Download the PDF file.
  49. Ehrhart clutters: regularity and max-flow min-cut (with J. Martinez-Bernal and E. O'Shea), Electron. J. Combin. 17 (2010), no. 1, R52. Download the PDF file.