Publications

Publications listed at MathSciNet.
http://www.ams.org/mathscinet/search/publications.html?pg1=INDI&s1=1785…

Preprints posted at the arXiv.
http://arxiv.org/a/villarreal_r_1

Google Scholar Citations.
http://scholar.google.com/citations?user=_jQO02kAAAAJ&hl=en

ORCID ID
http://orcid.org/0000-0001-9473-765X

BOOKS:

  1. Monomial Algebras, Second Edition, Monographs and Research Notes in Mathematics, Chapman and Hall/CRC, 2015.
  2. Graphs, Rings and Polyhedra, (with I. Gitler), Aportaciones Mat. Textos, 35, Soc. Mat. Mexicana, Mexico, 2011. ISBN: 978-607-02-1630-5. Book
  3. Monomial Algebras, Monographs and Textbooks in Pure and Applied Mathematics 238, Marcel Dekker, Inc., New York, 2001. Book

BOOK CHAPTERS:

  1. Symbolic powers of monomial ideals and Cohen-Macaulay vertex-weighted digraphs (with P. Gimenez, J. Martinez-Bernal, A. Simis and C. E. Vivares), in Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics (G. M. Greuel, et.al. Eds), Springer, Cham, pp. 491-510, 2018.
  2. Edge ideals: algebraic and combinatorial properties (with S. Morey), in Progress in Commutative Algebra, Combinatorics and Homology, Vol. 1 (C. Francisco, L. C. Klingler, S. Sather-Wagstaff and J. C. Vassilev, Eds.), De Gruyter, Berlin, 2012, pp. 85-126. Book Chapters
  3. Monomial Algebras and Polyhedral Geometry, in Handbook of Algebra, Vol. 3 (M. Hazewinkel Ed.), Elsevier, Amsterdam, 2003, pp. 257–314. Book Chapters

PAPERS:

  1. 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).
  2. Induced matchings and the v-number of graded ideals, (with G. Grisalde and E. Reyes), Mathematics 9 (2021), no. 22, Article number 2860.
  3. Unmixed and Cohen-Macaulay weighted oriented Konig graphs, (with Y. Pitones and E. Reyes), Studia Sci. Math. Hungar. 58 (2021), no. 3, 276-292.
  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. The dual of an evaluation code, (with H. H. López and I. Soprunov), Des. Codes Cryptogr. 89 (2021), no. 7, 1367-1403.
  6. The v-number of edge ideals, (with D. Jaramillo), J. Combin. Theory Ser. A 177 (2021), 105310.
  7. Evaluation codes and their basic parameters (with D. Jaramillo and M. Vaz Pinto), Des. Codes Cryptogr. 89 (2021), no. 2, 269-300.
  8. Joins, Ears and Castelnuovo-Mumford regularity, (with J. Neves and M. Vaz Pinto), J. Algebra 560 (2020), 67-88.
  9. Linear codes over signed graphs, (with M. A. Valencia-Bucio and J. Martinez-Bernal), Des. Codes Cryptogr. 88 (2020), 273-296.
  10. 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.
  11. 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 28(1) (2020), 205-217.
  12. 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.
  13. Regularity of the vanishing ideal over a parallel composition of paths (with A. Macchia, J. Neves and M. Vaz Pinto), J. Commut. Algebra 12 (2020), no. 3, 391-407.
  14. The dual of a constacyclic code, self dual, reversible constacyclic codes and constacyclic codes with complementary duals over finite local Frobenius non-chain rings with nilpotency index 3 (with C. A. Castillo-Guillen, C. Renteria, E. Sarmiento and H. Tapia-Recillas), Discrete Math. 342 (2019), no. 8, 2283-2296.
  15. Edge ideals of oriented graphs (with H. T. Ha, K.-N. Lin, S. Morey, E. Reyes and R. H. Villarreal), Internat. J. Algebra Comput. 29 (2019), no. 3, 535-559.
  16. Depth and regularity of monomial ideals via polarization and combinatorial optimization (with J. Martinez-Bernal, S. Morey and C. E. Vivares), Acta Math. Vietnam. 44 (2019), no. 1, 243-268.
  17. Vanishing ideals over finite fields (with A. Tochimani), Math. Notes 105 (2019), no. 3, 429-438.
  18. Indices of normalization of ideals (with C. Polini, B. Ulrich and W. V. Vasconcelos), J. Pure Appl. Algebra 223 (2019), no. 9, 3681-3694.
  19. Generalized minimum distance functions (with M. Gonzalez-Sarabia, J. Martinez-Bernal and C. E. Vivares), J. Algebraic Combin. 50 (2019), no. 3, 317-346.
  20. Complete intersection vanishing ideals on sets of clutter type over finite fields (with A. Tochimani), Bull. Malays. Math. Sci. Soc. 41 (2018), no. 1, 81-89.
  21. Footprint and minimum distance functions (with L. Nuñez-Betancourt and Y. Pitones), Commun. Korean Math. Soc. 33 (2018), no. 1, 85-101.
  22. The second generalized Hamming weight of some evaluation codes arising from a projective torus (with M. González-Sarabia, E. Camps and E. Sarmiento), Finite Fields Appl. 52 (2018), 370-394.
  23. Minimum distance functions of graded ideals and Reed-Muller-type codes (with J. Martinez-Bernal and Y. Pitones), J. Pure Appl. Algebra 221 (2017), 251-275.
  24. On complete monomial ideals (with P. Gimenez, A. Simis and W. V. Vasconcelos), J. Commut. Algebra 8 (2016), no. 2, 207-226.
  25. Direct products in projective Segre codes (with A. Tochimani and M. Vaz Pinto), Finite Fields Appl. 39 (2016), 96-110.
  26. Binomial vanishing ideals (with A. Tochimani), J. Algebra Comb. Discrete Struct. Appl. 2 (2015), no. 2, 151-156.
  27. Vanishing ideals over graphs and even cycles (with J. Neves and M. Vaz Pinto), Comm. Algebra 43 (2015), no. 3, 1050-1075.
  28. Regularity and algebraic properties of certain lattice ideals (with J. Neves and M. Vaz Pinto), Bull. Braz. Math. Soc. (N.S.) 45 (2014), no. 4, 1-30.
  29. Computing the degree of a lattice ideal of dimension one (with H. H. Lopez), J. Symbolic Comput. 65 (2014), 15-28.
  30. Degree and algebraic properties of lattice and matrix ideals (with L. O'Carroll and F. Planas-Vilanova), SIAM J. Discrete Math. 28 (2014), no. 1, 394-427.
  31. Affine cartesian codes (H. H. Lopez and C. Renteria), Des. Codes Cryptogr. 71 (2014), no. 1, 5-19.
  32. The degree and regularity of vanishing ideals of algebraic toric sets over finite fields (with M. Vaz Pinto), Comm. Algebra 41 (2013), no. 9, 3376-3396. Abstract
  33. Complete intersections in binomial and lattice ideals (with H. H. Lopez), Internat. J. Algebra Comput. 23 (2013), no. 6, 1419-1429. Abstract
  34. Complete intersection vanishing ideals on degenerate tori over finite fields (with H. H. Lopez and L. Zarate), Arab. J. Math. (Springer) 2 (2013), no. 2, 189-197. Abstract
  35. Parameterized affine codes (with H. H. Lopez, E. Sarmiento, M. Vaz Pinto), Studia Sci. Math. Hungar. 49 (2012), no. 3, 406-418. Abstract
  36. Associated primes of powers of edge ideals (with Martinez-Bernal and S. Morey), Collect. Math. 63 (2012), no. 3, 361--374. Abstract
  37. On the vanishing ideal of an algebraic toric set and its parameterized linear codes (with E. Sarmiento and M. Vaz Pinto), J. Algebra Appl. 11 (2012), no. 4, 1250072 (16 pages). Abstract
  38. Toric ideals generated by circuits (with J. Martinez-Bernal), Algebra Colloq. 19 (2012), no. 4, 665-672.
  39. Combinatorics of Cremona monomial maps (with A. Simis), Math. Comp. 81 (2012), no. 279, 1857-1867.
  40. Métodos algebraicos para códigos parametrizados por monomios (con E. Sarmiento, C. Renteria, A. Simis y M. Vaz Pinto), EMALCA 2010, Revista de Ciencias Basicas UJAT 9 (2011), no. 2, 17-28. Download PDF
  41. Algebra conmutativa y codigos evaluacion (with C. Renteria), Aportaciones Matematicas, Comunicaciones 42 (2011), 171-184.
  42. The minimum distance of parameterized codes on projective tori (with E. Sarmiento and M. Vaz Pinto), Appl. Algebra Engrg. Comm. Comput. 22 (2011), no. 4, 249-264.
  43. Combinatorics of symbolic Rees algebras of edge ideals of clutters (with J. Martinez-Bernal, C. Renteria), Contemp. Math. 555 (2011), 151-164.
  44. Algebraic and combinatorial properties of ideals and algebras of uniform clutters of TDI systems (with L. A. Dupont), J. Comb. Optim. 21 (2011), no. 3, 269-292.
  45. Algebraic methods for parameterized codes and invariants of vanishing ideals over finite fields (with C. Renteria and A. Simis), Finite Fields Appl. 17 (2011), no. 1, 81-104.
  46. Symbolic Rees algebras, vertex covers and irreducible representations of Rees cones (with L. A. Dupont), Algebra Discrete Math. 10 (2010), no. 2, 64-86.
  47. Systems with the integer rounding property in normal monomial subrings (with C. Renteria and L. A. Dupont), An. Acad. Brasil. Cienc 82 (2010), no. 4, 801-811.
  48. 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.
  49. 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.
  50. 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.
  51. 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.
  52. Cohen-Macaulay admissible clutters (with H. T. Ha and S. Morey), J. Commut. Algebra 1 (2009), no. 3, 463-480. Download the PDF file.
  53. 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.
  54. 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.
  55. 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.
  56. Rees cones and monomial rings of matroids, Linear Algebra Appl. 428 (2008), 2933-2940.
  57. Shellable graphs and sequentially Cohen-Macaulay bipartite graphs (with A. Van Tuyl), J. Combin. Theory Ser. A 115 (2008), no.5, 799-814.
  58. Rees algebras and polyhedral cones of ideals of vertex covers of perfect graphs, J. Algebraic Combin. 27(3) (2008), 293-305.
  59. Normalization of monomial ideals and Hilbert functions, Proc. Amer. Math. Soc. 136 (2008), 1933-1943.
  60. Unmixed bipartite graphs, Rev. Colombiana Mat. 41(2)(2007), 393-395.
  61. Ring graphs and toric ideals, (with I. Gitler and E. Reyes), Electronic Notes in Discrete Mathematics 28C (2007), 393-400.
  62. 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.
  63. 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.
  64. 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.
  65. Linear syzygies and birational combinatorics (with A. Simis), Results Math. 48 (2005), no. 3-4, 326-343. Download the PDF file.
  66. 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.
  67. 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.
  68. Normality of semigroups with some links to graph theory, Discrete Math., 302 (2005), 267-284.
  69. 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.
  70. Relative volumes and minors in monomial subrings (with C. Escobar and J. Martínez-Bernal), Linear Algebra Appl. 374 (2003), 275–290.
  71. Canonical modules of certain edge subrings (with C. E. Valencia), European J. Combin. 24(5) (2003), 471–487.
  72. Constraints for the normality of monomial subrings and birationality (with A. Simis), Proc. Amer. Math. Soc. 131 (2003), 2043–2048.
  73. 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
  74. Gráficas con una cubierta maximal independiente y cotas para algunos invariantes (con C. Valencia), Morfismos 6(1) (2002), 57–71.
  75. 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.
  76. On systems of binomials in the ideal of a toric variety (with S. Eliahou), Proc. Amer. Math. Soc. 130 (2002), 345–351.
  77. On the normality of monomial ideals of mixed products (with G. Restuccia), Comm. Algebra 29(8) (2001), 3571–3580.
  78. A note on affine toric varieties (with E. Reyes and L. Zárate), Linear Algebra Appl. 318 (2000), 173–179.
  79. The second Betti number of an edge ideal, (with S. Eliahou), Aportaciones Matemáticas, Comunicaciones 25 (1999), 115–119.
  80. Rees algebras of complete bipartite graphs, Mat. Contemp. 16 (1999), 281–289.
  81. On the equations of the edge cone of a graph and some applications, Manuscripta Math. 97 (1998), 309–317.
  82. Generic Gaussian ideals (with A. Corso and W. Vasconcelos), J. Pure & Applied Algebra 125 (1998), 117-127.
  83. The integral closure of subrings associated to graphs (with A. Simis and W. V. Vasconcelos), J. Algebra 199 (1998), 281–289.
  84. Degree bounds in monomial subrings (with W. Bruns and W. V. Vasconcelos), Illinois J. Math. 41 (1997), 341–353.
  85. Cohen–Macaulay bipartite graphs (with M. Estrada), Arch. Math. 68 (1997), 124–128.
  86. Normality of subrings generated by square free monomials, J. Pure & Applied Algebra 113 (1996), 91–106.
  87. A note on generators of least degree in Gorenstein ideals, (with M. Miller), Proc. Amer. Math. Soc. 124 (1996), 377–382.
  88. Rees algebras of edge ideals, Comm. Algebra 23 (1995), 3513–3524.
  89. On the ideal theory of graphs, (with A. Simis and W. V. Vasconcelos), J. Algebra, 167 (1994), 389–416.
  90. Critical binomials of monomial curves, (with A. Alcántar), Comm. Algebra 22 (1994), 3037–3052.
  91. Monomial algebras, Aportaciones Matemáticas, Investigación 6 (1992), 69–75.
  92. Koszul homology of Cohen–Macaulay rings with linear resolutions, (with C. Rentería), Proc. Amer. Math. Soc. 115 (1992), 51–58.
  93. Cohen–Macaulay graphs, Manuscripta Math. 66 (1990), 277–293.
  94. Rees algebras and Koszul homology, J. Algebra 119 (1988), 83–104.
  95. On Gorenstein ideals of codimension four, (with W. V. Vasconcelos), Proc. Amer. Math. Soc. 98 (1986), 205–210.
  96. Ideals with sliding depth, (with J. Herzog and W. V. Vasconcelos), Nagoya Math. J. 99 (1985), 159–172.

Computer Programs

NORMALIZ is my favorite computer program. It was written by Winfried Bruns and Robert Koch. This program computes integral closures of affine semigroups, monomial ideals, and Rees algebras.