Investigación

Investigación

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Proyectos en vigor y perfil

  • Investigador Principal del proyecto MTM2014-55367-P: Semigrupos Numéricos y Afines; Generalizaciones y Aplicaciones (histórico, MTM2010-15595: Semigrupos numéricos).

Publicaciones

Tesis

- Semigrupos Afines, Universidad de Granada, 1996, dirigida por José Carlos Rosales (ver en Mathematics Genealogy Project); premio extraordinario por la Universidad de Granada.

Libros

  1. J. C. Rosales y P. A. García-Sánchez, Finitely generated commutative monoids, Nova Science Publishers, Inc., New York, 1999.
  2. J. C. Rosales y P. A. García-Sánchez, Numerical semigroups, Springer, 2009.
  3. A. Assi, P. A. García-Sánchez, Numerical semigroups and applications, RSME Springer series 1, Springer, Switzerland, 2016.

Artículos y capítulos de libros

Los últimos trabajos en los que he participado se pueden consultar en arXiv.
  1. P. A. García-Sánchez, D. Llena, A. Moscariello, Delta sets for symmetric numerical semigroups with embedding dimension three, Aequationes Math. 91 (2017), 579–600.
  2. A. Assi, P. A. García-Sánchez, V. Micale, Bases of subalgebras of K[ [x] ] and K[x], Journal of Symbolic Computation 79(1) (2017), 4–22.
  3. P. A. García-Sánchez, B. A. Heredia, H. İ. Karakaş, J. C. Rosales, Parametrizing Arf numerical semigroups, J. Algebra Appl. Vol. 16, No. 11 (2017) 1750209 (31 pages)
  4. P. A. García-Sánchez, An overview of the computational aspects of nonunique factorization invariants, in Multiplicative Ideal Theory and Factorization Theory - Commutative and Non-Commutative Perspectives, Springer Proceedings in Mathematics & Statistics 170 (2016), Springer.
  5. A. Ciolan, P. A. García-Sánchez, P. Moree, Cyclotomic numerical semigroups, SIAM Journal on Discrete Mathematics 30 (2016), no. 2, 650-668.
  6. M. Delgado, and P. A. García-Sánchez, numericalsgps, a GAP package for numerical semigroups, ACM Communications in Computer Algebra 50 (2016), 12–14.
  7. M. Delgado, P. A. García-Sánchez, and A. M. Robles-Pérez, Numerical semigroups with a given set of pseudo-Frobenius numbers, LMS J. Comput. Math. 19(1) (2016), 186–205.
  8. A. Assi, P. A. García-Sánchez, Algorithms for curves with one place at infinity, Journal of Symbolic Computation 74 (2016), 475-492.
  9. S. T. Chapman, P. A. García-Sánchez, Z. Tripp, C. Viola, Measuring primality in numerical semigroups with embedding dimension three, Journal of Algebra and its Applications 15 (2016) 1650007 (16 pages).
  10. A. Assi, P. A. García-Sánchez, I. Ojeda, Frobenius vectors, Hilbert series and Gluings of Affine Semigroups, J. Commutative Algebra 7 (2015), 317 -335.
  11. F. Aguiló-Gost, P. A. García-Sánchez, D. Llena, On the number of L-shapes in embedding dimension four numerical semigroups, Discrete Math. 338 (2015),2168–2178.
  12. J. I. Farrán, P. A. García-Sánchez, The second Feng-Rao number for codes coming from inductive semigroups, IEEE Transactions on Information Theory 61 (2015), 4938–4947.
  13. P. A. García-Sánchez, C. Viola, When the catenary degree agrees with the tame degree in numerical semigroups of embedding dimension three, Involve, a Journal of Mathematics 8:4 (2015), 677–694.
  14. F. Aguiló-Gost, P. A. García-Sánchez, D. Llena, Denumerants of 3-numerical semigroups, Electron. Notes Discrete Math. 46C (2014), 3-10.
  15. F. Aguiló-Gost, P. A. García-Sánchez, D. Llena, An algorithm to compute the primitive elements of an embedding dimension three numerical semigroup, Electron. Notes Discrete Math. 46C (2014), 185–192.
  16. M. Delgado, J. I. Farrán, P. A. García-Sánchez, D. Llena, On the weight hierarchy of codes coming from semigroups with two generators, IEEE Trans Inf Theory, 60 (2014), 282-29.
  17. S. Abdelnaby, P. A. García-Sánchez, Homogenization of a nonsymmetric embedding-dimension-three numerical semigroup, Involve 7:1 (2014), 77–96.
  18. J. C. Rosales, P. A. García-Sánchez, Constructing almost symmetric numerical semigroups from almost irreducible numerical semigroups, Comm. Algebra. 42 (2014), 1362–1367.
  19. M. Bras-Amorós, P. A. García-Sánchez, A. Vico-Oton, Nonhomogeneous patterns on numerical semigroups, Internat. J. Algebra Comput. 23 (2013), 1469–1483
  20. P. A. García-Sánchez, M. J. Leamer, Huneke-Wiegand Conjecture for complete intersection numerical semigroup rings, J. Algebra 391 (2013), 114– 124
  21. A. Assi, P. A. García-Sánchez, Constructing the set of complete intersection numerical semigroups with a given Frobenius number, Applicable Algebra in Engineering, Communication and Computing, Volume 24, Issue 2 (2013), 133– 148
  22. M. Delgado, J. I. Farrán, P. A. García-Sánchez, D. Llena, On the generalized Feng-Rao numbers of numerical semigroups generated by intervals, Math. Comput.82 (2013), 1813–1836
  23. P. A. García-Sánchez, I. Ojeda, A. Sánchez-R.-Navarro , Factorization invariants in half-factorial affine semigroups, Internat. J. Algebra Comput. 23 (2013), 111-122.
  24. P. A. García-Sánchez, I. Ojeda, J. C. Rosales, Affine semigroups having a unique Betti element, J. Algebra Appl. 12 (2013), 1250177 (11 pages)
  25. M. Delgado, P. A. García-Sánchez and J. C. Rosales, Numerical semigroups problem list, CIM Bulletin 33 (2013), 15–26.
  26. S. T. Chapman, P. A. García-Sánchez, D. Llena, A. Malyshev, D. Steinberg, On the Delta set and the Betti elements of a BF-monoid, Arab J Math 1 (2012) 53--61.
  27. MR2948680 Bullejos, M.; García-Sánchez, Pedro A. Minimal presentations for monoids with the ascending chain condition on principal ideals, Semigroup Forum 85 (2012), 185--190.
  28. V. Blanco, P. A. García-Sánchez, A. Geroldinger, Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids, Illinois J. Math. Volume 55, Number 4, (2011), 1385-1414.
  29. MR2863434 Blanco, Víctor; García-Sánchez, Pedro A.; Puerto, Justo Counting numerical semigroups with short generating functions. Internat. J. Algebra Comput. 21 (2011), no. 7, 1217--1235.
  30. MR2797486 Chapman, S. T.; García-Sánchez, P. A.; Llena, D.; Marshall, J. Elements in a numerical semigroup with factorizations of the same length. Canad. Math. Bull. 54 (2011), no. 1, 39--43
  31. MR2729387 (2011j:11050) Aguiló-Gost, F.; García-Sánchez, P. A. Factoring in embedding dimension three numerical semigroups. Electron. J. Combin. 17 (2010), no. 1, Research Paper 138, 21 pp.
  32. García-Sánchez,P.A. Non-Unique Factorizations (by Alfred Geroldinger and Franz Halter-Koch, Chapman & Hall/CRC, Boca Raton, FL, 2006. xxii + 700 pages ISBN: 978-1-58488-576-4; 1-58488-576-9), Semigroup Forum (2010) 80, 346--350.
  33. MR2494887 Chapman, S. T.; García-Sánchez, P. A.; Llena, D. The catenary and tame degree of numerical monoids. Forum Math. 21 (2009), no. 1, 117--129.
  34. MR2447995 (2009g:20125) García-Sánchez, P. A.; Llena, D.; Rosales, J. C. Strongly taut finitely generated monoids. Monatsh. Math. 155 (2008), no. 2, 119--124.
  35. MR2440290 (2009g:20126) Rosales, J. C.; García-Sánchez, P. A. Every numerical semigroup is one half of infinitely many symmetric numerical semigroups. Comm. Algebra 36 (2008), no. 8, 2910--2916.
  36. MR2395197 Delgado, M.; García-Sánchez, P. A.; Rosales, J. C.; Urbano-Blanco, J. M. Systems of proportionally modular Diophantine inequalities. Semigroup Forum 76 (2008), no. 3, 469--488.
  37. MR2389850 Rosales, J. C.; García-Sánchez, P. A.; Urbano-Blanco, J. M. The set of solutions of a proportionally modular Diophantine inequality. J. Number Theory 128 (2008), no. 3, 453--467.
  38. MR2358486 Rosales, J. C.; García-Sánchez, P. A. Every numerical semigroup is one half of a symmetric numerical semigroup. Proc. Amer. Math. Soc. 136 (2008), no. 2, 475--477.
  39. MR2384746 Rosales, J. C.; García-Sánchez, P. A. Numerical semigroups having a Toms decomposition. Canad. Math. Bull. 51 (2008), no. 1, 134--139.
  40. MR2387740 Rosales, J. C.; García-Sánchez, P. A.; García-García, J. I.; Branco, M. B. Numerical semigroups with maximal embedding dimension [ MR2056070]. Focus on commutative rings research, 47--53, Nova Sci. Publ., New York, 2006.
  41. MR2254337 Chapman, S. T. ; García-Sánchez, P. A. ; Llena, D. ; Rosales, J. C. Presentations of finitely generated cancellative commutative monoids and nonnegative solutions of systems of linear equations. Discrete Appl. Math. 154 (2006), no. 14, 1947--1959.
  42. MR224356 Chapman, S. T. ; García-Sánchez, P. A. ; Llena, D. ; Ponomarenko, V. ; Rosales, J. C. The catenary and tame degree in finitely generated commutative cancellative monoids. Manuscripta Math. 120 (2006), no. 3, 253--264.
  43. MR2214415 (2007b:20129) Bras-Amorós, Maria ; García-Sánchez, Pedro A. Patterns on numerical semigroups. Linear Algebra Appl. 414 (2006), no. 2-3, 652--669.
  44. MR2246255 Rosales, J. C. ; García-Sánchez, P. A. ; Urbano-Blanco, J. M. Correction to: “Modular Diophantine inequalities and numerical semigroups” [Pacific J. Math. 218 (2005), no. 2, 379--398; MR2218353]. Pacific J. Math. 220 (2005), no. 1, 199.
  45. MR2218353 (2007a:20056) Rosales, J. C. ; García-Sánchez, P. A. ; Urbano-Blanco, J. M. Modular Diophantine inequalities and numerical semigroups. Pacific J. Math. 218 (2005), no. 2, 379--398.
  46. MR2158509 (2006e:20104) Rosales, J. C. ; García-Sánchez, P. A. Pseudo-symmetric numerical semigroups with three generators. J. Algebra 291 (2005), no. 1, 46--54.
  47. MR2153099 (2006d:20106) Rosales, J. C. ; García-Sánchez, P. A. ; García-García, J. I. ; Branco, M. B. Numerical semigroups with a monotonic Apéry set. Czechoslovak Math. J. 55(130) (2005), no. 3, 755--772.
  48. MR2140699 (2006a:20109) Rosales, J. C. ; García-Sánchez, Pedro A. ; García-García, Juan I. $k$-factorized elements in telescopic numerical semigroups. Arithmetical properties of commutative rings and monoids, 260--271, Lect. Notes Pure Appl. Math., 241, Chapman & Hall/CRC, Boca Raton, FL, 2005.
  49. García-Sánchez, P. A. Commutative Semigroups by P. A. Grillet Kluwer Academic Publishers, Dordrecht, 2001. xiv+436 pp. ISBN: 0-7923-7067-8. Semigroup Forum 69 (2004), 155-158.
  50. MR2105325 (2005i:20093) Rosales, J. C. ; García-Sánchez, P. A. Numerical semigroups with embedding dimension three. Arch. Math. (Basel) 83 (2004), no. 6, 488--496.
  51. MR2101389 (2005h:20139) García-Sánchez, Pedro A. ; Rosales, José C. Every positive integer is the Frobenius number of an irreducible numerical semigroup with at most four generators. Ark. Mat. 42 (2004), no. 2, 301--306.
  52. MR2096056 (2005j:20077) Rosales, J. C. ; García-Sánchez, P. A. ; García-García, J. I. ; Jiménez Madrid, J. A. Fundamental gaps in numerical semigroups with respect to their multiplicity. Acta Math. Sin. (Engl. Ser.) 20 (2004), no. 4, 629--646.
  53. MR2084905 (2005e:20090) Rosales, J. C. ; García-Sánchez, P. A. ; García-García, J. I. ; Branco, M. B. Saturated numerical semigroups. Houston J. Math. 30 (2004), no. 2, 321--330 (electronic).
  54. MR2054385 (2005b:20119) Rosales, J. C. ; García-Sánchez, P. A. ; García-García, J. I. ; Branco, M. B. Arf numerical semigroups. J. Algebra 276 (2004), no. 1, 3--12.
  55. MR2038577 (2004j:20116) Rosales, J. C. ; García-Sánchez, P. A. ; García-García, J. I. ; Jiménez Madrid, J. A. Fundamental gaps in numerical semigroups. J. Pure Appl. Algebra 189 (2004), no. 1-3, 301--313.
  56. MR2032333 (2004j:20117) Rosales, J. C. ; García-Sánchez, P. A. ; García-García, J. I. Every positive integer is the Frobenius number of a numerical semigroup with three generators. Math. Scand. 94 (2004), no. 1, 5--12.
  57. MR2027609 (2004m:20114) Rosales, J. C. ; García-Sánchez, P. A. ; García-García, J. I. Atomic commutative monoids and their elasticity. Semigroup Forum 68 (2004), no. 1, 64--86.
  58. MR2056070 Rosales, J. C. ; García-Sánchez, P. A. ; García-García, J. I. ; Branco, M. B. Numerical semigroups with maximal embedding dimension. Int. J. Commut. Rings 2 (2003), no. 1, 47--53.
  59. MR2020273 (2004k:20127) Rosales, J. C. ; García-Sánchez, P. A. ; García-García, J. I. ; Urbano-Blanco, J. M. Proportionally modular Diophantine inequalities. J. Number Theory 103 (2003), no. 2, 281--294.
  60. MR1978528 (2004b:20092) Rosales, J. C. ; García-Sánchez, P. A. ; García-García, J. I. ; Jiménez Madrid, J. A. The oversemigroups of a numerical semigroup. Semigroup Forum 67 (2003), no. 1, 145--158.
  61. MR1953505 (2003i:20106) Rosales, J. C. ; García-Sánchez, P. A. ; García-García, J. I. Ideals of finitely generated commutative monoids. Semigroup Forum 66 (2003), no. 2, 305--322.
  62. MR1942633 (2003i:11141) Chapman, S. T. ; García-García, J. I. ; García-Sánchez, P. A. ; Rosales, J. C. On the number of factorizations of an element in an atomic monoid. Adv. in Appl. Math. 29 (2002), no. 3, 438--453.
  63. MR1935569 (2004b:20090) Rosales, J. C. ; García-Sánchez, P. A. ; García-García, J. I. Presentations of finitely generated submonoids of finitely generated commutative monoids. Internat. J. Algebra Comput. 12 (2002), no. 5, 659--670.
  64. MR1895736 (2003b:20088) Rosales, J. C. ; García-Sánchez, P. A. ; García-García, J. I. ; Branco, M. B. Systems of inequalities and numerical semigroups. J. London Math. Soc. (2) 65 (2002), no. 3, 611--623.
  65. MR1887768 (2003c:13015) García-Sánchez, P. A. ; Rosales, J. C. On Buchsbaum simplicial affine semigroups. Pacific J. Math. 202 (2002), no. 2, 329--339.
  66. MR1895621 (2003b:20087) Rosales, J. C. ; García-Sánchez, P. A. Minimal presentations of full subsemigroups of $\bold N\sp 2$. Rocky Mountain J. Math. 31 (2001), no. 4, 1417--1422.
  67. MR1855399 (2002j:20107) Chapman, S. T. ; García-García, J. I. ; García-Sánchez, P. A. ; Rosales, J. C. Computing the elasticity of a Krull monoid. Linear Algebra Appl. 336 (2001), 191--200.
  68. MR1831513 Rosales, J. C. ; García-Sánchez, P. A. ; García-García, J. I. Commutative ideal extensions of abelian groups. Semigroup Forum 62 (2001), no. 2, 311--316.
  69. MR1822195 (2002a:20071) Rosales, J. C. ; García-Sánchez, P. A. ; García-García, J. I. Irreducible ideals of finitely generated commutative monoids. J. Algebra 238 (2001), no. 1, 328--344.
  70. R. L. Torres-Roldán, A. García-Casco y P. A. García-Sánchez, CSpace: An integrated workplace for the graphical and algebraic analysis of phase assemblages on 32-bit Wintel platform,. Computers and Geosciences, 26 (2000), 779-793.
  71. MR1805131 Rosales, José Carlos ; García-Sánchez, Pedro A. ; García-García, Juan Ignacio . How to check if a finitely generated commutative monoid is a principal ideal commutative monoid. Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (St. Andrews), 288--291 (electronic), ACM, New York, 2000.
  72. MR1800090 (2001j:20101) Rosales, J. C. ; García-Sánchez, P. A. On the structure of simplicial affine semigroups. Proc. Roy. Soc. Edinburgh Sect. A 130 (2000), no. 5, 1017--1028.
  73. MR1769997 (2001c:20130) Rosales, J. C. ; García-Sánchez, P. A. Reduced commutative monoids with two Archimedean components. Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 3 (2000), no. 2, 471--484
  74. MR1762770 (2001e:20057) Rosales, J. C. ; García-Sánchez, P. A. On full affine semigroups. J. Pure Appl. Algebra 149 (2000), no. 3, 295--303.
  75. MR1729450 (2000h:20103) Rosales, J. C. ; García-Sánchez, P. A. Presentations for subsemigroups of finitely generated commutative semigroups. Israel J. Math. 113 (1999), 269--283.
  76. MR1719711 (2000h:20102) Rosales, J. C. ; García-Sánchez, P. A. ; Urbano-Blanco, J. M. On presentations of commutative monoids. Internat. J. Algebra Comput. 9 (1999), no. 5, 539--553.
  77. MR1725463 (2000i:20095) García-Sánchez, P. A. ; Rosales, J. C. Numerical semigroups generated by intervals. Pacific J. Math. 191 (1999), no. 1, 75--83.
  78. MR1678508 (2000j:13020) Rosales, J. C. ; García-Sánchez, P. A. On free affine semigroups. Semigroup Forum 58 (1999), no. 3, 367--385.
  79. MR1671926 (2000a:20131) Rosales, J. C. ; García-Sánchez, P. A. On the structure of Cohen-Macaulay simplicial affine semigroups. Comm. Algebra 27 (1999), no. 2, 511--518.
  80. MR1661222 (99m:20144) Rosales, J. C. ; García-Sánchez, P. A. On normal affine semigroups. Linear Algebra Appl. 286 (1999), no. 1-3, 175--186.
  81. MR1697587 (2000e:20107) Rosales, J. C. ; García-Sánchez, Pedro A. On Cohen-Macaulay and Gorenstein simplicial affine semigroups. Proc. Edinburgh Math. Soc. (2) 41 (1998), no. 3, 517--537.
  82. MR1627892 (99g:13032) Rosales, J. C. ; García-Sánchez, P. A. ; Urbano-Blanco, J. M. On Cohen-Macaulay subsemigroups of $\bold N\sp 2$. Comm. Algebra 26 (1998), no. 8, 2543--2558.
  83. MR1622807 (99g:20108) Rosales, J. C. ; García-Sánchez, P. A. On numerical semigroups with high embedding dimension. J. Algebra 203 (1998), no. 2, 567--578.
  84. MR1484089 (99c:11027) Rosales, J. C. ; García-Sánchez, Pedro A. Nonnegative elements of subgroups of $Z\sp n$. Linear Algebra Appl. 270 (1998), 351--357.
  85. MR1363611 (96m:14068) Rosales, J. C. ; García-Sánchez, Pedro A. On complete intersection affine semigroups. Comm. Algebra 23 (1995), no. 14, 5395--5412.
  86. García Sánchez, P. A. Gröbner and Involutive bases for zero-dimensional ideals, ACM SIGSAM Bulletin 29(2) (1995), 12-15.

Comité editorial

Editor asociado de Le Matematiche.

Paquetes

Paquete numericalsgps para GAP, que mantengo junto con M. Delgado. La versión de desarrollo se aloja en GitHub.

Algunas contribuciones en GitHub.