Research

Main research interests: Computational Commutative Algebra, Semigroup Theory and applications. 

Master Tesis: "Caracterización de ideales iniciales y demostración automática de teoremas geométricos"

Ph. D. Tesis: "Álgebra de Semigrupos y Aplicaciones"

Participation in research groups:

• Lead researcher of the Project "Monoides y semigrupos afines (ProyExcel_00868)".

• Researcher of the Project PID2022-138906NB-C21 lead by Prof. Diego Ruano Benito (IMUVA). 

• Research group "Semigrupos conmutativos", granted by Plan Andaluz de Investigación (Junta de Andalucía), grant FQM 343. Lead researcher of the group: José Carlos Rosales.

• Member of SINGACOM reseach Group.

• Member of INDESS (Instituto Universitario para el Desarrollo Social Sostenible de la Universidad de Cádiz).

Publications

Publications listed in arXiv, MathSciNet, Orcid, Scholar Google, Scopus, Zentralblatt MATH.

Reviews in MathSciNet.

Papers

• • Vigneron-Tenorio, A. Semigroup ideals and linear diophantine equations. Linear Algebra and its Applications 295, no. 1-3,133--144 (1999). (ISSN: 0024-3795)

  • Pisón-Casares, P.; Vigneron-Tenorio, A. First syzygies of toric varieties and diophantine equations in congruence. Communications in Algebra 29, nº 4, 1445--1466 (2001). (ISSN: 0092-7872)

  • Briales-Morales, E.; Pisón-Casares, P.; Vigneron-Tenorio, A. The regularity of a toric variety. Journal of Algebra 237, nº 1, 165--185 (2001). (ISSN: 0021-8693)

  • Briales, E.; Campillo, A.; Pisón, P.; Vigneron, A. Simplicial complexes and syzygies of lattice ideals. Symbolic computation: solving equations in algebra, geometry, and engineering (South Hadley, MA, 2000), 169--183, Contemp. Math., 286, Amer. Math. Soc., Providence, RI, 2001. (ISBN 0-8218-2679-4)

  • García-Ramos, J. A.; Ramos-González, C.; Vigneron-Tenorio, A. El Teorema de Fermat y los modelos de urnas. Epsilon 51, 567--578 (2001). (ISSN: 1131-9321)

  • Briales, E.; Campillo, A.; Pisón, P.; Vigneron, A. Minimal resolutions of lattice ideals and integer linear programming. Revista Matemática Iberoamericana 19 (2), 287--306 (2003). (ISSN: 0213-2230)

  • Pisón-Casares, P.; Vigneron-Tenorio, A. N-solution to linear systems over Z. Linear Algebra and its Applications, 384, 135--154 (2004). (ISSN: 0024-3795)

  • Pisón-Casares, P.; Vigneron-Tenorio, A. On Lawrence semigroups. Journal of Symbolic Computation 4 (11), 804--810 (2008). (ISSN: 0747-7171)

  • Ojeda, I.; Vigneron-Tenorio, A. Simplicial complexes and minimal free resolution of monomial algebras. Journal of Pure and Applied Algebra 214, 850--861 (2010). (ISSN: 0022-4049). arXiv:0810.4836 [math.AC]

  • Ojeda, I.; Vigneron-Tenorio, A. Indispensable binomials in semigroup ideals. Proceedings of the American Mathematical Society 138, 4205--4216 (2010). (ISSN: 0002-9939). arXiv:0903.1030 [math.AC]

  • García-García, J. I.; Moreno-Frías, M.A.; Vigneron-Tenorio, A. On the decomposable semigroups and applications. Journal of Symbolic Computation 58, 103--116 (2013). https://doi.org/10.1016/j.jsc.2013.05.009. (ISSN: 0747-7171). arXiv:1006.2557 [math.AC]

  • García-García, J. I.; Moreno-Frías, M. A.; Sánchez-R.-Navarro, A.; Vigneron-Tenorio, A. Affine convex body semigroups. Semigroup Forum 87 (2), 331-350 (2013). https://doi.org/10.1007/s00233-012-9460-9. (ISSN: 0037-1912). arXiv:1203.2129 [math.AC]

  • García-García, J. I.; Moreno-Frías, M. A.; Vigneron-Tenorio, A. Combinatorial properties and characterization of glued semigroups. Abstract and Applied Analysis vol. 2014, 1--8 (2014). http://dx.doi.org/10.1155/2014/436417. (ISSN: 1085-3375). arXiv:1104.2835 [math.AC]

  • García-García, J. I.;  Vigneron-Tenorio, A. Computing families of Cohen-Macaulay and Gorenstein rings. Semigroup Forum 88, no. 3, 610–620 (2014). https://doi.org/10.1007/s00233-013-9556-x. (ISSN: 0037-1912). arXiv:1304.5089 [math.AC]

  • García-García, J. I.; Moreno-Frías, M. A.; Vigneron-Tenorio, A. Computation of the w-primality and asymptotic w-primality with applications to numerical semigroups. Israel Journal of Mathematics 206, no. 1, 395–-411 (2015). https://doi.org/10.1007/s11856-014-1144-6. (ISSN: 0021-2172)  arXiv:1307.5807 [math.AC]

  • García-García, J. I.; Moreno-Frías, M. A.; Vigneron-Tenorio, A. Computation of Delta sets of numerical monoids. Monatshefte für Mathematik. Volume 178, Issue 3 457--472 (2015).https://doi.org/10.1007/s00605-015-0785-9.  arXiv:1406.0280 [math.AC]

  • Ojeda, I.; Vigneron-Tenorio, A. The short resolution of a semigroup algebra. Bulletin of the Australian Mathematical Society. Volume 96 , Issue 3 400-411 (2017).  https://doi.org/10.1017/S0004972717000612. (ISSN: 0004-9727). arXiv:1512.00345 [math.RA]

  • García-García, J. I.; Moreno-Frías, M. A.; Vigneron-Tenorio, A. Proportionally modular affine semigroups. Journal of Algebra and Its Applications. Vol. 17, No. 1 (2018) 1850017 (17 pages).  http://dx.doi.org/10.1142/S0219498818500172 (ISSN: 0219-4988)  arXiv:1512.01513 [math.AC]

  • García-García, J. I.; Marín-Aragón, D.; Vigneron-Tenorio, A. An extension of Wilf's conjecture to affine semigroups. Semigroup Forum Vol. 96, Issue 2, 396-408 (2018). DOI: 10.1007/s00233-017-9906-1.(ISSN: 0037-1912). arXiv:1608.08528  [math.NT]

  • García-García, J. I.; Marín-Aragón, D.; Vigneron-Tenorio, A. A characterization of some families of Cohen--Macaulay, Gorenstein and/or Buchsbaum rings. Discrete Applied Mathematics Vol. 263, 166-176 (2019). https://doi.org/10.1016/j.dam.2018.03.021. (ISSN: 0166-218X). arXiv:1507.04536 [math.AC]

  • García-García, J. I.; Marín-Aragón, D.; Moreno-Frías, M.A.; Rosales, J.C.; Vigneron-Tenorio, A. Semigroups with fixed multiplicity and embedding dimension. Ars Mathematica Contemporanea Vol 17, No 2, 397-417 (2019). https://doi.org/10.26493/1855-3974.1937.5ea  (ISSN: 1855-3974)  arXiv:1710.03523 [math.AC] and arXiv:1712.05220 [math.AC]

  • García-García, J. I.; Ojeda, I.; Rosales, J. C.; Vigneron-Tenorio, A. On pseudo-Frobenius elements of submonoids of Nd. Collectanea Mathematica 71(1), 189-204 (2020). DOI: https://doi.org/10.1007/s13348-019-00267-0. (ISSN: 0010-0757) arXiv:1903.11028 [math.AC]

  • Díaz-Ramírez, J. D.; García-García, J. I.; Sánchez-R.-Navarro, A.; Vigneron-Tenorio, A. A geometrical characterization of proportionally modular affine semigroups. Results in Mathematics 75, 99 (2020). DOI: 10.1007/s00025-020-01230-3. (ISSN: 1422-6383) arXiv:1906.01585 [math.AC]

  • García-García, J. I.; Sánchez-R.-Navarro, A.; Vigneron-Tenorio, A. Multiple Convex Body Semigroups and Buchsbaum Rings.  Journal of Commutative Algebra. Vol. 12, no. 3, 309-318 (2020). https://doi.org/10.1216/jca.2020.12.309. (ISSN: 1939-2346) arXiv:1402.2597 [math.AC]

  • García-García, J. I.; Marín-Aragón, D.; Vigneron-Tenorio, A. Union of sets of lengths of numerical semigroups. Mathematics 8, no. 10: 1789 (2020). https://doi.org/10.3390/math8101789. (ISSN 2227-7390)  arXiv:1906.01266 [math.AC]

  • García Barroso, E. R.; García-García, J. I.; Vigneron-Tenorio, A. Generalized strongly increasing semigroups. Mathematics 9(12), 1370 (2021). https://doi.org/10.3390/math9121370. (ISSN 2227-7390)  arXiv:2003.13381 [math.AC]

  • Marijuán, C.; Ojeda, I.; Vigneron-Tenorio, A. A note on decomposable and reducible integer matrices. Symmetry 13(7), 1125 (2021). https://doi.org/10.3390/sym13071125. (ISSN 2073-8994)  arXiv:2003.01453 [math.CO] 

  • García-García, J. I.; Marín-Aragón, D.; Torres, F.; Vigneron-Tenorio, A. On reducible non-Weierstrass semigroups. Open Mathematics, vol. 19, no. 1, pp. 1134-1144 (2021). https://doi.org/10.1515/math-2021-0111 (ISSN 2391-5455) arXiv:2005.12896 [math.AG]

  • Díaz-Ramírez, J. D.; García-García, J. I.; Marín-Aragón, D.; Vigneron-Tenorio, A. Characterizing affine C-semigroups. Ricerche di Matematica, 71, 283-296 (2022). https://doi.org/10.1007/s11587-022-00693-6 (ISSN 0035-5038)  arXiv:1907.03276 [math.AC]

  • Eliahou, S.; García-García, J. I.; Marín-Aragón, D.; Vigneron-Tenorio, A. The Buchweitz set of a numerical semigroup. Bulletin of the Brazilian Mathematical Society, New Series, 54, 4 (2023). https://doi.org/10.1007/s00574-022-00322-8. (ISSN 1678-7544)  arXiv:2011.09187 [math.CO]

  • García-García, J. I.; Marín-Aragón, D.; Vigneron-Tenorio, A. Asymptotic ω-Primality of Finitely Generated Cancelative Commutative Monoids. Mathematics 11, no. 4: 790 (2023).  https://doi.org/10.3390/math11040790. (ISSN 2227-7390)

  • García Barroso, E. R.; García-García, J. I.; Santana Sánchez, L. J.; Vigneron-Tenorio, A. Conductors of Abhyankar-Moh semigroups of even degrees. Electronic Research Archive, volume 31, Issue 4: 2213-2229 (2023). https://doi.org/10.3934/era.2023113. (ISSN 2688-1594)  arXiv:2209.04232 [math.AG]

  • García-García, J. I.; Moreno-Frías, M. A.; Rosales, J. C.; Vigneron-Tenorio, A. The complexity of a numerical semigroup. Quaestiones Mathematicae, 46:9, 1847-1861(2023). https://doi.org/10.2989/16073606.2022.2114391  (ISSN 1607-3606)  arXiv:2202.00920 [math.NT]

  • García-García, J. I.; Marín-Aragón, D.; Sánchez-Loureiro, A.; Vigneron-Tenorio, A. Some properties of affine C-semigroups. Results in Mathematics 79, 52 (2024). https://doi.org/10.1007/s00025-023-02056-5. arXiv:2305.05044 [math.RA]

  • García Barroso, E. R.; García-García, J. I.; Santana Sánchez, L. J.; Vigneron-Tenorio, A. On p-Frobenius of affine semigroups. Mediterranean Journal of Mathematics, 21, 90 (2024). arXiv:2311.06050 [math.AC]

  • García-García, J. I.; Marín-Aragón, D.; Vigneron-Tenorio, A. On the ideals of some sumset semigroups. arXiv:2102.04100 [math.NT]

  • García-García, J. I.; Tapia-Ramos, R.; Vigneron-Tenorio, A. On the quotient of affine semigroups by a positive integer. arXiv:2402.09159 [math.AC]

  • García-García, J. I.; Tapia-Ramos, R.; Vigneron-Tenorio, A. On ideals of affine semigroups and affine semigroups with maximal embedding dimension. arXiv:2405.14648 [math.AC]

Other research publications

• • Vigneron-Tenorio, A.; Sánchez-Navarro, A. LLL.lib. Integral LLL-Algorithm. A Singular Introduction to Commutative Algebra, Berlin, Springer, 536-536 (2002). (ISBN: 3540428976)

  • Vigneron-Tenorio, A. Álgebras de Semigrupos y Aplicaciones (Ph. D. Thesis). Alicante: Biblioteca Virtual Miguel de Cervantes (2005). (ISBN: 84-689-1589-0)

  • Castro-Jiménez, F.J. (ed.); Vigneron-Tenorio. A. (ed.). Book of abstracts of the ICCCCA in memory of Pilar Pisón Casares (2008). (ISBN: 978-84-691-8887-3)

Software

• • Vigneron-Tenorio, A. Implementation of algorithms to compute semigroup ideals (MapleV). Reference: Linear Algebra Appl. 295, no. 1-3,133--144 (1999). (ISSN: 0024-3795)

  • Vigneron-Tenorio, A. Implementation of algorithms to solve diophantine equations (MapleV). Reference: Comm. Algebra 29, nº 4, 1445--1466 (2001). (ISSN: 0092-7872)

  • Vigneron-Tenorio, A.; Sánchez-Navarro, A.  Implementation of LLL-algorithm (Singular, C++) Reference: A Singular Introduction to Commutative Algebra, Berlin, Springer, 536--536 (2002). (ISBN: 3540428976)

  • García-Ramos, J.A.; Ramos-González, C.; Vigneron-Tenorio, A. Implementation of algorithm (MapleV). Reference: Epsilon 51, 567--578 (2001). (ISSN: 1131-9321)

  • Vigneron-Tenorio, A. Implementation of algorithms to compute the short resolution of lattice ideals (mix  MapleV + Singular). Reference: Pisón-Casares, P. The short resolution of a lattice ideal, Proceeding of AMS 131 (2003), 1081-1091. (ISSN 0002-9939)

  • García-García, J. I.; Moreno-Frías, M. A.; Sánchez-R.-Navarro, A.; Vigneron-Tenorio, A. Implementation of algorithms to compute the generating set of affine convex body semigroups (Wolfram Mathematica 7) . Reference: Semigroup Forum 87 (2), 331-350 (2013). (ISSN: 0037-1912). arXiv:1203.2129 [math.AC]. Index: "http://hdl.handle.net/10498/15832"

  • García-García, J. I.; Vigneron-Tenorio, A. Implementation of algorithms to compute the HNF-decomposition of an integer matrix (Wolfram Mathematica 7 + 4ti2) . Reference: Journal of Symbolic Computation 58, 103--116 (2013). (ISSN: 0747-7171). arXiv:1006.2557 [math.AC]. Index: "http://hdl.handle.net/10498/15837"

  • García-García, J. I.; Vigneron-Tenorio, A. OmegaPrimality, a package for computing the omega primality of finitely generated atomic monoids. Index: "http://hdl.handle.net/10498/15961"

  • García-García, J. I.; Vigneron-Tenorio, A. DeltaSetsNumericalMonoids, a Mathematica package for computing the Delta sets of numerical semigroups. Index: "http://hdl.handle.net/10498/17446"

  • García-García, J. I.; Vigneron-Tenorio, A. ProporcionallyModularAffineSemigroupN2, a software system to solve a proportionally modular inequality in N^2. Index: "http://hdl.handle.net/10498/18909"

  • García-García, J. I.; Sánchez-R.-Navarro, A.; Vigneron-Tenorio, A. PolySGTools, a Mathematica package for convex polygonal semigroups. Index: "http://hdl.handle.net/10498/19438"

  • García-García, J. I.; Marín-Aragón, D.; Vigneron-Tenorio, A. PyConvexHullSemigroup, a Python library for computations in convex hull semigroups. Index: "http://hdl.handle.net/10498/20125"

  • García-García, J. I.; Marín-Aragón, D.; Vigneron-Tenorio, A. FrobeniusNumberAndGenus, a Mathematica package for computations in numerical semigroups. Index: "http://hdl.handle.net/10498/21658"