Papers

Below there is a list of most of my publications in journals or in conference proceedings. With few exceptions, all have entries in MathSciNet.

All items have associated a link to its DOI (Digital Object Identifier) or some electronic version. As an alternative to using these links (some of which point to copyrighted versions) or even to get some other information, you may wish to take a look at my page in Google Scholar. I also have an identifier: here is a link to my ORCID (Open Researcher and Contributor ID).

If you are interested in my research, you may want to take a look at my contributions to the development of open-source mathematical software. To this end, follow the links in the above separator Software.

You may also want to read a post I wrote for Red de Matemática Discreta y Algorítmica.

Preprints

    1. With Shalom Eliahou and Jean Fromentin, A verification of Wilf’s conjecture up to genus 100. [arXiv]
    2. With Jaume Usó i Cubertorer, Kunz languages for numerical semigroups are context sensitive. [arXiv]
    3. Trimming the numerical semigroups tree to probe Wilf’s conjecture to higher genus. [arXiv]

Publications

  1. With C. Cisto and P. A. García-Sánchez, Algorithms for Generalized Numerical Semigroups. Journal of Algebra and its Applications, 20 (2021) 2150079 [arXiv][doi]
  2. Conjecture of Wilf: a survey. In: Barucci V., Chapman S., D’Anna M., Fröberg R. (eds) Numerical Semigroups. Springer INdAM Series, vol 40. Springer, Cham, 2020, pp. 39-62 [arXiv][doi]
  3. On a question of Eliahou and a conjecture of Wilf. Mathematische Zeitschrift, 288 (2018) 595-627 [arXiv][doi][Springer Nature SharedIt]
  4. With P. A. García-Sánchez, numericalsgps, a GAP package for numerical semigroups. ACM Communications in Computer Algebra, 50 (2016) 12-24 [arXiv][doi]
  5. With P. A. García-Sánchez and A. M. Robles-Pérez, Numerical semigroups with a given set of pseudo-Frobenius numbers. LMS Journal of Computation and Mathematics, 19 (2016) 186-205 [arXiv][doi][LMS]
  6. With J. I. Farrán, P. A. García-Sánchez and D. Llena, On the weight hierarchy of codes coming from semigroups with two generators. IEEE Trans. Inform. Theory, 60 (2014) 282-295 [arXiv][doi]
  7. With P. A. García-Sánchez and J.C. Rosales, Numerical semigroups problem list. CIM [ Bulletin, number 33], (2013) 15-26. [arXiv]
  8. With Vítor H. Fernandes, Rees quotients of numerical semigroups. Portugaliae Mathematica, 70 (2013) 93-112. [arXiv][doi]
  9. With J. I. Farrán, P. A. García-Sánchez and D. Llena, On the generalized Feng-Rao numbers of numerical semigroups generated by intervals. Mathematics of Computation, 82 (2013) 1813-1836.[arXiv][doi]
  10. With B. Steinberg, On iterated Mal’cev products with a pseudovariety of groups, International Journal of Algebra and Computation, 21 (2011) 1285–1304.[doi]
  11. With E. Cordeiro, On the relative solvability of certain inverse monoids, Semigroup Forum, 81 (2010) 531-547.[doi]
  12. With J.C. Rosales, Modular Diophantine inequalities and rotations of numerical semigroups, J. Austral. Math. Soc. 84 (2008) 315-328.[doi]
  13. With P.A. García-Sánchez, J.C. Rosales and J.M.Urbano-Blanco, Systems of proportionally modular Diophantine inequalities, Semigroup Forum 76 (2008) 469-488.[doi]
  14. With A. Masuda and B. Steinberg, Solving systems of equations modulo pseudovarieties of abelian groups and hyperdecidability, in “Semigroups and Formal Languages” J.M. André, M.J.J. Branco, V.H. Fernandes, J. Fountain,G.M.S. Gomes and J. Meakin (Eds), World Scientific, 2007.[doi]
  15. With J. C. Rosales, On the Frobenius number of a proportionally modular Diophantine inequality, Portugaliae Mathematica, 63 (2006) 415-425.[link]
  16. With José Morais, On the GAP package sgpviz, in “Proceedings of ICMS 2006”, A. Iglesias and N. Takayama (eds), vol. 4151, 403–406, LNCS. Springer-Verlag, Heidelberg, 2006.[doi]
  17. With P. A. García-Sánchez and J. Morais, On the GAP package numericalsgps, in “V Jornadas de Matemática Discreta y Algorítmica”, Edgar Martínez Moro (ed.), Univ. Valladolid, Secretariado de Publicaciones e Intercambio Editorial. Pgs. 271-278, 2006.[pdf]
  18. With E. Cordeiro, Computing relative abelian kernels of finite monoids, Journal of Algebra (Computational Algebra section), 303 (2006) 642-654.[doi]
  19. With E. Cordeiro and V.H. Fernandes, Relative abelian kernels of some classes of transformation monoids, Bulletin of the Australian Mathematical Society, 73 (2006) 375-404.[doi]
  20. With José Morais, Approximation to the smallest regular expression for a given regular language, in “Implementation and Application of Automata”, M. Domaratzki, A. Okhotin, K. Salomaa and S. Yu, (eds), vol. 3317, pgs. 312-314, LNCS. Springer-Verlag, Heidelberg, 2005[doi]
  21. With Vítor H. Fernandes, Solvable monoids with commuting idempotents, International Journal of Algebra and Computation, 15 (2005) 547-570.[doi]
  22. With J. Almeida, Tameness of the pseudovariety of Abelian groups, International Journal of Algebra and Computation, 15 (2005) 327-338.[doi]
  23. With Vítor H. Fernandes, Abelian kernels, solvable monoids and the abelian kernel length of a finite monoid, in “Proceedings of the Workshop on Semigroups and Languages” (Lisbon 2002), I. Araújo, M. Branco, V. Fernandes, G. Gomes (eds.) World Scientific, (2004), 68-85.[doi]
  24. With V. H. Fernandes, S. Margolis and B. Steinberg, On semigroups whose idempotent-generated subsemigroup is aperiodic, International Journal of Algebra and Computation, 14 (2004) 655-665.[doi]
  25. With Vítor H. Fernandes, Abelian kernels of monoids of order-preserving maps and of some of its extensions, Semigroup Forum, 68 (2004) 335-356.[doi]
  26. With P.-C. Héam, A polynomial time algorithm to compute the Abelian kernel of a finite monoid, Semigroup Forum, 67 (2003) 97-110.[doi]
  27. With S. Margolis and B. Steinberg, Combinatorial Group Theory, Inverse Monoids, Automata, and Global Semigroup Theory, International Journal of Algebra and Computation, 12 (2002) 179-211.[doi]
  28. With J. Almeida, Sur certains systèmes d’équations avec contraintes dans un groupe libre – addenda, Portugaliae Mathematica, 58 (2001) 379-387.[link]
  29. Commutative images of rational languages and the abelian kernel of a monoid, RAIRO – Theoretical Informatics and Applications, 35 (2001) 419-435.[doi]
  30. On the hyperdecidability of pseudovarieties of groups, International Journal of Algebra and Computation, 11 (2001) 753-771.[doi]
  31. With V. H. Fernandes, Abelian kernels of some monoids of injective partial transformations and an application, Semigroup Forum, 61 (2000) 435-452.[doi]
  32. With J. Almeida, Sur certains systèmes d’équations avec contraintes dans un groupe libre, Portugaliae Mathematica, 56 (1999) 409-417. [link]
  33. Abelian Pointlikes of a monoid, Semigroup Forum 56 (1998) 339-361. [doi]
  34. Type II theorem and hyperdecidability of pseudovarieties of groups, Semigroups and applications (St. Andrews, 1997), World Sci. Publ., River Edge, NJ, 1998, 62-71 (pdf file of corrected version available.)
    This paper in its published version contains an error. The formulation of Theorem 4.3 in the published version was based on a result whose proof was faulty. It has never been published since, contrary to what happened with these proceedings, the paper was not yet in print at the time of the discovery. I have to thank Ben Steinberg for discovering that error. Due to this, the title of Section 6 of the published paper “Hyperdecidability of Ab” changed to “The abelian kernel of a monoid” in the corrected version made available above. This is in fact the main change: the hyperdecidability of Ab has later been proved in a joint work with J. Almeida where we proved the “Tameness of the pseudovariety of Abelian groups”.