Research

• ResearcherID H-8562-2015
• ORCID 0000-0002-3481-004X
• Scopus Author ID 23007363700
• List of items in MathSciNet

Research groups and networks

• COPRICA (Codes, Privacy, and Algebraic Combinatorics)
• Discrete and Algorithmic Mathematics (Red de Matemática Discreta y Algorítmica)
• MatSI (Matemàticas en la Sociedad de la Información)
• Network on Monoids and Applications

Drawsgtree: a tool for visualizing properties in the semigroup tree

GitHub link

Selected talks

• Numerical semigroups, Journées de Combinatoire de Bordeaux, France, 2025.
• Numerical semigroups and music, Conference on Rings and Factorizations, Graz, Austria, 2023.
• On the seeds and the great-grandchildren of a numerical semigroup, International meeting on numerical semigroups, Roma, Italy, 2022.
• Numerical semigroups in coding theory Lesson 1, Lesson 2, Lesson 3, Lesson 4. CIMPA Research School "ALGEBRAIC METHODS IN CODING THEORY", Institute of Mathematics and Statistics - University of São Paulo, Brazil 2017.
• On numerical semigroups and their applications to algebraic geometry codes, Algebraic Geometry, Coding and Computing, Universidad de Valladolid, Segovia, 2007. (Introduction of the conjectures n_g≥n_g-1 and n_g≥n_g-1+n_g-2 and n_g+1/n_g→φ)

Submitted Preprints

1. M. Bras-Amorós, A. S. Castellanos, L. Quoos: Self-orthogonal flags of codes and translation of flags of algebraic geometry codes, 2024.
2. M. Bras-Amorós, M. Rosas-Ribeiro: Rarity of the infinite chains in the tree of numerical semigroups, 2024.

Journal Publications

1. M. Bras-Amorós, G. Moskowitz, V. Ponomarenko: Construction of an Endgame Rulebook for Sylver Coinage Using Trees of Numerical Semigroups,
   Communications in Algebra, Accepted, 2025. ISSN: 0092-7872.
2. M. Rosas-Ribeiro, M. Bras-Amorós: Infinite Chains in the Tree of Numerical Semigroups (arXiv),
   Semigroup Forum, Springer, vol. 110, pp. 229-248, February 2025. ISSN: 0037-1912.
3. H. Pérez-Rosés, J. M. Serradilla-Merinero, M. Bras-Amorós: Greedy Sets and Greedy Numerical Semigroups (arXiv),
   Communications in Algebra, Accepted, 2025. vol. 53, n. 6, pp. 2442-2455, 2025. ISSN: 0092-7872.
4. M. Bras-Amorós: On the Seeds and the Great-grandchildren of a Numerical Semigroup (arXiv),
   Mathematics of Computation, American Mathematical Society, vol. 93, n. 345, pp. 411-441, January 2024. ISSN: 1088-6842(online), ISSN: 0025-5718(print).
   • Associated code in GitHub
5. M. Bras-Amorós, A. S. Castellanos, L. Quoos: Isometry-Dual Flags of Many-Point AG Codes (arXiv),
   SIAM Journal on Applied Algebra and Geometry (SIAGA), Society for Industrial and Applied Mathematics, vol. 7, n. 4, pp. 786-808, 2023. ISSN: 2470-6566 (online).
6. H. Pérez-Rosés, M. Bras-Amorós, J. M. Serradilla-Merinero: Greedy Routing in Circulant Networks,
   Graphs and Combinatorics, Springer, vol. 38, n. 86, 2022. ISSN: 0911-0119.
7. M. Bras-Amorós, A. S. Castellanos, L. Quoos: The Isometry-Dual Property in Flags of Two-Point Algebraic Geometry Codes (arXiv),
   IEEE Transcations on Information Theory, vol. 68, n. 2, pp. 828-838, February 2022. ISSN: 0018-9448.
8. J. Domingo-Ferrer, K. Muralidhar, M. Bras-Amorós: General Confidentiality and Utility Metrics for Privacy-Preserving Data Publishing Based on the Permutation Model,
   IEEE Transactions on Dependable and Secure Computing, vol. 18, n.5, pp. 2506-2517, September-October 2021, ISSN: 1545-5971.
9. M. Bras-Amorós, H. Pérez-Rosés, J. M. Serradilla-Merinero: Quasi-Ordinarization Transform of a Numerical Semigroup (arXiv),
   Symmetry, MDPI, vol. 13, n. 6, 1084, June 2021. ISSN: 2073-8994.
10. M. Bras-Amorós, M. Gotti: Atomicity and Density of Puiseux Monoids (arXiv),
    Communications in Algebra, vol. 49, n. 4, pp. 1560-1570, 2021. ISSN: 0092-7872.
11. M. Bras-Amorós, I. Duursma, E. Hong: Isometry-Dual Flags of AG Codes (arXiv),
    Designs, Codes and Cryptography, Springer, vol. 88, pp. 1617-1638, August 2020. ISSN: 0925-1022.
12. A. S. Castellanos, M. Bras-Amorós: Weierstrass Semigroup at m+1 Rational Points in Maximal Curves which Cannot Be Covered by the Hermitian Curve (arXiv),
    Designs, Codes and Cryptography, Springer, vol. 88, pp. 1595-1616, August 2020. ISSN: 0925-1022.
13. M. Bras-Amorós, J. Fernández-González: The Right-Generators Descendant of a Numerical Semigroup (arXiv),
    Mathematics of Computation, American Mathematical Society, vol. 89, n. 324, pp. 2017-2030, July 2020. ISSN: 1088-6842(online), ISSN: 0025-5718(print).
    • Associated code in GitHub
14. M. Bras-Amorós: Increasingly Enumerable Submonoids of R: Music Theory as a Unifying Theme (arXiv),
    The American Mathematical Monthly, Mathematical Association of America, vol. 127, n. 1, pp. 33-44, January 2020. ISSN: 0002-9890.
15. M. Bras-Amorós: Ideals of Numerical Semigroups and Error-Correcting Codes,
    Symmetry, MDPI, vol. 11, n. 11, 1406, November 2019. ISSN: 2073-8994.
16. M. Bras-Amorós: Tempered Monoids of Real Numbers, the Golden Fractal Monoid, and the Well-Tempered Harmonic Semigroup (arXiv),
    Semigroup Forum, Springer, vol. 99, n. 2, pp. 496-516, November 2019. ISSN: 0037-1912.
17. M. Bras-Amorós, M. E. O'Sullivan: The Symmetric Key Equation for Reed-Solomon Codes and a New Perspective on the Berlekamp-Massey Algorithm,
    Symmetry, MDPI, vol. 11, n. 11, 1357, November 2019. ISSN: 2073-8994.
18. M. Bras-Amorós, J. Fernández-González: Computation of Numerical Semigroups by Means of Seeds (arXiv),
    Mathematics of Computation, American Mathematical Society, vol. 87, pp. 2539-2550, n. 313, September 2018. ISSN: 1088-6842(online), ISSN: 0025-5718(print).
19. M. Bras-Amorós: A Decoding Approach to Reed-Solomon Codes from Their Definition (arXiv),
    The American Mathematical Monthly, Mathematical Association of America, vol. 125, n. 4, pp. 320-338, March 2018. ISSN: 0002-9890.
20. M. Bras-Amorós, M. Pujol: Side Lengths of Equiangular Polygons (as Seen by a Coding Theorist),
    The American Mathematical Monthly, Mathematical Association of America, vol. 122, n. 5, pp. 476-478, May 2015. ISSN: 0002-9890.
21. M. Bras-Amorós, K. Lee, A. Vico-Oton: New Lower Bounds on the Generalized Hamming Weights of AG Codes (arXiv),
    IEEE Transactions on Information Theory, vol. 60, n. 10, pp. 5930-5937, October 2014. ISSN: 0018-9448.
22. K. Lee, M. Bras-Amorós, M. E. O'Sullivan: Unique Decoding of General AG Codes (arXiv),
    IEEE Transactions on Information Theory, vol. 60, n. 4, pp. 2038-2053, April 2014. ISSN: 0018-9448.
23. K. Stokes, M. Bras-Amorós: Linear, Non-Homogeneous, Symmetric Patterns and Prime Power Generators in Numerical Semigroups Associated to Combinatorial Configurations (arXiv),
    Semigroup Forum, Springer, vol. 88, n. 1, pp. 11-20, 2014. ISSN: 0037-1912.
24. M. Bras-Amorós, A. Vico-Oton: On the Geil-Matsumoto Bound and the Length of AG Codes (arXiv),
    Designs, Codes and Cryptography, Springer, vol. 70, n. 1-2, pp. 117-125, January 2014. ISSN: 0925-1022.
25. M. Bras-Amorós, P. A. García-Sánchez, A. Vico-Oton: Nonhomogeneous Patterns on Numerical Semigroups (arXiv),
    International Journal of Algebra and Computation, World Scientific, vol. 23, n. 6, pp. 1469-1483, September 2013. ISSN: 0218-1967.
26. M. Bras-Amorós: The Ordinarization Transform of a Numerical Semigroup and Semigroups with a Large Number of Intervals, (arXiv),
    Journal of Pure and Applied Algebra, Elsevier, vol. 216, n. 11, pp. 2507-2518, November 2012. ISSN:0022-4049.
27. K. Lee, M. Bras-Amorós, M. E. O'Sullivan: Unique Decoding of Plane AG Codes via Interpolation (arXiv),
    IEEE Transactions on Information Theory, vol. 58, n. 6, pp. 3941-3950, June 2012. ISSN: 0018-9448.
28. M. Bras-Amorós, K. Stokes: The Semigroup of Combinatorial Configurations (arXiv),
    Semigroup Forum, Springer, vol. 84, n. 1, pp. 91-96, January 2012. ISSN: 0037-1912.
29. M. Bras-Amorós, J. Domingo-Ferrer, A. Vico-Oton: Co-Citations and Relevance of Authors and Author Groups,
    International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems (IJUFKS), vol. 19, pp. 127-139, September 2011. ISSN: 0218-4885.
30. K. Stokes, M. Bras-Amorós: Associating a Numerical Semigroup to the Triangle-Free Configurations,
    Advances in Mathematics of Communication, American Institute of Mathematical Sciences, vol. 5, n. 2, pp. 351-371, May 2011. ISSN: 1930-5346.
31. M. Bras-Amorós, J. Domingo-Ferrer, V. Torra: A Bibliometric Index Based on the Collaboration Distance Between Cited and Citing Authors,
    Journal of Informetrics, Elsevier, vol. 5, n. 2, pp. 248-264, April 2011. ISSN: 1751-1577.
32. K. Stokes, M. Bras-Amorós: Optimal Configurations for Peer-to-Peer User-Private Information Retrieval,
    Computers and Mathematics with Applications, Elsevier, vol. 59, n. 4, pp. 1568-1577, February 2010. ISSN: 0898-1221.
33. M. Bras-Amorós, S. Bulygin: Towards a Better Understanding of the Semigroup Tree (arXiv),
    Semigroup Forum, Springer, vol. 79, n. 3, pp. 561-574, December 2009. ISSN: 0037-1912.
34. J. Domingo-Ferrer, M. Bras-Amorós, Q. Wu, J. Manjón: User-Private Information Retrieval Based on a Peer-to-Peer Community,
    Data and Knowledge Engineering, Elsevier, vol. 68, n. 11, pp. 1237-1252, November 2009. ISSN:0169-023X.
35. M. Bras-Amorós: On Numerical Semigroups and the Redundancy of Improved Codes Correcting Generic Errors ,
    Designs, Codes and Cryptography, Springer. vol. 53, n. 2, pp. 111-118, November 2009. ISSN: 0925-1022.
36. M. Bras-Amorós: Bounds on the Number of Numerical Semigroups of a Given Genus (arXiv),
    Journal of Pure and Applied Algebra, Elsevier, vol. 213, n. 6, pp. 997-1001, June 2009. ISSN: 0022-4049.
37. M. Bras-Amorós, M. E. O'Sullivan: Redundancies of Correction Capability Optimized Reed-Muller Codes (arXiv),
    Discrete Applied Mathematics, Elsevier, vol. 156, n. 15, pp. 3005-3010, August 2008. ISSN: 0166-218X.
38. M. Bras-Amorós: Fibonacci-Like Behavior of the Number of Numerical Semigroups of a Given Genus (arXiv),
    Semigroup Forum, Springer, vol. 76, n. 2, pp. 379-384, March 2008. ISSN: 0037-1912.
    • Associated entry in Neil J. A. Sloane's On-Line Encyclopedia of Integer Sequences
39. M. Bras-Amorós, M. E. O'Sullivan: Duality for Some Families of Correction Capability Optimized Evaluation Codes (arXiv),
    Advances in Mathematics of Communication, American Institute of Mathematical Sciences, vol. 2, n. 1, pp. 15-33, February 2008. ISSN: 1930-5346.
40. M. Bras-Amorós, A. de Mier: Representation of Numerical Semigroups by Dyck Paths (arXiv),
    Semigroup Forum, Springer, vol. 75, n. 3, pp. 676-681, December 2007. ISSN: 0037-1912.
41. M. Bras-Amorós, M. E. O'Sullivan: The Order Bound on the Minimum Distance of the One-Point Codes Associated to the Garcia-Stichtenoth Tower of Function Fields (arXiv),
    IEEE Transactions on Information Theory, vol. 53, n. 11, pp. 4241-4245, November 2007. ISSN: 0018-9448.
42. M. Bras-Amorós, M. E. O'Sullivan: On Semigroups Generated by Two Consecutive Integers and Improved Hermitian Codes (arXiv),
    IEEE Transactions on Information Theory, vol. 53, n. 7, pp. 2560-2566, July 2007. ISSN: 0018-9448.
43. M. Bras-Amorós: Algebraic-Geometry Codes, One-Point Codes and Evaluation Codes,
    Designs, Codes and Cryptography, Springer, vol. 43, n. 2-3, pp. 137-145, June 2007. ISSN: 0925-1022.
44. M. Bras-Amorós: A Note on Numerical Semigroups,
    IEEE Transactions on Information Theory, vol. 53 n. 2, pp. 821-823, February 2007. ISSN: 0018-9448.
45. M. Bras-Amorós, M. E. O'Sullivan: The Correction Capability of the Berlekamp-Massey-Sakata Algorithm with Majority Voting,
    Applicable Algebra in Engineering, Communication and Computing, Springer, vol. 17 n. 5, pp. 315-335, October 2006. ISSN: 0938-1279.
46. M. Bras-Amorós, P. A. García-Sánchez: Patterns on Numerical Semigroups (arXiv),
    Linear Algebra and its Applications, Elsevier, vol. 414, pp. 652-669, April 2006. ISSN: 0024-3795.
47. M. Bras-Amorós: Acute Semigroups, the Order Bound on the Minimum Distance and the Feng-Rao Improvements (arXiv),
    IEEE Transactions on Information Theory, vol. 50 n. 6, pp. 1282-1289, June 2004. ISSN: 0018-9448.

Book Chapters

1. M. Bras-Amorós: Numerical Semigroups and Codes (arXiv),
   Chapter 5 of Algebraic Geometry Modeling in Information Theory , E. Martinez-Moro (ed.), World Scientific, 2013. ISBN: 978-981-4335-75-1.
2. M. E. O'Sullivan, M. Bras-Amorós: The Key Equation for One-Point Codes (arXiv),
   Chapter 3 of Advances in Algebraic Geometry Codes, E. Martinez-Moro, C. Munuera, D. Ruano (eds.), World Scientific, 2008. ISBN: 978-981-279-400-0.

Selected Publications in Conference Proceedings

1. M. Bras-Amorós, C. Marín Rodríguez: New Eliahou Semigroups and Verification of the Wilf Conjecture for Genus up to 65, (arXiv)
   Lecture Notes in Artifical Intelligence, Modeling Decisions for Artificial Intelligence, V. Torra, Y. Narukawa (eds.), Springer, vol. 12898, pp.17-27. September 20, 2021.ISSN: 0302-9743.
2. M. Bras-Amorós: Different tree approaches to the problem of counting numerical semigroups by genus,
   Proceedings of the 11th International Conference on Random and Exhaustive Generation of Combinatorial Structures, CEUR Workshop Proceedings, Ed. Luca Ferrari, Malvina Vamvakari, vol. 2113, pp. 7-11, Athens, Greece June 18-20, 2018.ISSN: 1613-0073.
3. M. Bras-Amorós: Ordinarization of Numerical Semigroups,
   Electronic Notes in Discrete Mathematics, vol. 38, pp. 187-193, European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2011), org. Rényi Institute, Budapest, Hungary, Elsevier, August 2011 to September 2011.ISSN: 1571-0653.
4. M. Bras-Amorós, K. Stokes, M. Greferath: Problems Related to Combinatorial Configurations with Applications to P2P-User Private Information Retrieval,
   19th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2010, pp. 1267-1271, Budapest, Hungarian Academy of Sciences, Hungary, July 2010.ISBN: 978-963-311-370-7.
5. M. Bras-Amorós, M. E. O'Sullivan: From the Euclidean Algorithm for Solving a Key Equation for Dual Reed-Solomon Codes to the Berlekamp-Massey Algorithm,
   Lecture Notes in Computer Science, Applied Algebra, Algebraic Algorithms and Error- Correcting Codes, M. Bras-Amorós, T. Høholdt (eds.), Springer, vol. 5527, pp. 32-42, June 2009.ISSN: 0302-9743.
6. J. Domingo-Ferrer, M. Bras-Amorós: Peer-to-Peer Private Information Retrieval,
   Lecture Notes in Computer Science, Privacy in Statistical Databases, J. Domingo-Ferrer, Yucel Saygin (eds.), Springer, vol. 5262, pp. 315-323. September 2008.ISSN: 0302-9743.
7. M. Bras-Amorós, M. E. O'Sullivan: Extended Norm-Trace Codes with Optimized Correction Capability,
   Lecture Notes in Computer Science, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, P. V. Kumar, T. Høholdt, H. Janwa (eds.), Springer, vol. 4851, pp. 337-346, December 2007.ISSN: 0302-9743.
8. M. Bras-Amorós, P. Guitart, J. González, J. Serra, F. García: BISK Scheme Applied to Sign Encoding and Magnitude Refinement,
   Lecture Notes in Artificial Intelligence, Advanced Concepts for Intelligent Vision Systems, Springer, vol. 3708, pp. 442-451, September 2005.ISSN: 0302-9743, ISBN: 3-540-29032-X.
9. M. Bras-Amorós: Improvements to Evaluation Codes and New Characterizations of Arf Semigroups,
   Lecture Notes in Computer Science, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, M. Fossorier, T. Høholdt, A. Poli (eds.), Springer, vol. 2643, pp. 204-215, May 2003.ISSN: 0302-9743.

Article dans Les Conjectures du Trimestre - Images des Mathématiques - CNRS, France

• Shalom Eliahou, Jean Fromentin: Semigroupes Numériques et Nombre d'Or (I)
• Shalom Eliahou, Jean Fromentin: Semigroupes Numériques et Nombre d'Or (II)

Les semigroupes numériques sont des objets mathématiques fascinants, à l'origine de nombreux défis mathématiques malgré leur apparente simplicité. La suite de Fibonacci et le nombre d'or s'y trouvent impliqués de façon complètement inattendue!