Research papers

Publications

• I. García-Marco, K. Knauer. Coloring minimal Cayley graphs. arXiv:2405.19543 [math.CO]. Submitted

• I. García-Marco, Ph. Gimenez, M. González-Sánchez. Proyective Cohen-Macaulay monomial curves and their affine charts. arXiv:2405.15634 [math.AC]. Submitted.

• I. García-Marco, K. Knauer. Beyond symmetry in generalized Petersen graphs. J Algebr Comb 59, 331–357 (2024).

• I. García-Marco, P. A. García-Sánchez, I. Ojeda, Ch. Tatakis. Universally free numerical semigroups. J Pure Appl Algebra. 228(5), 107551 (2024).

• E. Camps-Moreno, I. García-Marco, H. H. López, I. Márquez-Corbella, E. Martínez-Moro, E. Sarmiento. On the generalized Hamming weights of hyperbolic codes. J. Algebra Appl. 23, (2024), no. 7, 2550062.

• I. García-Marco, Ch. Tatakis. On robustness and related properties on toric ideals. J Algbr Comb 57 (2023),  21–52. 

• I. García-Marco, I. Márquez-Corbella, E. Martínez-Moro, Y. Pitones. Free resolutions and Generalized Hamming Weights of binary linear codes.  Mathematics 2022, 10(12), 2079.

• I. García-Marco, K. Knauer. On sensitivity in bipartite Cayley graphs. J. Combin. Theory Ser. B. 154 (2022), 211-238,

• E. R. García Barroso, I. García-Marco, I. Márquez-Corbella. Factorizations of the same length in abelian monoids.   Ricerche mat 72, 679–707 (2023).

• I. García-Marco, K. Knauer, L. P. Montejano. Chomp on generalized Kneser graphs and others. Int J Game Theory 50, 603--621 (2021).

• I. García-Marco, K. Knauer, G. Mercui-Voyant. Cayley posets.  Mediterr. J. Math. 17, 186 (2020)

• I. García-Marco, I. Márquez-Corbella, D. Ruano. High dimensional affine codes whose square has a designed minimum distance. Des. Codes Cryptogr. 88, 1653–1672 (2020).

• I. García-Marco, P. Koiran, T. Pecatte. Polynomial equivalence problems for sums of affine powers. Conference version: ISSAC 2018, pp. 303-310, https://doi.org/10.1145/3208976.3208993

• I. García-Marco, K. Knauer. Chomp on numerical semigroups. Algebraic Combinatorics,  Volume 1 (2018) no. 3, pp. 371-394.

• I. García-Marco, P. Koiran, T. Pecatte. On the linear independence of shifted powers. J. Complexity 45 (2018), 67–82.  

• I. García-Marco, P. Koiran, T. Pecatte. Reconstruction algorithms for sums of affine powers. Conference version:  ISSAC 2017, pp. 317-324,  http://dx.doi.org/10.1145/3087604.3087605. Journal version: J. Symbolic Comput. 98 (2020) 284–318.

• I. Bermejo, E. García-Llorente, I. García-Marco, M. Morales. Noether resolutions in dimension 2. J. Algebra 482 (2017), 398-426.

• I. García-Marco, P. Koiran, T. Pecatte, S. Thomassé. On the complexity of partial derivatives. 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017) Leibniz International Proceedings in Informatics (LIPIcs) 66 (2017), 37:1-37:13.

• I. Bermejo, E. García-Llorente, I. García-Marco. Algebraic invariants of projective monomial curves associated to generalized arithmetic sequences. J. Symbolic Comput. 81 (2017), 1-19

• I. García-Marco, P. Koiran, Lower bounds by Birkhoff interpolation. J. Complexity 39 (2017), 38-50.

• I. García-Marco, J. L. Ramírez Alfonsín, Ø. J. Rødseth. Numerical semigroups II: pseudo-symmetric AA-semigroups. J. Algebra 470 (2017), 484–498.

• I. García-Marco, K. Knauer. Graph drawings with vertices and edges in convex position. Journal version: Computational Geometry 58 (2016) 25–33 . Conference version: LNCS 9411, pages 348-359, GD, (2015).

• I. García-Marco, J. L. Ramírez Alfonsín. Matroid toric ideals: complete intersections, minors and minimal systems of generators. SIAM J. Discrete Math. 29 (2015), no. 4, 2267–2276. 

• I. García-Marco, P. Koiran, S. Tavenas, Log-concavity and lower bounds for arithmetic circuits. Italiano et al. (Eds.): MFCS 2015, Part II, LNCS 9235, pp. 361–371, 2015.  

• J. Chappelon, I. García-Marco, L. P. Montejano, J. L. Ramírez Alfonsín. Möbius function of semigroup posets through Hilbert series. J. Combin. Theory Ser. A 136 (2015), 238–251. 

• I. Bermejo, I. García-Marco, E. Reyes. Graphs and complete intersection toric ideals. J. Algebra Appl. 14 (2015), no. 9, 1540011, 37 pp. 

• I. Bermejo, I. García-Marco. Complete intersections in simplicial toric varieties. J. Symbolic Comput. 68 (2015), part 1, 265-286. 

• I. Bermejo, I. García-Marco. Complete intersections in certain affine and projective monomial curves, Bull. Braz. Math. Soc. (N.S.) 45 (2014), no.4, 599-624. 

• I. Bermejo, I. García-Marco, J. J. Salazar-González. An algorithm for checking whether the toric ideal of an affine monomial curve is a complete intersection. J. Symbolic Comput. 42 (2007), no. 10, 971-991. 

Computer libraries

• I. Bermejo, I. García-Marco. cisimplicial.lib. A library for C++ and SINGULAR (available at www.singular.uni-kl.de), for checking whether a simplicial toric ideal is a complete intersection, Its version for SINGULAR is included in the software since its version 3-1-4, 2012.

• I. Bermejo, I. García-Marco, J. J. Salazar-González. cimonom.lib. A library for C++ and SINGULAR to check whether the toric ideal of an affine monomial curve is a complete intersection. Its version for SINGULAR is included in the software in its versions between 3-0-2 and 3-1-3.

Ph. D. Thesis

Title: Ideales tóricos intersección completa y algoritmos que provienen de estructuras geométricas y combinatorias

University: Universidad de La Laguna

Date: 10/07/2013 

Director: Isabel Bermejo