From the 1 of 7 linked papers with an AI index.
7 papers
Coloring semiminimal Cayley Graphs
Ignacio GarcÃa-Marco, Kolja Knauer, Giuliamaria Menara
The paper proves that semiminimal Cayley graphs of abelian and generalized dihedral groups have circular chromatic number at most 4, extending earlier results and addressing a ques…
Sensitivity and Hamming graphs
Sara Asensio, Yuval Filmus, Ignacio GarcÃa-Marco +1
For any we show that the Hamming graph admits an imbalanced partition into sets, each inducing a subgraph of low maximum degree. This improves previous resul…
On the minimum number of Toeplitz factors of a matrix
Ignacio GarcÃa-Marco, Irene Márquez-Corbella, Daniel Seco
We disprove a conjecture by Ye and Lim, by showing that there are complex matrices which can't be expressed as the product of two Toeplitz matrices of the same size. W…
Computational Aspects of the Short Resolution
Ignacio GarcÃa-Marco, Philippe Gimenez, Mario González-Sánchez
Let be a polynomial ring over a field , be a homogeneous ideal with respect to a weight vector $Ï= (Ï_1,\ldots,Ï_n) \in (\math…
Toric ideals of graphs minimally generated by a Gröbner basis
Ignacio GarcÃa-Marco, Irene Márquez-Corbella, Christos Tatakis
Describing families of ideals that are minimally generated by at least one, or by all, of their reduced Gröbner bases is a central topic in commutative algebra. In this paper, we…
Proyective Cohen-Macaulay monomial curves and their affine charts
Ignacio GarcÃa-Marco, Philippe Gimenez, Mario González-Sánchez
In this paper, we explore when the Betti numbers of the coordinate rings of a projective monomial curve and one of its affine charts are identical. Given an infinite field and…