9 papers
Rings are -bounded
Sara Asensio, Ignacio García-Marco, Kolja Knauer
We prove that there is a function such that for the zero-divisor graph of any ring , if the clique number is finite. On the on…
Coloring semiminimal Cayley Graphs
Ignacio García-Marco, Kolja Knauer, Giuliamaria Menara
In 1978 Babai raised the question whether all semiminimal Cayley graphs have bounded chromatic number. In this paper we show that semiminimal Cayley graphs of abelian and generaliz…
On the minimum number of Toeplitz factors of a matrix
Ignacio García-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…
Sensitivity and Hamming graphs
Sara Asensio, Yuval Filmus, Ignacio García-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…
Computational Aspects of the Short Resolution
Ignacio García-Marco, Philippe Gimenez, Mario González-Sánchez
Let be a polynomial ring over a field , be a homogeneous ideal with respect to a weight vector $ω= (ω_1,\ldots,ω_n) \in (\mathbb{…
Toric ideals of graphs minimally generated by a Gröbner basis
Ignacio García-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 a…
Sensitivity of -ary functions and low degree partitions of Hamming graphs
Sara Asensio, Ignacio García-Marco, Kolja Knauer
The study of complexity measures of Boolean functions led Nisan and Szegedy to state the sensitivity conjecture in 1994, claiming a polynomial relation between degree and sensitivi…
Coloring minimal Cayley graphs
Ignacio García-Marco, Kolja Knauer
In 1978 Babai raised the question whether all minimal Cayley graphs have bounded chromatic number; in 1994 he conjectured a negative answer. In this paper we show that any minimal…
Proyective Cohen-Macaulay monomial curves and their affine charts
Ignacio García-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…