4 papers · 1 filter
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…