15 citations · 20 across the 10 of their papers we have counts for
16 papers
A note on strong affine semigroups
I. García-Marco, R. Tapia-Ramos, A. Vigneron-Tenorio
This work introduces and studies strong affine semigroups, extending the notion of strong numerical semigroups to the higher-dimensional setting. We show that non-numerical strong…
Generalized Andrásfai graphs and special Betti diagrams of edge ideals
Sara Asensio, Ignacio García-Marco, Philippe Gimenez
Edge ideals of graphs were introduced by Villarreal in 1990, and have been the subject of many studies since then. In the same year, Fröberg characterized edge ideals with regulari…
Castelnuovo-Mumford regularity of toric varieties with at most one singular point
Ignacio García-Marco, Philippe Gimenez, Mario González-Sánchez
We establish upper bounds for the Castelnuovo--Mumford regularity of the coordinate ring of a simplicial projective toric variety with at most one singular point. In the smooth cas…
Universally free numerical semigroups
Ignacio García Marco, Pedro A. García-Sánchez, Ignacio Ojeda +1
A numerical semigroup is said to be universally free if it is free for any possible arrangement of its minimal generating set. In this work, we establish that toric ideals associat…
High dimensional affine codes whose square has a designed minimum distance
Ignacio García-Marco, Irene Márquez-Corbella, Diego Ruano
Given a linear code , its square code is the span of all component-wise products of two elements of . Motivated by applications in mul…
Chomp on numerical semigroups
Ignacio García-Marco, Kolja Knauer
We consider the two-player game chomp on posets associated to numerical semigroups and show that the analysis of strategies for chomp is strongly related to classical properties of…
On the linear independence of shifted powers
Ignacio García-Marco, Pascal Koiran, Timothée Pecatte
We call shifted power a polynomial of the form . The main goal of this paper is to obtain broadly applicable criteria ensuring that the elements of a finite family of…
On the complexity of partial derivatives
Ignacio Garcia-Marco, Pascal Koiran, Timothée Pecatte +1
The method of partial derivatives is one of the most successful lower bound methods for arithmetic circuits. It uses as a complexity measure the dimension of the span of the partia…
Reconstruction Algorithms for Sums of Affine Powers
Ignacio Garcia-Marco, Pascal Koiran, Timothée Pecatte
In this paper we study sums of powers of affine functions in (mostly) one variable. Although quite simple, this model is a generalization of two well-studied models: Waring decompo…
Algebraic invariants of projective monomial curves associated to generalized arithmetic sequences
Isabel Bermejo, Eva García-Llorente, Ignacio García-Marco
Let be an infinite field and let be a generalized arithmetic sequence of positive integers, i.e., there exist such that $m_i = h m_…
Drawing graphs with vertices and edges in convex position
Ignacio García-Marco, Kolja Knauer
A graph has strong convex dimension , if it admits a straight-line drawing in the plane such that its vertices are in convex position and the midpoints of its edges are also in…
Lower Bounds by Birkhoff Interpolation
Ignacio Garcia-Marco, Pascal Koiran
In this paper we give lower bounds for the representation of real univariate polynomials as sums of powers of degree 1 polynomials. We present two families of polynomials of degree…
Log-concavity and lower bounds for arithmetic circuits
Ignacio García-Marco, Pascal Koiran, Sébastien Tavenas
One question that we investigate in this paper is, how can we build log-concave polynomials using sparse polynomials as building blocks? More precisely, let $f = \sum\_{i = 0}^d a\…
Matroid toric ideals: complete intersection, minors and minimal systems of generators
Ignacio García-Marco, Jorge Luis Ramírez Alfonsín
In this paper, we investigate three problems concerning the toric ideal associated to a matroid. Firstly, we list all matroids such that its corresponding toric ideal…
Complete intersections in certain affine and projective monomial curves
I. Bermejo, I. García-Marco
Let be an arbitrary field, the purpose of this work is to provide families of positive integers such that either the toric ideal $I_{\mathcal…
Möbius function of semigroup posets through Hilbert series
Jonathan Chappelon, Ignacio García-Marco, Luis Pedro Montejano +1
In this paper, we investigate the M{ö}bius function associated to a (locally finite) poset arising from a semigroup of . We introduce…