17 citations · 27 across the 7 of their papers we have counts for
9 papers · 1 filter
On the socle of Artinian algebras associated to graphs
Jorge Neves
Given a simple graph, consider the polynomial ring with coefficients in a field and variables identified with the edges of the graph. Given a non-empty even cardinality Eulerian su…
Parameterized codes over graphs
Jorge Neves, Maria Vaz Pinto
In this article we review known results on parameterized linear codes over graphs, introduced by Rentería, Simis and Villarreal in 2011. Very little is known about their basic para…
Joins, Ears and Castelnuovo-Mumford regularity
Jorge Neves, Maria Vaz Pinto, Rafael H. Villarreal
We introduce a new class of polynomial ideals associated to a simple graph, . Let be the polynomial ring on the edges of and the polynomial ring on the ver…
Regularity of the vanishing ideal over a bipartite nested ear decomposition
Jorge Neves
We study the Castelnuovo-Mumford regularity of the vanishing ideal over a bipartite graph endowed with a decomposition of its edge set. We prove that, under certain conditions, the…
Regularity of the vanishing ideal over a parallel composition of paths
Antonio Macchia, Jorge Neves, Maria Vaz Pinto +1
Let G be a graph obtained by taking r>=2 paths and identifying all first vertices and identifying all the last vertices. We compute the Castelnuovo--Mumford regularity of the quoti…
Codes over a weighted torus
Eduardo Dias, Jorge Neves
We define weighted projective Reed-Muller codes over a subset of weighted projective space over a finite field. We focus on the case when the set X is a projective weighted torus.…
Vanishing ideals over complete multipartite graphs
Jorge Neves, Maria Vaz Pinto
We study the vanishing ideal of the parametrized algebraic toric associated to the complete multipartite graph $\G=\mathcal{K}_{α_1,...,α_r}$ over a finite field of order . We g…
Regularity and algebraic properties of certain lattice ideals
Jorge Neves, Maria Vaz Pinto, Rafael H. Villarreal
We study the regularity and the algebraic properties of certain lattice ideals. We establish a map I --> I\~ between the family of graded lattice ideals in an N-graded polynomial r…
Vanishing ideals over graphs and even cycles
Jorge Neves, Maria Vaz Pinto, Rafael H. Villarreal
Let X be an algebraic toric set in a projective space over a finite field. We study the vanishing ideal, I(X), of X and show some useful degree bounds for a minimal set of generato…