5 citations · 7 across the 8 of their papers we have counts for
14 papers
Normally torsion-free edge ideals of weighted oriented graphs
Gonzalo Grisalde, Jose Martinez-Bernal, Rafael H. Villarreal
Let be the edge ideal of a weighted oriented graph , let be the underlying graph of , and let be the -th symbolic power of defined using the min…
Hamming Polynomial of a Demimatroid
Jose Martinez-Bernal, Miguel A. Valencia-Bucio, Rafael H. Villarreal
Following Britz, Johnsen, Mayhew and Shiromoto, we consider demi\-ma\-troids as a(nother) natural generalization of matroids. As they have shown, demi\-ma\-troids are the appropria…
Linear codes over signed graphs
Jose Martinez-Bernal, Miguel A. Valencia, Rafael H. Villarreal
We give formulas, in terms of graph theoretical invariants, for the minimum distance and the generalized Hamming weights of the linear code generated by the rows of the incidence m…
Nonvanishing Betti Numbers of Weakly Chordal Graphs
Jose Martinez-Bernal, Oscar A. Piza-Morales
We show that Kimura's necessary and sufficient condition for the non-vanishingness of multigraded Betti numbers of chordal graphs can be extended to the wider class of weakly chord…
Generalized Hamming weights of projective Reed--Muller-type codes over graphs
Jose Martinez-Bernal, Miguel A. Valencia-Bucio, Rafael H. Villarreal
Let be a connected graph and let be the set of projective points defined by the column vectors of the incidence matrix of over a field of any characteristi…
Depth and regularity of monomial ideals via polarization and combinatorial optimization
Jose Martínez-Bernal, Susan Morey, Rafael H. Villarreal +1
In this paper we use polarization to study the behavior of the depth and regularity of a monomial ideal , locally at a variable , when we lower the degree of all the highes…
Generalized minimum distance functions
Manuel Gonzalez-Sarabia, Jose Martínez-Bernal, Rafael H. Villarreal +1
Using commutative algebra methods we study the generalized minimum distance function (gmd function) and the corresponding generalized footprint function of a graded ideal in a poly…
Symbolic powers of monomial ideals and Cohen-Macaulay vertex-weighted digraphs
Philippe Gimenez, Jose Martínez-Bernal, Aron Simis +2
In this paper we study irreducible representations and symbolic Rees algebras of monomial ideals. Then we examine edge ideals associated to vertex-weighted oriented graphs. These a…
Minimum distance functions of complete intersections
Yuriko Pitones, Jose Martinez-Bernal, Rafael H. Villarreal
We study the footprint function, with respect to a monomial order, of complete intersection graded ideals in a polynomial ring with coefficients in a field. For graded ideals of di…
Minimum distance functions of graded ideals and Reed-Muller-type codes
Jose Martinez-Bernal, Yuriko Pitones, Rafael H. Villarreal
We introduce and study the minimum distance function of a graded ideal in a polynomial ring with coefficients in a field, and show that it generalizes the minimum distance of proje…
Associated primes of powers of edge ideals
Jose Martinez-Bernal, Susan Morey, Rafael H. Villarreal
Let G be a graph and let I be its edge ideal. Our main result shows that the sets of associated primes of the powers of I form an ascending chain. It is known that the sets of asso…
Combinatorics of symbolic Rees algebras of edge ideals of clutters
Jose Martinez-Bernal, Carlos Renteria, Rafael H. Villarreal
Let C be a clutter and let I be its edge ideal. We present a combinatorial description of the minimal generators of the symbolic Rees algebra Rs(I) of I. It is shown that the minim…
Ehrhart clutters: Regularity and Max-Flow Min-Cut
Jose Martinez-Bernal, Edwin O'Shea, Rafael H. Villarreal
If C is a clutter with n vertices and q edges whose clutter matrix has column vectors V={v1,...,vq}, we call C an Ehrhart clutter if {(v1,1),...,(vq,1)} is a Hilbert basis. Letting…
Toric ideals generated by circuits
Jose Martinez-Bernal, Rafael H. Villarreal
Let I be the toric ideal of a homogeneous normal configuration. We prove that I is generated by circuits if and only if each unbalanced circuit of I has a "connector" which is a li…