5 citations · 7 across the 8 of their papers we have counts for
12 papers · 1 filter
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…
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…