Enrique Reyes

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Let I = (x v1 ,. .. , x vq) be a square-free monomial ideal of a polynomial ring K[x 1 ,. .. , x n ] over an arbitrary field K and let A be the incidence matrix with column vectors v 1 ,. .. , v q. We will establish some connections between algebraic properties of certain graded algebras associated to I and combinatorial optimization properties of certain(More)
[1] Salt marshes are delicate landforms at the boundary between the sea and land. These ecosystems support a diverse biota that modifies the erosive characteristics of the substrate and mediates sediment transport processes. Here we present a broad overview of recent numerical models that quantify the formation and evolution of salt marshes under different(More)
Let C be a clutter with a perfect matching e1,. .. , eg of König type and let ∆C be the Stanley-Reisner complex of the edge ideal of C. If all c-minors of C have a free vertex and C is unmixed, we show that ∆C is pure shellable. We are able to describe in combinatorial terms when ∆C is pure. If C has no cycles of length 3 or 4, then it is shown that ∆C is(More)
Let G = (V, E) be a graph. If G is a König graph or if G is a graph without 3-cycles and 5-cycles, we prove that the following conditions are equivalent: ∆ G is pure shellable, R/I ∆ is Cohen-Macaulay, G is an unmixed vertex decomposable graph and G is well-covered with a perfect matching of König type e 1 ,. .. , e g without 4-cycles with two e i 's.(More)
We study the family of graphs whose number of primitive cycles equals its cycle rank. It is shown that this family is precisely the family of ring graphs. Then we study the complete intersection property of toric ideals of bipartite graphs and oriented graphs. An interesting application is that complete intersection toric ideals of bipartite graphs(More)
Let C be a uniform clutter and let I = I(C) be its edge ideal. We prove that if C satisfies the packing property (resp. max-flow min-cut property), then there is a uniform Cohen-Macaulay clutter C 1 satisfying the packing property (resp. max-flow min-cut property) such that C is a minor of C 1. For arbitrary edge ideals of clutters we prove that the(More)
We introduce 2-partitionable clutters as the simplest case of the class of k-partitionable clutters and study some of their combinatorial properties. In particular , we study properties of the rank of the incidence matrix of these clutters and properties of their minors. A well known conjecture of Conforti and Cornuéjols [1, 2] states: That all the clutters(More)
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