64 citations · 304 across the 49 of their papers we have counts for
7 papers · 1 filter
Duality, a-invariants and canonical modules of rings arising from linear optimization problems
Joseph P. Brennan, Luis A. Dupont, Rafael H. Villarreal
The aim of this paper is to study integer rounding properties of various systems of linear inequalities to gain insight about the algebraic properties of Rees algebras of monomial…
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…
Cohen-Macaulay clutters with combinatorial optimization properties and parallelizations of normal edge ideals
Luis A. Dupont, Enrique Reyes-Espinoza, Rafael H. Villarreal
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-Maca…
Cohen-Macaulay admissible clutters
Huy Tai Ha, Susan Morey, Rafael H. Villarreal
There is a one-to-one correspondence between square-free monomial ideals and clutters, which are also known as simple hypergraphs. It was conjectured that unmixed admissible clutte…
Systems with the integer rounding property in normal monomial subrings
Luis A. Dupont, Carlos Renteria-Marquez, Rafael H. Villarreal
Let C be a clutter and let A be its incidence matrix. If the linear system x>=0;xA<=1 has the integer rounding property, we give a description of the canonical module and the a-inv…
Edge ideals of clique clutters of comparability graphs and the normality of monomial ideals
Luis A. Dupont, Rafael H Villarreal
Let (P,<) be a finite poset and let G be its comparability graph. If cl(G) is the clutter of maximal cliques of G, we prove that cl(G) satisfies the max-flow min-cut property and t…