Blowup algebras of square-free monomial ideals and some links to combinatorial optimization problems
Abstract
Let I=(xv1,...,xvq be a square-free monomial ideal of a polynomial ring K[x1,...,xn] over an arbitrary field K and let A be the incidence matrix with column vectors v1,...,vq. We will establish some connections between algebraic properties of certain graded algebras associated to I and combinatorial optimization properties of certain polyhedrons and clutters associated to A and I respectively. Some applications to Rees algebras and combinatorial optimization are presented. We study a conjecture of Conforti and Cornu\'ejols using an algebraic approach.
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