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Blowup algebras of square-free monomial ideals and some links to combinatorial optimization problems

I. Gitler·E. Reyes·R. H. Villarreal
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Abstract

Let I=(x^{v_1},...,x^{v_q} 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 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 Cornuéjols using an algebraic approach.

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I. Gitler, E. Reyes, R. H. Villarreal. 2009-01-27. Blowup algebras of square-free monomial ideals and some links to combinatorial optimization problems. https://arxiv.org/abs/math/0609609

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