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

الأصل · EN

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 Cornuéjols using an algebraic approach.