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

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

2006-09-21

arxiv.org/abs/math/0609609v3

Rocky Mountain J. Math. 39 (2009), no. 1, 71--102

Mathematics

Commutative Algebra

Rocky Mountain J. Math. 39 (2009), no. 1, 71--102

Scientific paper

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 Cornu\'ejols using an algebraic approach.

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