Details:
Title  Algebraic and combinatorial properties of ideals and algebras of uniform clutters of TDI systems.  Author(s)  Luis A. Dupont, Rafael H. Villarreal  Type  Article in Journal  Abstract  Let  be a uniform clutter and let A be the incidence matrix of  . We denote the column vectors of A by v 1,…,v q . Under certain conditions we prove that  is vertex critical. If  satisfies the maxflow mincut property, we prove that A diagonalizes over ℤ to an identity matrix and that v 1,…,v q form a Hilbert basis. We also prove that if  has a perfect matching such that  has the packing property and its vertex covering number is equal to 2, then A diagonalizes over ℤ to an identity matrix. If A is a balanced matrix we prove that any regular triangulation of the cone generated by v 1,…,v q is unimodular. Some examples are presented to show that our results only hold for uniform clutters. These results are closely related to certain algebraic properties, such as the normality or torsionfreeness, of blowup algebras of edge ideals and to finitely generated abelian groups. They are also related to the theory of Gröbner bases of toric ideals and to Ehrhart rings.  Keywords  Uniform clutter, Maxflow mincut, Normality, Rees algebra, Ehrhart ring, Balanced matrix, Edge ideal, Hilbert bases, Smith normal form, Unimodular regular, triangulation  ISSN  13826905; 15732886/e 
URL 
http://link.springer.com/article/10.1007%2Fs1087800992447 
Language  English  Journal  J. Comb. Optim.  Volume  21  Number  3  Pages  269292  Publisher  Springer US, New York, NY  Year  2011  Edition  0  Translation 
No  Refereed 
No 
