Name
Title | ||
|---|---|---|
Algebraic and combinatorial properties of ideals and algebras of uniform clutters of TDI systems |
Abstract | ||
|---|---|---|
Let $\mathcal{C}$ be a uniform clutter and let A be the incidence matrix of $\mathcal{C}$ . We denote the column vectors of A by v 1,驴,v q . Under certain conditions we prove that $\mathcal{C}$ is vertex critical. If $\mathcal{C}$ satisfies the max-flow min-cut property, we prove that A diagonalizes over 驴 to an identity matrix and that v 1,驴,v q form a Hilbert basis. We also prove that if $\mathcal{C}$ has a perfect matching such that $\mathcal{C}$ has the packing property and its vertex covering number is equal to 2, then A diagonalizes over 驴 to an identity matrix. If A is a balanced matrix we prove that any regular triangulation of the cone generated by v 1,驴,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 torsion-freeness, 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. |
Year | DOI | Venue |
|---|---|---|
2011 | https://doi.org/10.1007/s10878-009-9244-7 | Journal of Combinatorial Optimization |
Keywords | Field | DocType |
Uniform clutter,Max-flow min-cut,Normality,Rees algebra,Ehrhart ring,Balanced matrix,Edge ideal,Hilbert bases,Smith normal form,Unimodular regular triangulation | Hilbert basis,Abelian group,Discrete mathematics,Mathematical optimization,Combinatorics,Vertex (geometry),Balanced matrix,Smith normal form,Identity matrix,Unimodular matrix,Mathematics,Incidence matrix | Journal |
Volume | Issue | ISSN |
21 | 3 | 1382-6905 |
Citations | PageRank | References |
1 | 0.41 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Luis A. Dupont | 1 | 1 | 0.41 |
| Rafael H. Villarreal | 2 | 75 | 15.69 |