Edge ideals of clique clutters of comparability graphs and the normality of monomial ideals

Authors

  • Luis A. Dupont
  • Rafael H. Villarreal

DOI:

https://doi.org/10.7146/math.scand.a-15126

Abstract

The normality of a monomial ideal is expressed in terms of lattice points of blocking polyhedra and the integer decomposition property. For edge ideals of clutters this property characterizes normality. Let $G$ be the comparability graph of a finite poset. If $\mathrm{cl}(G)$ is the clutter of maximal cliques of $G$, we prove that $\mathrm{cl}(G)$ satisfies the max-flow min-cut property and that its edge ideal is normally torsion free. Then we prove that edge ideals of complete admissible uniform clutters are normally torsion free.

Downloads

Published

2010-03-01

Issue

Section

Articles