Bounding the Projective Dimension of a Square-Free Monomial Ideal via Domination in Clutters
arXiv:1301.2665
Abstract
We introduce the concept of edgewise domination in clutters, and use it to provide an upper bound for the projective dimension of any squarefree monomial ideal. We then use a simple recursion to recover a formula for the projective dimension of a monomial ideal associated to a chordal clutter, as defined by Woodroofe in \cite{russ}. We also study a family of clutters associated to graphs, and show that these clutters are chordal if and only if the associated graph is. Finally, we compute domination parameters for certain classes of these clutters.
Theorem 4.5 from the previous version and some related statement has been removed due to a gap in its proof