Further Applications of Clutter Domination Parameters to Projective Dimension
نویسندگان
چکیده
We study the relationship between the projective dimension of a squarefree monomial ideal and the domination parameters of the associated graph or clutter. In particular, we show that the projective dimensions of graphs with perfect dominating sets can be calculated combinatorially. We also generalize the wellknown graph domination parameter τ to clutters, obtaining bounds on the projective dimension analogous to those for graphs. Through Hochster’s Formula, our bounds on projective dimension also give rise to bounds on the homologies of the associated Stanley-Reisner complexes.
منابع مشابه
Bounding the Projective Dimension of a Squarefree Monomial Ideal via Domination in Clutters
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 compare this bound to a bound given by Faltings. Finally, we study a family of clutters associated to graphs and compute domination parameters for certain classes of these clutters.
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