Hypergraphs with high projective dimension and 1-dimensional Hypergraphs
Abstract
We prove a sufficient and a necessary condition for a square-free monomial ideal J associated to a (dual) hypergraph to have projective dimension equal to the minimal number of generators of J minus 2. We also provide an effective explicit procedure to compute the projective dimension of 1-dimensional hypergraphs H when each connected component contains at most one cycle. An algorithm to compute the projective dimension is also included. Applications of these results are given; they include, for instance, computing the projective dimension of monomial ideals whose associated hypergraph has a spanning Ferrers graph.
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