Lattices and Hypergraphs associated to square-free monomial ideals
arXiv:1804.05919
Abstract
Given a square-free monomial ideal in a polynomial ring over a field , one can associate it with its LCM-lattice and its hypergraph. In this short note, we establish the connection between the LCM-lattice and the hypergraph, and in doing so we provide a sufficient condition for removing higher dimension edges of the hypergraph without impacting the projective dimension of the square-free monomial ideal. We also offer algorithms to compute the projective dimension of a class of square-free monomial ideals built using the new result and previous results of Lin-Mantero.
The paper is split into two via the suggestion of the editor. The second part will be submitted soon