Linear quotients, linear resolutions and the lcm-lattice

Abstract: Linear resolutions and the stronger notion of linear quotients are important properties of monomial ideals. In this paper, we fully characterize linear resolutions and linear quotients in terms of the lcm-lattice of monomial ideals. These results complement characterizations of these two properties in terms of the Alexander dual of the corresponding Stanley-Reisner simplicial complex. In addition, we discuss applications to the case of edge ideals.