Minimal cellular resolutions of monomial ideals with five generators and their Artinian reductions

Abstract: We prove that monomial ideals with at most five generators and their Artinian reductions have minimal generalized Barile-Macchia resolutions. As a corollary, these ideals have minimal cellular resolutions, extending a result by Faridi, D.G, Ghorbanic, and Pour. This corollary is independently obtained by Montaner, Garc\'{i}a, and Mafi, using a different class of cellular resolutions called pruned resolutions.