Morse resolutions of powers of square-free monomial ideals of projective dimension one

Abstract

Let I be a square-free monomial ideal of projective dimension one. Starting with the Taylor complex on the generators of $$I^r$$ , we use discrete Morse theory to describe a CW complex that supports a minimal free resolution of $$I^r$$ . To do so, we concretely describe the acyclic matching on the faces of the Taylor complex.