Stanley-Reisner Ideals with Pure Resolutions

Abstract

We investigate Stanley-Reisner ideals with pure resolutions. To do this, we introduce the family of PR complexes, simplicial complexes whose dual Stanley-Reisner ideals have pure resolutions. We present two infinite families of highly-symmetric PR complexes. We also prove a partial analogue to the first Boij-S\"{o}derberg Conjecture for Stanley-Reisner ideals, by detailing an algorithm for constructing Stanley-Reisner ideals with pure Betti diagrams of any given shape, save for the initial shift $c_0$.