Stanley-Reisner Ideals with Pure Resolutions

Abstract

This paper investgates Stanley-Reisner ideals with pure resolutions. We first describe two infinite families of such ideals associated to highly symmetric complexes. We then prove a partial analogue to the first Boij-Söderberg Conjecture for Stanley-Reisner ideals, by detailing an algorithm for constructing Stanley-Reisner ideals with pure Betti diagrams of any given shape, save for an initial shift.

42 pages