Stanley-Reisner Ideals with Pure Resolutions

TL;DR

This paper studies Stanley-Reisner ideals with pure resolutions, describing infinite families linked to symmetric complexes and providing an algorithm to construct ideals with specified pure Betti diagrams, advancing understanding of their algebraic structure.

Contribution

It introduces two infinite families of Stanley-Reisner ideals with pure resolutions and presents an algorithm for constructing ideals with any pure Betti diagram shape, except for an initial shift.

Findings

Identified two infinite families of ideals with pure resolutions

Developed an algorithm for constructing ideals with arbitrary pure Betti diagrams

Proved a partial analogue to the first Boij-Söderberg Conjecture for these ideals

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-S\"oderberg 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.