A criterion for a monomial ideal to have a linear resolution in characteristic 2

TL;DR

This paper establishes a combinatorial criterion for when monomial ideals have linear resolutions specifically over fields of characteristic 2, and provides a new proof of Fröberg's theorem in this setting.

Contribution

It introduces a necessary and sufficient combinatorial condition for linear resolutions of monomial ideals over characteristic 2 fields and offers a new proof of Fröberg's theorem.

Findings

Provides a combinatorial criterion for linear resolutions in characteristic 2

Proves a new version of Fröberg's theorem for characteristic 2

Enhances understanding of monomial ideals in specific field characteristics

Abstract

In this paper we give a necessary and sufficient combinatorial condition for a monomial ideal to have a linear resolution over fields of characteristic 2. We also give a new proof of Fr\"oberg's theorem over fields of characteristic 2.