An inductive method for $\mathrm{OI}$-modules

Abstract

In this paper we introduce an inductive method to study $\mathrm{OI}$-modules presented in finite degrees, where $\mathrm{OI}$ is a skeleton of the category of finitely totally ordered sets and strictly increasing maps. As an application, we obtain an explicit upper bound for the Castelnuovo-Mumford regularity of $\mathrm{OI}$-modules.

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References in corpus (9)

• FI-modules and stability for representations of symmetric groups
• Representation theory and homological stability
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• Homology of FI-modules
• Homological Invariants of FI-modules and FI_G-modules
• A long exact sequence for homology of FI-modules
• Periodicity in the cohomology of symmetric groups via divided powers
• Depth and the Local Cohomology of FI_G-modules
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