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

Wee Liang Gan, Liping Li

Published 2019-09-03, updated 2020-06-01Version 2

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.