An explicit double-exponential upper bound on the regularity of OI-modules presented in finite degrees, together with a new inductive method for proving their structural properties.
Upper bounds of homological invariants of $FI_G$-modules
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abstract
In this paper we use a homological approach to obtain upper bounds for a few homological invariants of $FI_G$-modules $V$. These upper bounds are expressed in terms of the generating degree and torsion degree, which measure the top and socle of $V$ under actions of non-invertible morphisms in the category respectively.
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An inductive method for $\mathrm{OI}$-modules
An explicit double-exponential upper bound on the regularity of OI-modules presented in finite degrees, together with a new inductive method for proving their structural properties.