Abstract
We survey recent studies and results on the following problem: for which function \(f: {\mathbb N} \rightarrow {\mathbb Z}_{\ge 0}\) does there exist a homogeneous ideal Q in a polynomial ring S such that (a) depthS∕Qt = f(t) for all t ≥ 1, or (b) depthS∕Q(t) = f(t) for all t ≥ 1?
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