Existence of non-unimodal codimension-four Hilbert vectors

Determine whether non-unimodal Hilbert vectors exist for standard graded Artinian Gorenstein algebras of codimension four.

Background

The paper discusses the classification of Hilbert vectors for standard graded Artinian Gorenstein algebras. Codimensions at most three are known to admit only unimodal Hilbert vectors, while non-unimodal vectors are known in every codimension at least five. The unresolved intermediate case is codimension four.