2604.01142 Explicit Non-Unimodal Hilbert Functions for Graded Artinian Gorenstein Algebras: Computer-Verified Constructions in Codimension 5 and 6
We construct the smallest known graded Artinian Gorenstein algebras whose Hilbert functions fail to be unimodal. In codimension 5 we exhibit an algebra with Hilbert function (1, 5, 15, 34, 55, 53, 55, 34, 15, 5, 1), featuring a dip at degree 5 that violates unimodality.