Given any ordering of the first half of a Hilbert series, there exists an artinian Gorenstein algebra realizing it, proved via Nagata idealization of whiskered graphs and the graph Roller Coaster theorem.
Algebra 23 (1995), no
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Roller Coaster Gorenstein algebras and Koszul algebras failing the weak Lefschetz property
Given any ordering of the first half of a Hilbert series, there exists an artinian Gorenstein algebra realizing it, proved via Nagata idealization of whiskered graphs and the graph Roller Coaster theorem.