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We give an alternate proof for a theorem of Migliore and Nagel. Inparticular, we show that if $\mathcal H$ is an SI-sequence, then the collectionof Betti diagrams for all Artinian Gorenstein $k$-algebras with the weakLefschetz property and Hilbert function $\mathcal H$ has a unique largestelement.

Unique maximal Betti diagrams for Artinian Gorenstein $k$-algebras with the weak Lefschetz property