Abstract
Let Δ be a finite simplicial complex, and K [ Δ] its Stanley-Reisner ring. We show that if Δ is Eulerian, then every depth of K[ Δ] is possible, and we find all possible depths of K [ Δ] for Buchsbaum Eulerian Δ, dealing with the orientable and nonorientable cases separately. In addition, we find all possible betti sequences of Buchsbaum-Eulerian, Eulerian, and semi-Eulerian complexes.
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