Buchsbaum and Eulerian complexes Original Research Article

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.