... varieties, and related results,” in Commutative Algebra and Combinatorics (M. Nagata and H.Matsumura, eds.), Advanced Studies in Pure Mathematics 11,Kinokuniya,Tokyo, and North-Holland, Amsterdam/New ... Section 3, and al-gebraic shifting in Section 4. In Section 5, we prove our main result. Finally, Section 6 con-tains two corollaries concerning nonpure shellability and iterated Betti numbers (a ... (Theorem 5.1). In Section 2, we introduce basic definitions, including the f-triangle and the h-triangle.Cohen-Macaulayness and sequential Cohen-Macaulayness are discussed in Section 3, and al-gebraic...