Face numbers of generalized balanced Cohen-Macaulay complexes

Abstract

A common generalization of two theorems on the face numbers of Cohen-Macaulay (CM, for short) simplicial complexes is established: the first is the theorem of Stanley (necessity) and Björner-Frankl-Stanley (sufficiency) that characterizes all possible face numbers of abalanced CM complexes, while the second is the theorem of Novik (necessity) and Browder (sufficiency) that characterizes the face numbers of CM subcomplexes of the join of the boundaries of simplices.

A Tale of Centrally Symmetric Polytopes and Spheres

“…Note also that the proof of Theorem 5.3 almost does not use the central symmetry assumption: instead, it relies on a much weaker condition, namely, on the existence of a free involution φ : V (∆) → V (∆) on the vertex set of ∆ such that {v, φ(v)} is not an edge of ∆ for all v ∈ V (∆). We refer our readers to [59] for more details on the h-vectors of simplicial spheres and manifolds possessing this weaker property and to [17] for a complete characterization of h-vectors of CM complexes with this property.…”

Face Numbers of Certain Cohen–Macaulay Flag Complexes

“…Outline. We first outline our approach, which is adapted from that used in [10] and [2]. Throughout the following, let ∆ be a (d−1)-dimensional k-CM complex on V , n = |V |, and…”