 
Summary: DOI:
c 2008 by Institut MittagLeffler. All rights reserved
Ark. Mat., 00 (2008), 112
Some combinatorial properties of flag simplicial
pseudomanifolds and spheres
Christos A. Athanasiadis
Dedicated to Anders Bjšorner on the occasion of his sixtieth birthday
Abstract. A simplicial complex is called flag if all minimal nonfaces of have at most two
elements. The following are proved: First, if is a flag simplicial pseudomanifold of dimension d
1, then the graph of (i) is (2d2)vertexconnected and (ii) has a subgraph which is a subdivision
of the graph of the ddimensional crosspolytope. Second, the hvector of a flag simplicial homology
sphere of dimension d1 is minimized when is the boundary complex of the ddimensional
crosspolytope.
1. Introduction
We will be interested in finite simplicial complexes. Such a complex is called
flag if every set of vertices which are pairwise joined by edges in is a face of
. For instance, every order complex (meaning the simplicial complex of all chains
in a finite partially ordered set) is a flag complex. According to [11, p. 100], flag
complexes form a fascinating class of simplicial complexes which deserves further
study. The class of flag complexes coincides with that of clique complexes of finite
