Coxeter-like complexes 
V. Reiner and E. Babson

ABSTRACT: Motivated by the Coxeter complex associated 
to a Coxeter system (W,S), we introduce a simplicial 
regular cell complex with a G-action associated to any 
pair (G,S) where G is a group and S is a finite set of 
generators for G which is minimal with respect to inclusion. 
We examine the topology of this complex (G,S), and in 
particular the representations of G on its homology groups. 
We look closely at the case of the symmetric group on n 
letters along with a choice of a minimal set of generating 
transpositions. This corresponds to a choice of a spanning 
tree on vertex set {1,2,...,n}. This naturally leads to the 
study of a slightly larger class of simplicial complexes, 
including not only the Coxeter complexes of type A and all 
of their type-selected subcomplexes, but also the well-studied 
chessboard complexes.