Discrete Mathematics & Theoretical Computer Science, Vol 6, No 2 (2004)

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Coxeter-like complexes

Eric Babson, Victor Reiner


Motivated by the Coxeter complex associated to a Coxeter system (W,S), we introduce a simplicial regular cell complex Δ(G,S) 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 Δ(G,S), and in particular the representations of G on its homology groups. We look closely at the case of the symmetric group Sn minimally generated by (not necessarily adjacent) transpositions, and their type-selected subcomplexes. These include not only the Coxeter complexes of type A, but also the well-studied chessboard complexes.

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