Coxeter-like complexes

Abstract : 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 S_n 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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Discrete Mathematics and Theoretical Computer Science, DMTCS, 2004, 6 (2), pp.223-252
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Eric Babson, Victor Reiner. Coxeter-like complexes. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2004, 6 (2), pp.223-252. 〈hal-00959006〉

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