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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2004

Coxeter-like complexes


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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hal-00959006 , version 1 (13-03-2014)



Eric Babson, Victor Reiner. Coxeter-like complexes. Discrete Mathematics and Theoretical Computer Science, 2004, Vol. 6 no. 2 (2), pp.223-252. ⟨10.46298/dmtcs.312⟩. ⟨hal-00959006⟩


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