Geodesic
Coxeter-like complexes
Discrete mathematics & theoretical computer science, Tome 6 (2003-2004) no. 2.

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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. 
@article{DMTCS_2004_6_2_a3,
     author = {Babson, Eric and Reiner, Victor},
     title = {Coxeter-like complexes},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
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     number = {2},
     year = {2003-2004},
     doi = {10.46298/dmtcs.312},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.312/}
}
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Babson, Eric; Reiner, Victor. Coxeter-like complexes. Discrete mathematics & theoretical computer science, Tome 6 (2003-2004) no. 2. doi : 10.46298/dmtcs.312. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.312/

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