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

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DMTCS vol 6 no 2 (2004), pp. 223-252

Discrete Mathematics & Theoretical Computer Science


Volume 6 n° 2 (2004), pp. 223-252

author:Eric Babson and Victor Reiner
title:Coxeter-like complexes
keywords:Coxeter complex, simplicial poset, Boolean complex, chessboard complex, Shephard group, unitary reflection group, simplex of groups, homology representation
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 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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reference: Eric Babson and Victor Reiner (2004), Coxeter-like complexes, Discrete Mathematics and Theoretical Computer Science 6, pp. 223-252
bibtex:For a corresponding BibTeX entry, please consider our BibTeX-file.
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