{"docId":312,"paperId":312,"url":"https:\/\/dmtcs.episciences.org\/312","doi":"10.46298\/dmtcs.312","journalName":"Discrete Mathematics & Theoretical Computer Science","issn":"","eissn":"1365-8050","volume":[{"vid":78,"name":"Vol. 6 no. 2"}],"section":[],"repositoryName":"HAL","repositoryIdentifier":"hal-00959006","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-00959006v1","dateSubmitted":"2015-03-26 16:18:10","dateAccepted":"2015-06-09 14:45:41","datePublished":"2004-01-01 08:00:00","titles":{"fr":"Coxeter-like complexes"},"authors":["Babson, Eric","Reiner, Victor"],"abstracts":{"en":"Motivated by the Coxeter complex associated to a Coxeter system (W,S), we introduce a simplicial regular cell complex \u0394 (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 \u0394 (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."},"keywords":{"en":["Coxeter complex","simplicial poset","Boolean complex","chessboard complex","Shephard group","unitary reflection group","simplex of groups","homology representation"],"0":"[INFO.INFO-DM]Computer Science [cs]\/Discrete Mathematics [cs.DM]"}}