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...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2004-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/312/pdf |
| _version_ | 1797270235231813632 |
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| author | Eric Babson Victor Reiner |
| author_facet | Eric Babson Victor Reiner |
| author_sort | Eric Babson |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T02:01:02Z |
| format | Article |
| id | doaj.art-c3c1e6b5157246b084422fc7454d6bc7 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:01:02Z |
| publishDate | 2004-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-c3c1e6b5157246b084422fc7454d6bc72024-03-07T15:06:37ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502004-01-01Vol. 6 no. 210.46298/dmtcs.312312Coxeter-like complexesEric Babson0Victor Reiner1Department of Mathematics [Seattle]School of MathematicsMotivated 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.https://dmtcs.episciences.org/312/pdfcoxeter complexsimplicial posetboolean complexchessboard complexshephard groupunitary reflection groupsimplex of groupshomology representation[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Eric Babson Victor Reiner Coxeter-like complexes Discrete Mathematics & Theoretical Computer Science coxeter complex simplicial poset boolean complex chessboard complex shephard group unitary reflection group simplex of groups homology representation [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Coxeter-like complexes |
| title_full | Coxeter-like complexes |
| title_fullStr | Coxeter-like complexes |
| title_full_unstemmed | Coxeter-like complexes |
| title_short | Coxeter-like complexes |
| title_sort | coxeter like complexes |
| topic | coxeter complex simplicial poset boolean complex chessboard complex shephard group unitary reflection group simplex of groups homology representation [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/312/pdf |
| work_keys_str_mv | AT ericbabson coxeterlikecomplexes AT victorreiner coxeterlikecomplexes |