On the fully commutative elements of Coxeter groups
dc.contributor.author | Stembridge, John R. | en_US |
dc.date.accessioned | 2006-09-11T17:33:59Z | |
dc.date.available | 2006-09-11T17:33:59Z | |
dc.date.issued | 1996-10 | en_US |
dc.identifier.citation | Stembridge, John R.; (1996). "On the fully commutative elements of Coxeter groups." Journal of Algebraic Combinatorics 5(4): 353-385. <http://hdl.handle.net/2027.42/46260> | en_US |
dc.identifier.issn | 0925-9899 | en_US |
dc.identifier.issn | 1572-9192 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/46260 | |
dc.description.abstract | Let W be a Coxeter group. We define an element w ε W to be fully commutative if any reduced expression for w can be obtained from any other by means of braid relations that only involve commuting generators. We give several combinatorial characterizations of this property, classify the Coxeter groups with finitely many fully commutative elements, and classify the parabolic quotients whose members are all fully commutative. As applications of the latter, we classify all parabolic quotients with the property that (1) the Bruhat ordering is a lattice, (2) the Bruhat ordering is a distributive lattice, (3) the weak ordering is a distributive lattice, and (4) the weak ordering and Bruhat ordering coincide. | en_US |
dc.format.extent | 1624607 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Kluwer Academic Publishers; Springer Science+Business Media | en_US |
dc.subject.other | Mathematics | en_US |
dc.subject.other | Computer Science, General | en_US |
dc.subject.other | Group Theory and Generalizations | en_US |
dc.subject.other | Order, Lattices, Ordered Algebraic Structures | en_US |
dc.subject.other | Combinatorics | en_US |
dc.subject.other | Convex and Discrete Geometry | en_US |
dc.subject.other | Coxeter Group | en_US |
dc.subject.other | Reduced Word | en_US |
dc.subject.other | Heap | en_US |
dc.subject.other | Weak Order | en_US |
dc.subject.other | Bruhat Order | en_US |
dc.title | On the fully commutative elements of Coxeter groups | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, 48109-1109, Ann Arbor, Michigan | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/46260/1/10801_2004_Article_BF00193185.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/BF00193185 | en_US |
dc.identifier.source | Journal of Algebraic Combinatorics | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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