arXiv Analytics

Sign in

arXiv:math/0507186 [math.CO]AbstractReferencesReviewsResources

Clusters, Coxeter-sortable elements and noncrossing partitions

Nathan Reading

Published 2005-07-08, updated 2005-12-14Version 2

We introduce Coxeter-sortable elements of a Coxeter group W. For finite W, we give bijective proofs that Coxeter-sortable elements are equinumerous with clusters and with noncrossing partitions. We characterize Coxeter-sortable elements in terms of their inversion sets and, in the classical cases, in terms of permutations.

Comments: Minor changes in exposition, including: More precise statement in Remark 6.8; Added Remark 6.9, an observation which is helpful in the sequel (math.CO/0512339); Updated textual references to the sequel and to a paper in preparation (with D. Speyer). 28 pages, 8 figures
Categories: math.CO
Subjects: 20F55, 05E15, 05A15
Related articles: Most relevant | Search more
arXiv:1111.7172 [math.CO] (Published 2011-11-30, updated 2014-08-12)
EL-Shellability and Noncrossing Partitions Associated with Well-Generated Complex Reflection Groups
arXiv:math/0701792 [math.CO] (Published 2007-01-27, updated 2009-03-30)
Cyclic sieving of noncrossing partitions for complex reflection groups
arXiv:math/0702177 [math.CO] (Published 2007-02-07)
Alternating subgroups of Coxeter groups

Links

Toolbox