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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Clusters, Coxeter-sortable elements and noncrossing partitions


Author: Nathan Reading
Journal: Trans. Amer. Math. Soc. 359 (2007), 5931-5958
MSC (2000): Primary 20F55; Secondary 05E15, 05A15
Published electronically: June 27, 2007
MathSciNet review: 2336311
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Abstract: 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.


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Additional Information

Nathan Reading
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043
Address at time of publication: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205
Email: nreading@umich.edu, nathan_reading@ncsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04319-X
PII: S 0002-9947(07)04319-X
Received by editor(s): August 18, 2005
Published electronically: June 27, 2007
Additional Notes: The author was partially supported by NSF grant DMS-0202430.
Article copyright: © Copyright 2007 Nathan Reading