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Clusters, Coxeter-sortable elements and noncrossing partitions
Author(s):
Nathan
Reading
Journal:
Trans. Amer. Math. Soc.
359
(2007),
5931-5958.
MSC (2000):
Primary 20F55;
Secondary 05E15, 05A15
Posted:
June 27, 2007
MathSciNet review:
2336311
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Abstract |
References |
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Abstract:
We introduce Coxeter-sortable elements of a Coxeter group  For finite  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:
10.1090/S0002-9947-07-04319-X
PII:
S 0002-9947(07)04319-X
Received by editor(s):
August 18, 2005
Posted:
June 27, 2007
Additional Notes:
The author was partially supported by NSF grant DMS-0202430.
Copyright of article:
Copyright
2007,
Nathan Reading
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