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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Clusters, Coxeter-sortable elements and noncrossing partitions
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by Nathan Reading PDF
Trans. Amer. Math. Soc. 359 (2007), 5931-5958

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.
References
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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
  • MR Author ID: 643756
  • Email: nreading@umich.edu, nathan_reading@ncsu.edu
  • Received by editor(s): August 18, 2005
  • Published electronically: June 27, 2007
  • Additional Notes: The author was partially supported by NSF grant DMS-0202430.
  • © Copyright 2007 Nathan Reading
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 5931-5958
  • MSC (2000): Primary 20F55; Secondary 05E15, 05A15
  • DOI: https://doi.org/10.1090/S0002-9947-07-04319-X
  • MathSciNet review: 2336311