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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Computing reflection length in an affine Coxeter group
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by Joel Brewster Lewis, Jon McCammond, T. Kyle Petersen and Petra Schwer PDF
Trans. Amer. Math. Soc. 371 (2019), 4097-4127 Request permission

Abstract:

In any Coxeter group, the conjugates of elements in its Coxeter generating set are called reflections, and the reflection length of an element is its length with respect to this expanded generating set. In this article we give a simple formula that computes the reflection length of any element in any affine Coxeter group and we provide a simple uniform proof.
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Additional Information
  • Joel Brewster Lewis
  • Affiliation: Department of Mathematics, George Washington University, Washington, DC 20052
  • MR Author ID: 864355
  • Email: jblewis@gwu.edu
  • Jon McCammond
  • Affiliation: Department of Mathematics, University of California, Santa Barbara, Santa Barbara, California 93106
  • MR Author ID: 311045
  • Email: jon.mccammond@math.ucsb.edu
  • T. Kyle Petersen
  • Affiliation: Department of Mathematical Sciences, De Paul University, Chicago, Illinois 60614
  • MR Author ID: 723840
  • Email: tpeter21@depaul.edu
  • Petra Schwer
  • Affiliation: Department of Mathematics, Karlsruhe Institute of Technology, Englerstrasse 2, 76133 Karlsruhe, Germany
  • MR Author ID: 810162
  • Email: petra.schwer@kit.edu
  • Received by editor(s): October 18, 2017
  • Received by editor(s) in revised form: November 21, 2017
  • Published electronically: December 7, 2018
  • Additional Notes: The first author’s work was supported by NSF grant DMS-1401792
    The third author’s work was supported by a Simons Foundation collaboration travel grant.
    The fourth author’s work was supported by DFG grant SCHW 1550 4-1 within SPP 2026.
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 4097-4127
  • MSC (2010): Primary 20F55
  • DOI: https://doi.org/10.1090/tran/7472
  • MathSciNet review: 3917218