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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Signed words and permutations, I: A fundamental transformation
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by Dominique Foata and Guo-Niu Han PDF
Proc. Amer. Math. Soc. 135 (2007), 31-40 Request permission

Abstract:

The statistics major index and inversion number, usually defined on ordinary words, have their counterparts in signed words, namely the so-called flag-major index and flag-inversion number. We give the construction of a new transformation on those signed words that maps the former statistic onto the latter one. It is proved that the transformation also preserves two other set-statistics: the inverse ligne of route and the lower records.
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Additional Information
  • Dominique Foata
  • Affiliation: Institut Lothaire, 1 rue Murner, F-67000 Strasbourg, France
  • Email: foata@math.u-strasbg.fr
  • Guo-Niu Han
  • Affiliation: I.R.M.A. UMR 7501, Université Louis Pasteur et CNRS, 7 rue René-Descartes, F-67084 Strasbourg, France
  • MR Author ID: 272629
  • Email: guoniu@math.u-strasbg.fr
  • Received by editor(s): April 11, 2005
  • Received by editor(s) in revised form: August 4, 2005
  • Published electronically: June 29, 2006

  • Dedicated: This paper is dedicated to the memory of Percy Alexander MacMahon
  • Communicated by: John R. Stembridge
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 31-40
  • MSC (2000): Primary 05A15, 05A30, 05E15
  • DOI: https://doi.org/10.1090/S0002-9939-06-08436-X
  • MathSciNet review: 2280171