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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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Formulae for Askey-Wilson moments and enumeration of staircase tableaux
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by S. Corteel, R. Stanley, D. Stanton and L. Williams PDF
Trans. Amer. Math. Soc. 364 (2012), 6009-6037 Request permission

Abstract:

We explain how the moments of the (weight function of the) Askey-Wilson polynomials are related to the enumeration of the staircase tableaux introduced by the first and fourth authors. This gives us a direct combinatorial formula for these moments, which is related to, but more elegant than the formula given in their earlier paper. Then we use techniques developed by Ismail and the third author to give explicit formulae for these moments and for the enumeration of staircase tableaux. Finally we study the enumeration of staircase tableaux at various specializations of the parameterizations; for example, we obtain the Catalan numbers, Fibonacci numbers, Eulerian numbers, the number of permutations, and the number of matchings.
References
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Additional Information
  • S. Corteel
  • Affiliation: LIAFA, Centre National de la Recherche Scientifique et Université Paris Diderot, Paris 7, Case 7014, 75205 Paris Cedex 13 France
  • MR Author ID: 633477
  • Email: corteel@liafa.univ-paris-diderot.fr
  • R. Stanley
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02138
  • MR Author ID: 166285
  • Email: rstan@math.mit.edu
  • D. Stanton
  • Affiliation: Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
  • Email: stanton@math.umn.edu
  • L. Williams
  • Affiliation: Department of Mathematics, University of California, Berkeley, Evans Hall Room 913, Berkeley, California 94720
  • MR Author ID: 611667
  • Email: williams@math.berkeley.edu
  • Received by editor(s): August 13, 2010
  • Received by editor(s) in revised form: March 16, 2011
  • Published electronically: May 2, 2012
  • Additional Notes: The first author was partially supported by ANR grant ANR-08-JCJC-0011
    The second author was partially supported by NSF grant No. 0604423
    The fourth author was partially supported by NSF grant DMS-0854432 and an Alfred Sloan Fellowship.
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 6009-6037
  • MSC (2010): Primary 05A15; Secondary 33C45, 82B23
  • DOI: https://doi.org/10.1090/S0002-9947-2012-05588-7
  • MathSciNet review: 2946941