Formulae for Askey-Wilson moments and enumeration of staircase tableaux
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S0002-9947-2012-05588-7.pdf
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370.2 KB
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Checksum (MD5)
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Author(s)
Corteel, S.
Stanton, D.
Williams, L.
Stanley, Richard P
Date Issued
May 2012
Journal
Transactions of the American Mathematical Society
Publisher
American Mathematical Society (AMS)
Citation
Corteel, S. et al. “Formulae for Askey-Wilson Moments and Enumeration of Staircase Tableaux.” Transactions of the American Mathematical Society 364, 11 (November 2012): 6009–6037 © 2012 American Mathematical Society
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1090/S0002-9947-2012-05588-7
