Formulae for Askey-Wilson moments and enumeration of staircase tableaux

S. Corteel, R. Stanley, D. Stanton, L. Williams

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)6009-6037
Number of pages29
JournalTransactions of the American Mathematical Society
Volume364
Issue number11
DOIs
StatePublished - 2012

Keywords

  • Askey-Wilson polynomials
  • Asymmetric exclusion process
  • Matchings
  • Permutations
  • Staircase tableaux

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