2010/07/29 by Sylvie Corteel, Richard P. Stanley, Richard Stanley +6
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Authorship Attribution and Profiling #Combinatorics (math.CO) #FOS: Mathematics #math.CO #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1007.5174
28 pages; added acknowledgements
openalex publication_date 2010/07/29 · arxiv created 2010/08/13 · arxiv updated 2010/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. 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.