Formulae for Askey-Wilson moments and enumeration of staircase tableaux

Details Formulae for Askey-Wilson moments and enumeration of staircase tableaux Formulae for Askey-Wilson moments and enumeration of staircase tableaux

2010-07-29

arxiv.org/abs/1007.5174v2

Mathematics

Combinatorics

28 pages; added acknowledgements

Scientific paper

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.

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