Formulae for Askey-wilson Moments and Enumeration of Staircase Tableaux
نویسنده
چکیده
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 [11, 12]. This gives us a direct combinatorial formula for these moments, which is related to, but more elegant than the formula given in [11]. 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. [
منابع مشابه
Moments of Askey-Wilson polynomials
New formulas for the n moment μn(a, b, c, d; q) of the Askey-Wilson polynomials are given. These are derived using analytic techniques, and by considering three combinatorial models for the moments: Motzkin paths, matchings, and staircase tableaux. A related positivity theorem is given and another one is conjectured. Résumé. Nous présentons de nouvelles formules pour les n-moments μn(a, b, c, d...
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