Formulae for Askey-Wilson moments and enumeration of staircase tableaux

By Sylvie Corteel, Richard P. Stanley, Dennis Stanton, Lauren K. Williams. 2010

54 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7848b8b598946e464f0fb560b9081eb8272b10d2

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Statistics and Probability

Citations in the corpus

Tableaux combinatorics for the asymmetric exclusion process and Askey-Wilson polynomials (2009, background): “In [13], we prove this with an explicit bijection, and also develop connections to other combinatorial objects, including matchings, permutations, and trees.”