TY - JOUR

T1 - Formulae for Askey-Wilson moments and enumeration of staircase tableaux

AU - Corteel, S.

AU - Stanley, R.

AU - Stanton, D.

AU - Williams, L.

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Askey-Wilson polynomials

KW - Asymmetric exclusion process

KW - Matchings

KW - Permutations

KW - Staircase tableaux

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U2 - 10.1090/S0002-9947-2012-05588-7

DO - 10.1090/S0002-9947-2012-05588-7

M3 - Article

AN - SCOPUS:84864113246

SN - 0002-9947

VL - 364

SP - 6009

EP - 6037

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 11

ER -