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 -