Moments of Askey-Wilson polynomials

Recently, Stanton and the speaker found new formulas for the moment mu_n(a,b,c,d;q) of Askey-Wilson polynomials. They also found a nice combinatorial formula for the moment when d = 0. However, their proof was not combinatorial. In this talk I will explain a combinatorial way to compute the Askey-Wilson moment using an idea in the work of Ismail, Stanton, and Viennot in 1987. Then I will show a new and nicer (in a combinatorial sense) formula for the Askey-Wilson moment which reduces to the formula of Kim and Stanton when d = 0. Using this new formula we can prove a positivity conjecture of Kim and Stanton. This is joint work with Dennis Stanton.