Combinatorial proofs of some limit formulas involving orthogonal polynomials (Q910404)

Over ten years ago M. Hoare listed the classical orthogonal at the Hahn polynomial level and their limits in a chart. This was at an Oberwolfach meeting. Since the audience loved the chart, and had ignored my similar treatment in an earlier talk at the same meeting, a more general chart was made, but including all the classical hypergeometric orthogonal polynomials from Racah and Wilson on down to Hermite. This appeared in an AMS memoir Wilson and I wrote. The author of the present paper takes Hoare's version of this chart augmented with the Meixner-Pollaczek polynomials and not only finds combinatorial models for the polynomials, but deforms the models to prove the limit results. Some of the models are very interesting, and shed new light both on the polynomials and the combinatorial settings.