Weights on Walls & Combinatorial Calculations with Orthogonal Polynomials
by Judy-anne Osborn
Abstract: Recently an open problem from the 1970's, that of enumerating directed lattice paths in a slit, each wall of which has an independent weight associated with it, was solved using the Constant Term Method. In this
talk I will describe that solution, as well as presenting its generalization to the case where each wall has any finite number of independent weights layered against it.
The method utilizes rational functions which come from orthogonal polynomials subject to a geometrically apt variable change. I will also present a combinatorial method to directly calculate these transformed orthogonal polynomials.