The enumeration of restricted random walks by Sheffer polynomials with applications to statistics
Sheffer polynomials are solutions of certain systems of operator equations. Difference equations, which frequently occur in path enumeration, belong in that class. To find representations of the solutions, the restriction on the paths has to be in the form of boundaries. Such problems have applications in two-sample tests. We also consider paths with more than two step vectors. The gambler's ruin problem illustrates the method. If paths with a given area underneath are counted, q-binomial coefficients come into play. Eulerian Sheffer sequence solve some of such problems.
scientific article; zbMATH DE number 4004189
scientific article