Abstract
Multivariate linear recurrences appear in such diverse fields of mathematics as numerical analysis, probability theory, and combinatorics. Whereas in the univariate case the solution of a constant-coefficient recurrence always has a rational generating function, this is no longer true in the multivariate case where this generating function can be very complicated from the algebraic point of view. However, there are some important cases where the solution can nevertheless be computed exactly. Examples include many lattice-paths problems such as enumeration of Dyck, Motzkin, and Schroeder paths. An implementation of our methods in Mathematica is in progress.
This is joint work with Mireille Bousquet-Melou
(Univ. Bordeaux I and CNRS, France).