Marko Petkovsek, 
 
Solving discrete initial and boundary value problems with Mathematica

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).