Lattice walks and elliptic functions

Abstract

Gessel walks are lattice walks confined to the positive quarter plane (NxN) which start at the origin (0,0) and have step set S={NE,E,SW,W}. In a recent article, Alin Bostan, Irina Kurkova, and Kilian Raschel showed that the generating function for Gessel walks is algebraic. The goal of this thesis was to fully understand the method presented in this article and, using this knowledge, reproduced the result with improvements where possible.