Abstarct: In this thesis, we are interested in the number of fixed points of functions f: An→An over a finite alphabet A defined on a given signed digraph D. We first use techniques from network coding to derive some lower bounds on the number of fixed points that only depends on D. We then study relationships between the number of fixed points of f and problems in coding theory, especially the design of codes for the asymmetric channels. Using these relationships, we bring upper and lower bounds on the number of fixed points, which significantly improve those given in the literature. We also unveil some interesting behavior of the number of fixed points of functions with a given signed digraph when the alphabet varies. We finally prove that signed digraphs with more (disjoint) positive cycles actually do not necessarily have functions with more fixed points.