Modeles avec particules dures, animaux diriges et series en variables partiellement commutatives

摘要

We give a systematic presentation of relations between lattice gas modelswith hard-core interactions, enumeration of directed-site animals, and thealgebra of formal power-series in the partially commutative case, along thework of X.G.Viennot. We present a complete and simplified solution, using thisalgebra, of the directed animals enumeration problem in two dimensions,including a fast program for random generation of such animals (with uniformdistribution) and images produced by this program.