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