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

Abstract

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.

French, 49 pages, see http://dept-info.labri.u-bordeaux.fr/~betrema/animaux/

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