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

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

2001-06-25

arxiv.org/abs/math/0106210v1

Mathematics

Combinatorics

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

Scientific paper

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.

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