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

Jean Betrema·Jean-Guy Penaud
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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.

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Jean Betrema, Jean-Guy Penaud. 2001-06-25. Modeles avec particules dures, animaux diriges et series en variables partiellement commutatives. https://arxiv.org/abs/math/0106210

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