Directed animals and Gas Models Revisited

Yvan Le Borgne (1) , Jean-François Marckert (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

In this paper, we revisit the enumeration of directed animals using gas models. We show that there exists a natural construction of random directed animals on any directed graph together with a particle system that explains at the level of objects the formal link known between the density of the gas model and the generating function of directed animals counted according to the area. This provides some new methods to compute the generating function of directed animals counted according to area, and leads in the particular case of the square lattice to new combinatorial results and questions. A model of gas related to directed animals counted according to area and perimeter on any directed graph is also exhibited.

Mots clés: directed animals; gas models; square lattice

Domaines: Probabilités [math.PR]; Mathématique discrète [cs.DM]

Yvan Le Borgne, Jean-François Marckert. Directed animals and Gas Models Revisited. The Electronic Journal of Combinatorics, 2007, R71, pp.1-36. ⟨hal-00112181⟩