Related papers: Haruspicy 3: The directed bond-animal generating f…
We prove that an irreducible lattice acting on a product of two or more locally finite, biregular trees is finitely generated.
We provide combinatorial arguments based on a two-dimensional extension of a locally-free semigroup allowing us to compute the growth rate, $\Lambda$, of the partition function $Z_N=N^{\theta}\Lambda^N$ of the $N$-particle directed animals…
We consider inhomogeneous lattice walk models in a half-space and in the quarter plane. For the models in a half-space, we show by a generalization of the kernel method to linear systems of functional equations that their generating…
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…
In this paper, we count acyclic and strongly connected uniform directed labeled hypergraphs. For these combinatorial structures, we introduce a specific generating function allowing us to recover and generalize some results on the number of…
We call a finitely generated group lacunary hyperbolic if one of its asymptotic cones is an R-tree. We characterize lacunary hyperbolic groups as direct limits of Gromov hyperbolic groups satisfying certain restrictions on the hyperbolicity…
These lectures provide an introduction to the directed percolation and directed animals problems, from a physicist's point of view. The probabilistic cellular automaton formulation of directed percolation is introduced. The planar duality…
We establish three independent results on groups acting on trees. The first implies that a compactly generated locally compact group which acts continuously on a locally finite tree with nilpotent local action and no global fixed point is…
We identify Grandis' directed spaces as a full reflective subcategory of the category of multipointed $d$-spaces. When the multipointed $d$-space realizes a precubical set, its reflection coincides with the standard realization of the…
Lattice animals provide a discretized model for the theta transition displayed by branched polymers in solvent. Exact graph enumeration studies have given some indications that the phase diagram of such lattice animals may contain two…
We introduce $\infty$-dimensional versions of three common models of random hetero-polymers, in which both the polymer density and the density of the polymer-solvent mixture are finite. These solvable models give valuable insight into the…
We use very efficient algorithms to calculate low-density series for bond and site percolation on the directed triangular, honeycomb, kagom\'e, and $(4.8^2)$ lattices. Analysis of the series yields accurate estimates of the critical point…
We consider the reversible adsorption of dimers on a regular lattice, where adsorption occurs on a finite fraction of sites selected randomly. By comparing this system to the pure system where all sites are available for adsorption, we show…
Locomotion in segmented animals, such as annelids and myriapods (centipedes and millipedes), is generated by a coordinated movement known as metameric locomotion, which can be also implemented in robots designed to perform specific tasks.…
Bacterial colonies can form a wide variety of shapes and structures based on ambient and internal conditions. To help understand the mechanisms that determine the structure of and the diversity within these colonies, various numerical…
Let D be an irreducible lattice in a connected, semisimple Lie group G with finite center. Assume that the real rank of G is at least two, that G/D is not compact, and that G has more than one noncompact simple factor. We show that D has no…
We introduce a formula for translating any upper bound on the percolation threshold of a lattice \g into a lower bound on the exponential growth rate of lattice animals $a(G)$ and vice-versa. We exploit this to improve on the best known…
The general d-dimensional twisted group lattice is solved. The irreducible representations of the corresponding group are constructed by an explicit procedure. It is proven that they are complete. All matrix representation solutions to the…
Assign to each site of the integer lattice $\Zd$ a real score, sampled according to the same distribution $F$, independently of the choices made at all other sites. A lattice animal is a finite connected set of sites, with its weight being…
We have calculated analytically the mean value and the variance of the number of bonds on the lattices of dimension $d$ for the given occupation of sites. We consider both kinds of site occupation: with the fixed concentration $n_s$ of…