Automata, Groups, Limit Spaces, and Tilings

We explore the connections between automata, groups, limit spaces of self-similar actions, and tilings. In particular, we show how a group acting ``nicely'' on a tree gives rise to a self-covering of a topological groupoid, and how the group can be reconstructed from the groupoid and its covering. The connection is via finite-state automata. These define decomposition rules, or self-similar tilings, on leaves of the solenoid associated with the covering.Comment: to appear in J. Algebr

An extensive English language bibliography on graph theory and its applications

Bibliography on graph theory and its application

Analytic combinatorics : functional equations, rational and algebraic functions

This report is part of a series whose aim is to present in a synthetic way the major methods and models in analytic combinatorics. Here, we detail the case of rational and algebraic functions and discuss systematically closure properties, the location of singularities, and consequences regarding combinatorial enumeration. The theory is applied to regular and context-free languages, finite state models, paths in graphs, locally constrained permutati- ons, lattice paths and walks, trees, and planar maps