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Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important concepts, providing a clear exposition of some recent results, and emphasise the emerging connections between these different fields. Topics include combinatorics on words, pattern avoidance, graph theory, tilings and theory of computation, multidimensional subshifts, discrete dynamical systems, ergodic theory, numeration systems, dynamical arithmetics, automata theory and synchronised words, analytic combinatorics, continued fractions and probabilistic models. Each topic is presented in a way that links it to the main themes, but then they are also extended to repetitions in words, similarity relations, cellular automata, friezes and Dynkin diagrams. The book will appeal to graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, tilings and stringology. It will also interest biologists using text algorithms.

Combinatorial analysis. --- Symbolic dynamics. --- Computer science. --- Informatics --- Science --- Dynamics, Symbolic --- Differentiable dynamical systems --- Combinatorics --- Algebra --- Mathematical analysis

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Symbolic dynamics. --- Topological dynamics. --- Differentiable dynamical systems. --- Dynamique symbolique --- Dynamique topologique --- Dynamique différentiable --- Symbolic dynamics --- Topological dynamics --- Differentiable dynamical systems --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Geometry --- Graph algorithms --- Mathematics. --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Differential equations. --- Numerical analysis. --- Global Analysis and Analysis on Manifolds. --- Numerical Analysis. --- Ordinary Differential Equations. --- Mathematical analysis --- 517.91 Differential equations --- Differential equations --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Math --- Science --- Computer algorithms --- Graph theory --- Global analysis. --- Differential Equations. --- Global analysis (Mathematics) --- Systèmes dynamiques --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Dynamics, Topological --- Dynamics, Symbolic