A vertex colouring of a graph $ G $ is" nonrepetitive" if $ G $ contains no path for which the
first half of the path is assigned the same sequence of colours as the second half. Thue's …

This collaborative volume presents recent trends arising from the fruitful interaction between
the themes of combinatorics on words, automata and formal language theory, and number …

Automatic sequences are sequences over a finite alphabet generated by a finite-state
machine. This book presents a novel viewpoint on automatic sequences, and more …

We implement a decision procedure for answering questions about a class of infinite words
that might be called (for lack of a better name)“Fibonacci-automatic”. This class includes, for …

We show that various aspects of k-automatic sequences—such as having an unbordered
factor of length n—are both decidable and effectively enumerable. As a consequence it …

In this paper we use the framework of automatic sequences to study combinatorial
sequences modulo prime powers. Given a sequence whose generating function is the …

We show how some problems in additive number theory can be attacked in a novel way,
using techniques from the theory of finite automata. We start by recalling the relationship …

In this paper we prove the decidability of the following problem: Input: Two finite alphabets A
and B, an endomorphism σ: A∗→ A∗, a word w∈ A∗ and a morphism φ: A∗→ B∗ …

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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 …