We discuss a well-known binary sequence called the Thue-Morse sequence, or the Prouhet-
Thue-Morse sequence. This sequence was introduced by Thue in 1906 and rediscovered by …

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 …

The notion of Abelian complexity of infinite words was recently used by the three last authors
to investigate various Abelian properties of words. In particular, using van der Waerden's …

We revisit a technique of S. Lehr on automata and use it to prove old and new results in a
simple way. We give a very simple proof of the 1986 theorem of Honkala that it is decidable …

Internationally recognised researchers look at developing trends in combinatorics with
applications in the study of words and in symbolic dynamics. They explain the important …

In this talk I will report on some recent results concerning decidability and enumeration for
properties of automatic sequences. This is work with Jean-Paul Allouche, Émilie Charlier …

Good words are binary words avoiding factors 11 and 1001, and patterns 0000 and
00010100. We show that good words bear the same relationship to the period-doubling …

We prove that a recent result of Komornik and Loreti on the smallest real number q in (1, 2)
such that the number 1 admits a unique q-expansion can be deduced from a result of the …

We consider the position and number of occurrences of squares in the Thue-Morse
sequence, and show that the corresponding sequences are 2-regular. We also prove that …

We give another proof of a theorem of Fife—understood broadly as providing a finite
automaton that gives a complete description of all infinite binary overlap-free words. Our …