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 …

Symbolic dynamics is essential in the study of dynamical systems of various types and is
connected to many other fields such as stochastic processes, ergodic theory, representation …

We study aperiodic balanced sequences over finite alphabets. A sequence v of this type is
fully characterised by a Sturmian sequence u and two constant gap sequences y and y …

In a recent paper of Rampersad et al., the authors conjectured that the smallest possible
critical exponent of an infinite balanced word over a 5-letter alphabet is 3/2. We prove this …

We extend the notion of k-automatic sequences to Ostrowski-automatic sequences, and
develop a procedure to computationally decide certain combinatorial and enumeration …

A word of length n is rich if it contains n nonempty palindromic factors. An infinite word is rich
if all of its finite factors are rich. Baranwal and Shallit produced an infinite binary rich word …

The repetition threshold of a class C of infinite d-ary sequences is the smallest real number r
such that in the class C there exists a sequence that avoids e-powers for all e> r. This notion …

We extend the notion of automatic sequences to a broader class, the Ostrowski-automatic
sequences. We develop a procedure for computationally deciding certain combinatorial and …

We study the threshold between avoidable and unavoidable repetitions in infinite balanced
sequences over finite alphabets. The conjecture stated by Rampersad, Shallit and …

The complement $\overline {x} $ of a binary word $ x $ is obtained by changing each $0 $ in
$ x $ to $1 $ and vice versa. We study infinite binary words $\bf w $ that avoid sufficiently …