We survey known results and open problems in abelian combinatorics on words. Abelian
combinatorics on words is the extension to the commutative setting of the classical theory of …

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 the first-order theory of Sturmian words over Presburger arithmetic is
decidable. Using a general adder recognizing addition in Ostrowski numeration systems by …

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 1875, Elwin Bruno Christoffel introduced a special class of words on a binary alphabet
linked to continued fractions which would go onto be known as Christoffel words. Some …

Over an alphabet of size 3 we construct an infinite balanced word with critical exponent 2+
2/2. Over an alphabet of size 4 we construct an infinite balanced word with critical exponent …

We illustrate a general technique for enumerating factors of k-automatic sequences by
proving a conjecture on the number f (n) of unbordered factors of the Thue-Morse sequence …

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 …

Abstract Richomme, Saari and Zamboni (2011)[39] proved that at every position of a
Sturmian word starts an abelian power of exponent k for every k> 0. We improve on this …