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 …

The critical exponent $ E (\mathbf u) $ of an infinite sequence $\mathbf u $ over a finite
alphabet expresses the maximal repetition of a factor in $\mathbf u $. By the famous …

This collaborative volume aims at presenting and developing recent trends at the interface
between the study of sequences, groups, and number theory, as the title may suggest. It is …

We say a binary word is good if the only antisquares it contains are 01 and 10. We
characterize the minimal antisquares, that is, those words that are antisquares but all proper …

Repetition threshold is the smallest number RT (n) such that infinitely many n-ary words
contain no repetition of order greater than RT (n). These “extremal” repetition-free words are …

The critical exponent $ E (\mathbf u) $ of an infinite sequence $\mathbf u $ over a finite
alphabet expresses the maximal repetition of a factor in $\mathbf u $. By the famous …

We investigate the finite repetition threshold for k-letter alphabets, k≥ 4, that is the smallest
number r for which there exists an infinite r+-free word containing a finite number of r …

We consider a recently defined notion of k-abelian equivalence of words by concentrating
on avoidance problems. The equivalence class of a word depends on the numbers of …

It is commonly admitted that the origin of combinatorics on words goes back to the work of
Axel Thue in the beginning of the twentieth century, with his results on repetition-free words …

We consider special patterns of lengths 5 and 6 in a ternary alphabet. We show that some of
them are unavoidable in square-free words and prove avoidability of the other ones. Proving …