Dejean conjectured that the repetition threshold for a k-letter alphabet is kk− 1 when k≥ 5.
Dejean's conjecture has already been proved for k≤ 14 and for k≥ 27. We present here a …

A PROOF OF DEJEAN’S CONJECTURE 1. Introduction Repetitions in words have been
studied since the beginning of the previous cen- Page 1 MATHEMATICS OF COMPUTATION …

The aim of this paper is to survey the area formed by the intersection of two popular lines of
research in formal language theory. The first line, originated by Thue in 1906, concerns …

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

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 …

An overlap-free (or $\beta $-free) word $ w $ over a fixed alphabet $\Sigma $ is extremal if
every word obtained from $ w $ by inserting a single letter from $\Sigma $ at any position …

Threshold languages, which are the (k/(k–1))+-free languages over k-letter alphabets with
k≥ 5, are the minimal infinite power-free languages according to Dejean's conjecture, which …

For a rational number r such that 1< r≤ 2, an undirected r-power is a word of the form xyx′,
where the word x is nonempty, the word x′ is in {x, x R}, and we have| xyx′|/| xy|= r. The …

We give lower bounds on the growth rate of Dejean words, ie minimally repetitive words,
over a k-letter alphabet, for 5≤ k≤ 10. Put together with the known upper bounds, we …

The study of combinatorics on words dates back at least to the beginning of the 20th century
and the work of Axel Thue [93, 94] on repetitions in words. The study of repetitions in words …