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 …

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

We prove game‐theoretic versions of several classical results on nonrepetitive sequences,
showing the existence of winning strategies using an extension of the Lovász Local Lemma …

Dejean\'s conjecture holds for N ≥ 27 Page 1 RAIRO-Theor. Inf. Appl. 43 (2009) 775–778
Available online at: DOI: 10.1051/ita/2009017 www.rairo-ita.org DEJEAN’S CONJECTURE …

We study the number uα (n) of α-power-free binary words of length n, and the asymptotics of
this number when n tends to infinity, for a fixed rational number α in (2, 7/3]. For any such α …

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 …

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 …

For δ∈ ℝ+, maximal δ-repetitions (δ-subrepetitions) are fractional powers in strings with
exponent of at least 2+ δ (and 1+ δ, respectively) which are non-extendable with respect to …