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#### Dejean's conjecture holds for n ≥ 27

(EDP Sciences, 2009)

We show that Dejean’s conjecture holds for n ≥ 27. This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasible.

#### Infinite words containing squares at every position

(EDP Sciences, 2010)

Richomme asked the following question: what is the infimum of the real numbers α > 2 such that there exists an infinite word that avoids α-powers but contains arbitrarily large squares beginning at every position? We resolve ...

#### The Number of Ternary Words Avoiding Abelian Cubes Grows Exponentially

(2004-06-19)

We show that the number of ternary words of length n avoiding abelian cubes grows
faster than r^n, where r = 2^{1/24}

#### A family of formulas with reversal of high avoidability index

(World Scientific, 2017)

We present an infinite family of formulas with reversal whose avoidability index is bounded between 4 and 5, and we show that several members of the family have avoidability index 5. This family is particularly interesting ...