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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.
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}
Binary Words Containing Infinitely Many Overlaps
(The Electronic Journal of Combinatorics, 2006-09-22)
We characterize the squares occurring in infinite overlap-free binary words and construct various α power-free binary words containing infinitely many overlaps.