Dejean's conjecture and letter frequency
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 42 (2008) no. 3, pp. 477-480.

We prove two cases of a strong version of Dejean’s conjecture involving extremal letter frequencies. The results are that there exist an infinite $\left({\frac{5}{4}}^{+}\right)$-free word over a 5 letter alphabet with letter frequency $\frac{1}{6}$ and an infinite $\left({\frac{6}{5}}^{+}\right)$-free word over a 6 letter alphabet with letter frequency $\frac{1}{5}$.

DOI: 10.1051/ita:2008013
Classification: 68R15
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Chalopin, Jérémie; Ochem, Pascal. Dejean's conjecture and letter frequency. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 42 (2008) no. 3, pp. 477-480. doi : 10.1051/ita:2008013. http://www.numdam.org/articles/10.1051/ita:2008013/

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