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Dejean's conjecture and letter frequency

Jérémie Chalopin; Pascal Ochem — 2008

RAIRO - Theoretical Informatics and Applications

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

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