Dejean's conjecture and letter frequency

Jérémie Chalopin (1) , Pascal Ochem (2)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166
2 LRI - Laboratoire de Recherche en Informatique

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 $\frac{1}{5}$.

Domaines: Mathématique discrète [cs.DM]

Jérémie Chalopin, Pascal Ochem. Dejean's conjecture and letter frequency. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2008, 42, pp.477-480. ⟨10.1051/ita:2008013⟩. ⟨hal-00432200⟩