RAIRO - Theoretical Informatics and Applications (RAIRO: ITA)

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RAIRO-Theor. Inf. Appl. 42, 477-480 (2008)
DOI: 10.1051/ita:2008013

Dejean's conjecture and letter frequency

Jérémie Chalopin¹ and Pascal Ochem²

¹ LIF, CNRS, Université de Provence, CMI, 39 rue Joliot-Curie, 13453 Marseille, France; jeremie.chalopin@lif.univ-mrs.fr
² LRI, CNRS, Université Paris-Sud 11, Bât 490, 91405 Orsay Cedex, France; ochem@lri.fr

Published online: 3 June 2008

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