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Dejean's conjecture and letter frequency

Published online by Cambridge University Press:  03 June 2008

Jérémie Chalopin  and
Pascal Ochem
Jérémie Chalopin
Affiliation:
LIF, CNRS, Université de Provence, CMI, 39 rue Joliot-Curie, 13453 Marseille, France; jeremie.chalopin@lif.univ-mrs.fr
Pascal Ochem
Affiliation:
LRI, CNRS, Université Paris-Sud 11, Bât 490, 91405 Orsay Cedex, France; ochem@lri.fr
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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 $\left({\frac{5}{4}^+}\right)$-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 $\frac{1}{5}$.

Keywords

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 3: JM'06 , July 2008 , pp. 477 - 480
Copyright
© EDP Sciences, 2008

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References

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