## Dejean’s conjecture and letter frequency.(English)Zbl 1147.68612

Summary: We prove two cases of a strong version of Dejean’s conjecture involving extremal letter frequencies. The results are that there exist an infinite $$(\frac54^+)$$-free word over a 5 letter alphabet with letter frequency $$\frac16$$ and an infinite $$(\frac65^+)$$-free word over a 6 letter alphabet with letter frequency $$\frac15$$.

### MSC:

 68R15 Combinatorics on words
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### References:

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