Geodesic
Repetition threshold for circular words
Irina A. Gorbunova1
1Ural Federal University
The electronic journal of combinatorics, Tome 19 (2012) no. 4
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We find the threshold between avoidable and unavoidable repetitions in circular words over $k$ letters for any $k\ge6$. Namely, we show that the number $CRT(k)=\frac{\left\lceil {k/2}\right\rceil{+}1}{\left\lceil {k/2}\right\rceil}$ satisfies the following properties. For any $n$ there exists a $k$-ary circular word of length $n$ containing no repetition of exponent greater than $CRT(k)$. On the other hand, $k$-ary circular words of some lengths must have a repetition of exponent at least $CRT(k)$.
DOI : 10.37236/2365
Classification : 68R15
Mots-clés : Dejean's conjecture, repetition threshold, circular words

Irina A. Gorbunova  1

1 Ural Federal University 
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Irina A. Gorbunova. Repetition threshold for circular words. The electronic journal of combinatorics, Tome 19 (2012) no. 4. doi: 10.37236/2365

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