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On the repetition threshold for large alphabets. (English) Zbl 1132.68515

Královič, Rastislav (ed.) et al., Mathematical foundations of computer science 2006. 31st international symposium, MFCS 2006, Stará Lesná, Slovakia, August 28–September 1, 2006. Proceedings. Berlin: Springer (ISBN 3-540-37791-3/pbk). Lecture Notes in Computer Science 4162, 226-237 (2006).
Summary: The (maximal) exponent of a finite non-empty word is the ratio among its length and its period. Dejean (1972) conjectured that for any \(n \geq 5\) there exists an infinite word over \(n\) letters with no factor of exponent larger than \(n/(n-1)\). We prove that this conjecture is true for \(n \geq 38\).
For the entire collection see [Zbl 1114.68008].

MSC:

68R15 Combinatorics on words
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