On Dejean’s conjecture over large alphabets

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Abstract

The (maximal) exponent of a non-empty finite word is the ratio of its length to its period. Dejean (1972) conjectured that for any n5 there exists an infinite word over n letters with no factor of its exponent larger than n/(n1). We prove that this conjecture is true for n33.

Keywords

Fractional repetition
Repetition threshold
Dejean conjecture

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