The (maximal) exponent of a non-empty finite word is the ratio of its length to its period. Dejean (1972) conjectured that for any n >= 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 >= 33.
On Dejean's conjecture over large alphabets
CARPI, Arturo
2007
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 n >= 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 >= 33.File in questo prodotto:
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