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We show that any positive integer is the least period of a factor of the Thue-Morse word. We also characterize the set of least periods of factors of a sturmian word. In particular, the corresponding set for the Fibonacci word is the set of Fibonacci numbers. As a by-product of our results, we give several new proofs and tightenings of well-known properties of sturmian words.
We show that any positive integer is the least period of a factor of the Thue-Morse word.
We also characterize the set of least periods of factors of a Sturmian word. In particular,
the corresponding set for the Fibonacci word is the set of Fibonacci numbers.
As a by-product of our results, we give several new proofs and tightenings
of well-known properties of Sturmian words.
Among the various ways to construct a characteristic Sturmian word, one of the most used consists in defining an infinite sequence of prefixes that are standard. Nevertheless in any characteristic word , some standard words occur that are not prefixes of . We characterize all standard words occurring in any characteristic word (and so in any Sturmian word) using firstly morphisms, then standard prefixes and finally palindromes.
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