Displaying similar documents to “On a class of Thue-Morse type sequences.”

Least Periods of Factors of Infinite Words

James D. Currie, Kalle Saari (2008)

RAIRO - Theoretical Informatics and Applications

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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.

Episturmian words: a survey

Amy Glen, Jacques Justin (2009)

RAIRO - Theoretical Informatics and Applications

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In this paper, we survey the rich theory of infinite which generalize to any finite alphabet, in a rather resembling way, the well-known family of on two letters. After recalling definitions and basic properties, we consider that allow for a deeper study of these words. Some properties of factors are described, including factor complexity, palindromes, fractional powers, frequencies, and return words. We also consider lexicographical properties of episturmian words, as well as their...

Standard factors of Sturmian words

Gwénaël Richomme, Kalle Saari, Luca Q. Zamboni (2010)

RAIRO - Theoretical Informatics and Applications

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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.

On a characteristic property of ARNOUX–RAUZY sequences

Jacques Justin, Giuseppe Pirillo (2010)

RAIRO - Theoretical Informatics and Applications

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Here we give a characterization of Arnoux–Rauzy sequences by the way of the lexicographic orderings of their alphabet.