Jacques Justin (2010)
RAIRO - Theoretical Informatics and Applications
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Fine and Wilf's theorem has recently been extended to words having three periods. Following the method of the authors we extend it to an arbitrary number of periods and deduce from that a characterization of generalized Arnoux-Rauzy sequences or episturmian infinite words.
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...
Jacques Justin, Giuseppe Pirillo (2002)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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Here we give a characterization of Arnoux–Rauzy sequences by the way of the lexicographic orderings of their alphabet.
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.