Displaying similar documents to “The theorem of Fine and Wilf for relational periods”

Least periods of factors of infinite words

James D. Currie, Kalle Saari (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et 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.

The theorem of Fine and Wilf for relational periods

Vesa Halava, Tero Harju, Tomi Kärki (2008)

RAIRO - Theoretical Informatics and Applications

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We consider relational periods, where the relation is a compatibility relation on words induced by a relation on letters. We prove a variant of the theorem of Fine and Wilf for a (pure) period and a relational period.

On some problems related to palindrome closure

Michelangelo Bucci, Aldo de Luca, Alessandro De Luca, Luca Q. Zamboni (2008)

RAIRO - Theoretical Informatics and Applications

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In this paper, we solve some open problems related to (pseudo)palindrome closure operators and to the infinite words generated by their iteration, that is, standard episturmian and pseudostandard words. We show that if is an involutory antimorphism of , then the right and left -palindromic closures of any factor of a -standard word are also factors of some -standard word. We also introduce the class of pseudostandard words with “seed”, obtained by iterated pseudopalindrome closure...