Displaying similar documents to “On some problems related to palindrome closure”

Directive words of episturmian words : equivalences and normalization

Amy Glen, Florence Levé, Gwénaël Richomme (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Episturmian morphisms constitute a powerful tool to study episturmian words. Indeed, any episturmian word can be infinitely decomposed over the set of pure episturmian morphisms. Thus, an episturmian word can be defined by one of its morphic decompositions or, equivalently, by a certain directive word. Here we characterize pairs of words directing the same episturmian word. We also propose a way to uniquely define any episturmian word through a normalization of its directive words. As...

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...

Directive words of episturmian words: equivalences and normalization

Amy Glen, Florence Levé, Gwénaël Richomme (2008)

RAIRO - Theoretical Informatics and Applications

Similarity:

Episturmian morphisms constitute a powerful tool to study episturmian words. Indeed, any episturmian word can be infinitely decomposed over the set of pure episturmian morphisms. Thus, an episturmian word can be defined by one of its morphic decompositions or, equivalently, by a certain directive word. Here we characterize pairs of words directing the same episturmian word. We also propose a way to uniquely define any episturmian word through a normalization of its directive words....

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.