On the distribution of characteristic parameters of words

Arturo Carpi; Aldo de Luca

Displaying similar documents to “On the distribution of characteristic parameters of words”

On the distribution of characteristic parameters of words II

Arturo Carpi, Aldo de Luca (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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The characteristic parameters $K_{w}$ and $R_{w}$ of a word $w$ over a finite alphabet are defined as follows: $K_{w}$ is the minimal natural number such that $w$ has no repeated suffix of length $K_{w}$ and $R_{w}$ is the minimal natural number such that $w$ has no right special factor of length $R_{w}$ . In a previous paper, published on this journal, we have studied the distributions of these parameters, as well as the distribution of the maximal length of a repetition, among the words of each length on a given alphabet. In...

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...

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.

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...