Displaying similar documents to “The wildcard set's size in the density Hales-Jewett theorem.”

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...

On extremal properties of the Fibonacci word

Julien Cassaigne (2008)

RAIRO - Theoretical Informatics and Applications

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We survey several quantitative problems on infinite words related to repetitions, recurrence, and palindromes, for which the Fibonacci word often exhibits extremal behaviour.

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...