Displaying similar documents to “The critical exponent of the Arshon words”

On critical exponents in fixed points of k -uniform binary morphisms

Dalia Krieger (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Let 𝐰 be an infinite fixed point of a binary k -uniform morphism f , and let E ( 𝐰 ) be the critical exponent of 𝐰 . We give necessary and sufficient conditions for E ( 𝐰 ) to be bounded, and an explicit formula to compute it when it is. In particular, we show that E ( 𝐰 ) is always rational. We also sketch an extension of our method to non-uniform morphisms over general alphabets.

Squares and cubes in Sturmian sequences

Artūras Dubickas (2009)

RAIRO - Theoretical Informatics and Applications

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We prove that every Sturmian word has infinitely many prefixes of the form , where and lim In passing, we give a very simple proof of the known fact that every Sturmian word begins in arbitrarily long squares.

Infinite words containing squares at every position

James Currie, Narad Rampersad (2010)

RAIRO - Theoretical Informatics and Applications

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Richomme asked the following question: what is the infimum of the real numbers > 2 such that there exists an infinite word that avoids -powers but contains arbitrarily large squares beginning at every position? We resolve this question in the case of a binary alphabet by showing that the answer is = 7/3.

Binary words avoiding the pattern AABBCABBA

Pascal Ochem (2010)

RAIRO - Theoretical Informatics and Applications

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We show that there are three types of infinite words over the two-letter alphabet {0,1} that avoid the pattern . These types, , , and , differ by the factor complexity and the asymptotic frequency of the letter 0. Type has polynomial factor complexity and letter frequency 1 2 . Type has exponential factor complexity and the frequency of the letter 0 is at least 0.45622 and at most 0.48684. Type is obtained from type ...

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...

Transcendence of numbers with an expansion in a subclass of complexity 2 + 1

Tomi Kärki (2006)

RAIRO - Theoretical Informatics and Applications

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We divide infinite sequences of subword complexity into four subclasses with respect to left and right special elements and examine the structure of the subclasses with the help of Rauzy graphs. Let ≥ 2 be an integer. If the expansion in base of a number is an Arnoux-Rauzy word, then it belongs to Subclass I and the number is known to be transcendental. We prove the transcendence of numbers with expansions in the subclasses II and III.