Displaying similar documents to “Pattern occurrence in the dyadic expansion of square root of two and an analysis of pseudorandom number generators.”

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.

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.

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 ...

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...

The critical exponent of the Arshon words

Dalia Krieger (2010)

RAIRO - Theoretical Informatics and Applications

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Generalizing the results of Thue (for ) [Norske Vid. Selsk. Skr. Mat. Nat. Kl. (1912) 1–67] and of Klepinin and Sukhanov (for ) [Discrete Appl. Math. (2001) 155–169], we prove that for all ≥ 2, the critical exponent of the Arshon word of order is given by (3–2)/(2–2), and this exponent is attained at position 1.