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

Dalia Krieger

Displaying similar documents to “On critical exponents in fixed points of $k$ -uniform binary morphisms”

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.

For each $α > 2$ there is an infinite binary word with critical exponent $α$ .

Currie, James D., Rampersad, Narad (2008)

The Electronic Journal of Combinatorics [electronic only]

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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.

On a class of infinite words with bounded repetitions

Anton Černý (1985)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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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.