Critical exponents of words over 3 letters.
Vaslet, Elise (2011)
The Electronic Journal of Combinatorics [electronic only]
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Displaying similar documents to “For each there is an infinite binary word with critical exponent .”
Critical exponents of words over 3 letters.
There exist binary circular power free words of every length.
Aberkane, Ali, Currie, James D. (2004)
The Electronic Journal of Combinatorics [electronic only]
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Counting bordered partial words by critical positions.
Allen, Emily, Blanchet-Sadri, F., Byrum, Cameron, Cucuringu, Mihai, Mercaş, Robert (2011)
The Electronic Journal of Combinatorics [electronic only]
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Binary words containing infinitely many overlaps.
Currie, James, Rampersad, Narad, Shallit, Jeffrey (2006)
The Electronic Journal of Combinatorics [electronic only]
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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.
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.
Least Periods of Factors of Infinite Words
James D. Currie, Kalle Saari (2008)
RAIRO - Theoretical Informatics and Applications
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We show that any positive integer is the least period of a factor of the Thue-Morse word. We also characterize the set of least periods of factors of a Sturmian word. In particular, the corresponding set for the Fibonacci word is the set of Fibonacci numbers. As a by-product of our results, we give several new proofs and tightenings of well-known properties of Sturmian words.
Density of Critical Factorizations
Tero Harju, Dirk Nowotka (2010)
RAIRO - Theoretical Informatics and Applications
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We investigate the density of critical factorizations of infinite sequences of words. The density of critical factorizations of a word is the ratio between the number of positions that permit a critical factorization, and the number of all positions of a word. We give a short proof of the Critical Factorization Theorem and show that the maximal number of noncritical positions of a word between two critical ones is less than the period of that word. Therefore, we consider only...