The minimal density of a letter in an infinite ternary square-free word is .
Tarannikov, Yuriy (2002)
Journal of Integer Sequences [electronic only]
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Tarannikov, Yuriy (2002)
Journal of Integer Sequences [electronic only]
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Harju, Tero, Nowotka, Dirk (2008)
The Electronic Journal of Combinatorics [electronic only]
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Pascal Ochem (2006)
RAIRO - Theoretical Informatics and Applications
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We present an algorithm which produces, in some cases, infinite words avoiding both large fractional repetitions and a given set of finite words. We use this method to show that all the ternary patterns whose avoidability index was left open in Cassaigne's thesis are 2-avoidable. We also prove that there exist exponentially many -free ternary words and -free 4-ary words. Finally we give small morphisms for binary words containing only the squares , 1 and (01)² and for binary words...
Harju, Tero, Kärki, Tomi, Nowotka, Dirk (2011)
The Electronic Journal of Combinatorics [electronic only]
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Kucherov, Gregory, Ochem, Pascal, Rao, Michaël (2003)
The Electronic Journal of Combinatorics [electronic only]
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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.
Currie, James D. (2002)
The Electronic Journal of Combinatorics [electronic only]
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Allouche, Jean-Paul, Currie, James, Shallit, Jeffrey (1998)
The Electronic Journal of Combinatorics [electronic only]
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