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Infinite words containing squares at every position
 In Proceedings of Journées Montoises D’Informatique Théorique
, 2008
"... Richomme asked the following question: what is the infimum of the real numbers α> 2 such that there exists an infinite word that avoids αpowers 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 ..."
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Richomme asked the following question: what is the infimum of the real numbers α> 2 such that there exists an infinite word that avoids αpowers 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 α = 7/3. 1
CUBEFREE WORDS WITH MANY SQUARES
, 811
"... Abstract. We construct infinite cubefree binary words containing exponentially many distinct squares of length n. We also show that for every positive integer n, there is a cubefree binary square of length 2n. 1. ..."
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Abstract. We construct infinite cubefree binary words containing exponentially many distinct squares of length n. We also show that for every positive integer n, there is a cubefree binary square of length 2n. 1.
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, 2008
"... For each α> 2 there is an infinite binary word with critical exponent α ..."
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For each α> 2 there is an infinite binary word with critical exponent α
Article 13.2.7 On Highly Repetitive and Power Free Words
"... Answering a question of Richomme, Currie and Rampersad proved that 7/3 is the infimum of the real numbers α> 2 such that there exists an infinite binary word that avoids αpowers but is highly 2repetitive, i.e., contains arbitrarily large squares beginning at every position. In this paper, we pr ..."
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Answering a question of Richomme, Currie and Rampersad proved that 7/3 is the infimum of the real numbers α> 2 such that there exists an infinite binary word that avoids αpowers but is highly 2repetitive, i.e., contains arbitrarily large squares beginning at every position. In this paper, we prove similar statements about βrepetitive words, for some other β’s, over the binary and the ternary alphabets. 1