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A generator of morphisms for infinite words. (English) Zbl 1110.68122

Summary: 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 \(\frac{7}{4}^+\)-free ternary words and \(\frac{7}{5}^+\)-free 4-ary words. Finally we give small morphisms for binary words containing only the squares \(0^2\), \(1^2\) and \((01)^2\) and for binary words avoiding large squares and fractional repetitions.

MSC:

68R15 Combinatorics on words
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References:

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