On finite pattern-free sets of integers

Karl Dilcher; Lutz G. Lucht

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