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Characterization of test-sets for overlap-free morphisms. (English) Zbl 0946.68114

Summary: We give a characterization of all the sets \(X\) such that any morphism \(h\) on \(\{a,b\}\) is overlap-free if and only if for each \(x\) in \(X\), \(h(x)\) is overlap-free. As a consequence, we observe the particular case \(X= \{bbabaa\}\) which improves the previous characterization of J. Berstel and P. Séébold [ibid. 46, No. 3, 275-281 (1993; Zbl 0824.68093)].

MSC:

68R15 Combinatorics on words

Citations:

Zbl 0824.68093
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References:

[2] Berstel, J.; Séébold, P., A characterization of overlap-free morphism, Discrete Appl. Math., 46, 275-281 (1993) · Zbl 0824.68093
[3] Séébold, P., Fibonacci morphisms and Sturmian words, Theoret. Comput. Sci., 88, 365-384 (1991) · Zbl 0737.68068
[4] Thue, A., Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen, Kra. Vidensk. Selsl. Skrifter. I. Mat.-Nat. Kl. Christania, 10, 1-67 (1912) · JFM 44.0462.01
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