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On a class of infinite words with bounded repetitions. (English) Zbl 0578.68058

Summary: The well-known sequence of Thue and Morse contains no factor of the form xvxvx, x being a letter and v a word. In the present paper an analogous property of a class of sequences called generalized words of Thue-Morse is proved.

MSC:

68Q45 Formal languages and automata
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References:

[1] G. CHRISTOL, T. KAMAE, M. MENDES-FRANCE et G. RAUZY, Suites algébriques, automates et substitutions, Bull. Soc. math. Fr., Vol. 108, 1980, pp. 401-419. Zbl0472.10035 MR614317 · Zbl 0472.10035
[2] A. COBHAM, Uniform Tag Sequences, Math. Syst. Theory, Vol. 6, 1972, pp. 164-192. Zbl0253.02029 MR457011 · Zbl 0253.02029
[3] H. M. MORSE, Recurrent Geodesics on a Surface of Negative Curvature, Trans. Amer. Math. Soc., Vol. 22, 1921, pp. 84-100. MR1501161 JFM48.0786.06 · JFM 48.0786.06
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