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Limit values of the recurrence quotient of Sturmian sequences. (English) Zbl 0916.68115
Summary: The recurrence quotient is a real number associated to any symbolic sequence. In the case of Sturmian sequences, Morse and Hedlund proved that the smallest possible value is \((5+5)/2\). We study here the structure of the set of values taken by the recurrence quotient for a Sturmian sequence.

68R15 Combinatorics on words
68Q45 Formal languages and automata
Full Text: DOI
[1] J.-P. Allouche, Personal communication.
[2] Allouche, J.-P.; Cosnard, M., Itérations de fonctions unimodales et suites engendrées par automates, C. R. acad. sci. Paris Sér. I math., 296, 3, 159-162, (1983) · Zbl 0547.58027
[3] Arnoux, P.; Rauzy, G., Représentation géométrique des suites de complexité 2n + 1, Bull. soc. math. France, 119, 199-215, (1991) · Zbl 0789.28011
[4] Berstel, J., Recent results on Sturmian words, (), 13-24 · Zbl 1096.68689
[5] Coven, E.M.; Hedlund, G.A., Sequences with minimal block growth, Math. systems theory, 7, 138-153, (1973) · Zbl 0256.54028
[6] Cusick, T.; Flahive, M., The markoff and Lagrange spectra, () · Zbl 0685.10023
[7] Morse, M.; Hedlund, G.A., Symbolic dynamics II: Sturmian trajectories, Amer. J. math., 61, 1-42, (1940) · JFM 66.0188.03
[8] Rauzy, G., Suites à termes dans un alphabet fini, (), 25.01-25.16
[9] Tchékhovaya, N., Nombres de recouvrement, ()
[10] Wen, Z.-X.; Wen, Z.-Y., Some properties of the singular words of the Fibonacci word, European J. combin., 15, 587-598, (1994) · Zbl 0823.68087
[11] Davison, J.L., A class of transcendental numbers with bounded partial quotients, (), 365-371 · Zbl 0693.10028
[12] Queffélec, M., Transcendance des fractions continues de thue-Morse, J. number theory, 73, 201-211, (1998) · Zbl 0920.11045
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