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Generalized thue-morse sequences

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Fundamentals of Computation Theory (FCT 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 199))

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Abstract

In a recent paper (8), Christol and al. introduce the following generalized Thue-Morse sequences over two letters a and b. Given a finite word u over {0,1}, the infinite word u has its i-th letter equal to a or b according to the number of occurrences of u in the binary expansion of i be even or odd.

Černý (7) has shown that these words do not contain any factor of the form (xy)nx, with n=2|u|.

We considerably strengthen this result, and prove that these words contain no cube exepted ap and bp, p≤n.

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Authors and Affiliations

  1. UER de Mathématiques, Université Paris VII, France

    Patrice Séébold

  2. Laboratoire d'Informatique Théorique et Programmation-LA 248 du CNRS, 2 Place Jussieu, 75221, Paris Cedex 05, France

    Patrice Séébold

Authors
  1. Patrice Séébold
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Lothar Budach

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© 1985 Springer-Verlag Berlin Heidelberg

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Séébold, P. (1985). Generalized thue-morse sequences. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1985. Lecture Notes in Computer Science, vol 199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028824

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  • DOI: https://doi.org/10.1007/BFb0028824

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15689-5

  • Online ISBN: 978-3-540-39636-9

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