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The Ubiquitous Prouhet-Thue-Morse Sequence

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Sequences and their Applications

Part of the book series: Discrete Mathematics and Theoretical Computer Science ((DISCMATH))

Abstract

We discuss a well-known binary sequence called the Thue-Morse sequence, or the Prouhet-Thue-Morse sequence. This sequence was introduced by Thue in 1906 and rediscovered by Morse in 1921. However, it was already implicit in an 1851 paper of Prouhet. The Prouhet-Thue-Morse sequence appears to be somewhat ubiquitous, and we describe many of its apparently unrelated occurrences.

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Author information

Authors and Affiliations

  1. CNRS, LRI, Université Paris-Sud, Bâtiment 490, F-91405, Orsay Cedex, France

    Jean-Paul Allouche

  2. Department of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

    Jeffrey Shallit

Authors
  1. Jean-Paul Allouche
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  2. Jeffrey Shallit
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Editor information

Editors and Affiliations

  1. Department of Computer Science, School of Computing, National University of Singapore, Lower Kent Ridge Road, Singapore, 119260

    C. Ding

  2. Department of Informatics, University of Bergen, N-5020, Bergen, Norway

    T. Helleseth

  3. Institute of Information Processing, Austrian Academy of Sciences, Sonnenfelsgasse 19, A01010, Vienna, Austria

    H. Niederreiter

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© 1999 Springer-Verlag London

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Allouche, JP., Shallit, J. (1999). The Ubiquitous Prouhet-Thue-Morse Sequence. In: Ding, C., Helleseth, T., Niederreiter, H. (eds) Sequences and their Applications. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0551-0_1

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  • DOI: https://doi.org/10.1007/978-1-4471-0551-0_1

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-196-2

  • Online ISBN: 978-1-4471-0551-0

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