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The Ubiquitous Prouhet-Thue-Morse Sequence

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Sequences and their Applications

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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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

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