Abstract
The aim of this chapter is to introduce substitutions by showing some typical and important examples of situations in number theory where they appear. Special stress will be given to the statistical properties of these sequences. We first recall some properties of the Morse sequence, then we introduce the Rudin-Shapiro sequence and focus on its spectral properties. We also evoke the Baum-Sweet sequence, the Cantor sequence and the Fibonacci sequence. For all the definitions related to words, substitutions and automata, we refer the reader to Chap. 1 (see also [158] and [340]).
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© 2002 Springer-Verlag Berlin Heidelberg
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(2002). Substitutions, arithmetic and finite automata: an introduction. In: Fogg, N.P., Berthé, V., Ferenczi, S., Mauduit, C., Siegel, A. (eds) Substitutions in Dynamics, Arithmetics and Combinatorics. Lecture Notes in Mathematics, vol 1794. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45714-3_2
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DOI: https://doi.org/10.1007/3-540-45714-3_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44141-0
Online ISBN: 978-3-540-45714-5
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