Abstract
Combinatorial properties of finite and infinite words are of increasing importance in various fields of science (for a general reference, the reader should consul [271], [272] and the references therein). The combinatorial properties of the Fibonacci infinite word have been studied extensively by many authors (see for examples [67], [142], [176], [450]).
This chapter looks at infinite words generated by invertible substitutions. As we shall see, words of this family generalize the Fibonacci infinite word.
The combinatorial properties of those infinite words are of great interest in various fields of mathematics, such as number theory [25], [95], [164], [229], dynamical systems [327], [340], [350], [401], fractal geometry [40], [101], [218], [274], tiling theory [40], [400], formal languages and computational complexity [67], [69], [201], [202], [233], [293], [384], [385], [447], and also in the study of quasicrystals [82], [99], [258], [257], [274], [455], [456], [454], [459].
This chapter has been written by Z. -Y. Wen
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© 2002 Springer-Verlag Berlin Heidelberg
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(2002). Infinite words generated by invertible substitutions. 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_9
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DOI: https://doi.org/10.1007/3-540-45714-3_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44141-0
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