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Asymptotic bit frequency in Fibonacci words

Jean-Luc Baril
Jean-Luc Baril
, 
Sergey Kirgizov
Sergey Kirgizov
 and 
Vincent Vajnovszki
Vincent Vajnovszki
   | Jun 18, 2022
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Published Online: Jun 18, 2022
Page range: 23 - 30
Received: Mar 31, 2022
Accepted: May 15, 2022
DOI: https://doi.org/10.2478/puma-2022-0005
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© 2022 Jean-Luc Baril et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

It is known that binary words containing no k consecutive 1s are enumerated by k-step Fibonacci numbers. In this note we discuss the expected value of a random bit in a random word of length n having this property.

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