<abstract xmlns="http://www.w3.org/1999/xhtml">

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

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.

Asymptotic bit frequency in Fibonacci words

Pure Mathematics and Applications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Asymptotic bit frequency in Fibonacci words"}

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...

Asymptotic bit frequency in Fibonacci words

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

Keywords
Fibonacci, word, pattern, frequency, asymptotics

© 2022 Jean-Luc Baril et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Asymptotic bit frequency in Fibonacci words

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

KeywordsFibonacci, word, pattern, frequency, asymptotics

© 2022 Jean-Luc Baril et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Fibonacci, word, pattern, frequency, asymptotics