Asymptotic bit frequency in Fibonacci words-Reference-Cited by-同舟云学术

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Asymptotic bit frequency in Fibonacci words

Published:2022-06-01 Issue:1 Volume:30 Page:23-30
ISSN:1788-800X
Container-title:Pure Mathematics and Applications
language:en
Short-container-title:

Author:

Baril Jean-Luc¹,Kirgizov Sergey¹,Vajnovszki Vincent¹

Affiliation:

1. LIB , Université de Bourgogne Franche-Comté , B.P. 47 870 , Dijon Cedex France

Abstract

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/puma-2022-0005

Reference19 articles.

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2. [2] J.-L Baril, S. Kirgizov and V. Vajnovszki, Gray codes for Fibonacci q-decreasing words, arXiv:2010.09505.

3. [3] A. Bernini, S. Bilotta, R. Pinzani and V. Vajnovszki, A Gray code for cross-bifix-free sets, Math. Structures Computer Sci., 27 (2017) 184–196.10.1017/S0960129515000067

4. [4] A. Brauer, On algebraic equations with all but one root in the interior of the unit circle. To my teacher and former colleague Erhard Schmidt on his 75th birthday, Math. Nachr., 4 (1950) 250–257.10.1002/mana.3210040123

5. [5] Y. M. Chee, H. M. Kiah, P. Purkayastha and C. Wang, Cross-bifix-free codes within a constant factor of optimality, IEEE Trans. Inform. Theory, 59 (2013) 4668—4674.10.1109/TIT.2013.2252952

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