Asymptotic bit frequency in Fibonacci words

06/25/2021 ∙ by Jean-Luc Baril, et al. ∙ 0

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. This expectation can reveal new properties of some telecommunication protocols or interconnection networks.

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