Asymptotic bit frequency in Fibonacci words
نویسندگان
چکیده
Abstract It is known that binary words containing no k consecutive 1s are enumerated by -step Fibonacci numbers. In this note we discuss the expected value of a random bit in word length n having property.
منابع مشابه
Lyndon words and Fibonacci numbers
It is a fundamental property of non-letter Lyndon words that they can be expressed as a concatenation of two shorter Lyndon words. This leads to a naive lower bound ⌈log 2 (n)⌉ + 1 for the number of distinct Lyndon factors that a Lyndon word of length n must have, but this bound is not optimal. In this paper we show that a much more accurate lower bound is ⌈logφ(n)⌉ + 1, where φ denotes the gol...
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ژورنال
عنوان ژورنال: Pure mathematics and applications
سال: 2022
ISSN: ['1218-4586', '1788-800X']
DOI: https://doi.org/10.2478/puma-2022-0005