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Prefixes of the Fibonacci word
- Publication Year :
- 2023
-
Abstract
- Mignosi, Restivo, and Salemi (1998) proved that for all $\epsilon > 0$ there exists an integer $N$ such that all prefixes of the Fibonacci word of length $\geq N$ contain a suffix of exponent $\alpha^2-\epsilon$, where $\alpha = (1+\sqrt{5})/2$ is the golden ratio. In this note we show how to prove an explicit version of this theorem with tools from automata theory and logic. Along the way we gain a better understanding of the repetitive structure of the Fibonacci word.
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2302.04640
- Document Type :
- Working Paper