Note on a Fibonacci Parity Sequence
Jeffrey Shallit
TL;DR
This paper investigates the Fibonacci analogue of the Thue-Morse sequence using the Walnut theorem-prover, strengthening existing theorems and disproving a conjecture about its complexity.
Contribution
It demonstrates how to analyze the Fibonacci Thue-Morse sequence's complexity with Walnut, improving prior results and resolving a conjecture.
Findings
Strengthened a theorem on Fibonacci Thue-Morse complexity
Disproved a conjecture related to its properties
Provided a new measure of complexity for the sequence
Abstract
Let ftm = 0111010010001... be the analogue of the Thue-Morse sequence in Fibonacci representation. In this note we show how, using the Walnut theorem-prover, to obtain a measure of its complexity, previously studied by Jamet, Popoli, and Stoll. We strengthen one of their theorems and disprove one of their conjectures.
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Taxonomy
Topicssemigroups and automata theory · Advanced Combinatorial Mathematics · Mathematical Dynamics and Fractals