Subword complexity of the Fibonacci-Thue-Morse sequence: the proof of Dekking's conjecture

TL;DR

This paper proves Dekking's conjecture on the subword complexity of the Fibonacci-Thue-Morse sequence using computational methods with Walnut.

Contribution

It provides a proof of Dekking's conjecture on subword complexity through computational verification, a novel approach for this problem.

Findings

Confirmed the specific form of the subword complexity function

Validated Dekking's conjecture computationally

Demonstrated the effectiveness of Walnut for such proofs

Abstract

Recently Dekking conjectured the form of the subword complexity function for the Fibonacci-Thue-Morse sequence. In this note we prove his conjecture by purely computational means, using the free software Walnut.