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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.09387 |
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Table of Contents:
- Word ${\mathbf G}$ is the fixed point of the morphism $γ=[01,2,02]$. In 2019, Shallit and Shur showed that ${\mathbf G}$ has factor complexity $2n+1$. They also showed that ${\mathbf G}$ has critical exponent $μ=2+\frac{1}{λ^2-1}= 2.4808726\cdots$, where $λ=1.7548777$ is the real zero of $x^3-2x+x-1=0$. They conjectured that this was the least possible critical exponent among words with factor complexity $2n+1$. We confirm their conjecture. The proof, using an intricate case analysis, is by computer. The relevant program generates a `human readable' proof.