3AP-free permutations have no exponential growth rate

Boon Suan Ho

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arXiv · 2602.13617

3AP-free permutations have no exponential growth rate

Boon Suan Ho

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Abstract

Let $θ(n)$ be the number of permutations of $\{1,\dots,n\}$ with no $3$-term arithmetic progressions. We prove that $\lim_{n\to\infty}θ(n)^{1/n}$ does not exist.

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Boon Suan Ho. 2026-02-14. 3AP-free permutations have no exponential growth rate. https://arxiv.org/abs/2602.13617

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