3AP-free permutations have no exponential growth rate
Boon Suan Ho·2026-02-14·via math.CO updates on arXiv.org
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.