3AP-free permutations have no exponential growth rate

Abstract

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

4 pages