Stanley–Wilf conjecture for permutation pattern avoidance

Let $S_n$ denote the set of permutations of $[n]=\{1,2,\ldots,n\}$, and let $S_n(\tau)$ be the set of permutations avoiding a pattern $\tau\in S_\ell$. Stanley–Wilf conjecture. For any pattern $\tau\in S_\ell$, the limit

$$\lim_{n\rightarrow\infty}|S_n(\tau)|^{\frac{1}{n}}$$

exists and is finite. This conjecture concerns the exponential growth rate of permutation classes defined by pattern avoidance; the supplied text does not state whether it has been resolved.