• 1 Department of Mathematics [Seattle]

In this paper we study pattern avoidance for affine permutations. In particular, we show that for a given pattern $p$, there are only finitely many affine permutations in $\widetilde{S}_n$ that avoid $p$ if and only if $p$ avoids the pattern $321$. We then count the number of affine permutations that avoid a given pattern $p$ for each $p$ in $S_3$, as well as give some conjectures for the patterns in $S_4$. This paper is just an outline; the full version will appear elsewhere.