Enumerating Pattern Avoidance for Affine Permutations

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 S̃n 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 S3, as well as give some conjectures for the patterns in S4.