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We consider the set of affine permutations that avoid a fixed permutationpattern. Crites has given a simple characterization for when this set isinfinite. We find the generating series for this set using the Coxeter lengthstatistic and prove that it can always be represented as a rational function.We also give a characterization of the patterns for which the coefficients ofthe generating series are periodic. The proofs exploit a new polyhedralencoding for the affine symmetric group.

Rational generating series for affine permutation pattern avoidance