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We use local limits of Galton-Watson trees to establish local limit theoremsfor permutations conditioned to avoid a pattern of length three. In the case of321-avoiding permutations our results resolve an open problem of Pinsky. In theother cases our results give new descriptions of the limiting objects in termsof size-biased Galton-Watson trees.

A Galton-Watson tree approach to local limits of permutations avoiding a pattern of length three