| Following the techniques initiated in [MP], we continue to study the limit shapes of random permutations avoiding a specific subset of patterns. We consider patterns in S3 extensively, and also prove some results regarding pairs of permutations with one in S3 and another in S3. We analyze the limiting distribution of a pattern-avoiding permutation, and calculate the asymptotic behavior of distributions of positions of numbers in the permutations. The distributions vary significantly depending on which patterns are avoided. We also apply our results to obtain results on various permutation statistics. |
