Limit Shapes of Restricted Permutations
Samuel Miner · eScholarship (California Digital Library) · 2015
Following the techniques initiated in \\cite{MP}, we continue to study the limit shapes of random permutations avoiding a specific subset of patterns. We consider patterns in $S_3$ extensively, and also prove some results regarding pairs of permutations with one in $S_3$ and another in $S_4$. 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 variouspermutation statistics.