Patterns in random permutations avoiding the pattern 132

Abstract

We consider a random permutation drawn from the set of 132-avoiding permutations of length $n$ and show that the number of occurrences of another pattern $σ$ has a limit distribution, after scaling by $n^{λ(σ)/2}$ where $λ(σ)$ is the length of $σ$ plus the number of descents. The limit is not normal, and can be expressed as a functional of a Brownian excursion. Moments can be found by recursion.

32 pages