Patterns in Random Permutations Avoiding the Pattern 132

Source 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.