Counting consecutive pattern matches in Sn(132) and Sn(123)

In this paper, we study the distribution of consecutive patterns in the set of 123-avoiding permutations and the set of 132-avoiding permutations, that is, in Sn(123) and Sn(132). We first study the distribution of consecutive pattern γ-matches in Sn(123) and Sn(132) for each length 3 consecutive pattern γ. Then we extend our methods to study the joint distributions of multiple consecutive patterns. Some more general cases are discussed in this paper as well.