  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 $\mathcal{S}_n(123)$ and $\mathcal{S}_n(132)$. We first study the
distribution of consecutive pattern $\gamma$-matches in $\mathcal{S}_n(123)$
and $\mathcal{S}_n(132)$ for each length 3 consecutive pattern $\gamma$. 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.
