Counting consecutive pattern matches in [formula omitted] and [formula omitted].

Abstract 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 S n (123) and S n (132). We first study the distribution of consecutive pattern γ -matches in S n (123) and S n (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. [ABSTRACT FROM AUTHOR]