Counting Consecutive Pattern Matches in ${\mathcal{S}}_n(132)$ and ${\mathcal{S}}_n(123)$

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 ${\mathcal{S}}_n(123)$ 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.

arXiv comment31 pages, 10 figures

References in corpus (3)

• Distributions of Statistics over Pattern-Avoiding Permutations
• Quadrant marked mesh patterns in 123-avoiding permutations
• Patterns in words of ordered set partitions