## Dun Qiu ; Jeffrey Remmel - Classical pattern distributions in $\mathcal{S}_{n}(132)$ and $\mathcal{S}_{n}(123)$

dmtcs:5088 - Discrete Mathematics & Theoretical Computer Science, November 4, 2019, Vol. 21 no. 2, Permutation Patters 2018 - https://doi.org/10.23638/DMTCS-21-2-4
Classical pattern distributions in $\mathcal{S}_{n}(132)$ and $\mathcal{S}_{n}(123)$

Authors: Dun Qiu ; Jeffrey Remmel

Classical pattern avoidance and occurrence are well studied in the symmetric group $\mathcal{S}_{n}$. In this paper, we provide explicit recurrence relations to the generating functions counting the number of classical pattern occurrence in the set of 132-avoiding permutations and the set of 123-avoiding permutations.

Volume: Vol. 21 no. 2, Permutation Patters 2018
Section: Permutation Patterns
Published on: November 4, 2019
Submitted on: January 17, 2019
Keywords: Mathematics - Combinatorics,05A05, 05A10, 05A15, 05A19