## Bona, Miklos and Cory, Michael - Cyclic permutations avoiding pairs of patterns of length three

dmtcs:5014 - Discrete Mathematics & Theoretical Computer Science, November 26, 2019, Vol. 21 no. 2, Permutation Patters 2018
Cyclic permutations avoiding pairs of patterns of length three

Authors: Bona, Miklos and Cory, Michael

We complete the enumeration of cyclic permutations avoiding two patterns of length three each by providing explicit formulas for all but one of the pairs for which no such formulas were known. The pair $(123,231)$ proves to be the most difficult of these pairs. We also prove a lower bound for the growth rate of the number of cyclic permutations that avoid a single pattern $q$, where $q$ is an element of a certain infinite family of patterns.

Volume: Vol. 21 no. 2, Permutation Patters 2018
Section: Permutation Patterns
Published on: November 26, 2019
Submitted on: December 5, 2018
Keywords: Mathematics - Combinatorics,05A05