Cyclic permutations avoiding pairs of patterns of length three

Miklos Bona, Michael Cory

Published 2018-05-14Version 1

We complete the enumeration of cyclic permutations avoiding two patterns of length three each by providing explicit formulas for each 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.