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.