  We consider the distribution of ascents, descents, peaks, valleys, double
ascents, and double descents over permutations avoiding a set of patterns. Many
of these statistics have already been studied over sets of permutations
avoiding a single pattern of length 3. However, the distribution of peaks over
321-avoiding permutations is new and we relate it statistics on Dyck paths. We
also obtain new interpretations of a number of well-known combinatorial
sequences by studying these statistics over permutations avoiding two patterns
of length 3.
