Enumeration and Wilf-classification of permutations avoiding five patterns of length 4

Let Sn be the symmetric group of all permutations of n letters. We show that there are exactly 3441 distinct Wilf classes for the permutations avoiding five patterns of length 4. Moreover, for each T ⊂ S4 with #T = 5, we determine the generating
function for the number of permutations in Sn(T ), the set of all permutations of length n that avoid each pattern in T .