Counting 1324, 4231-Avoiding Permutations

Classes of permutations are sets of permutations that are closed downwards under taking subpermutations. They are usually presented as sets C that avoid a given set B of permutations (i.e. the permutations of C have no subpermutation in the set B). We express this by the notation C = Av(B). Much of the inspiration for elucidating the structure of pattern classes has been driven by the enumeration problem: given C = Av(B), howmany permutations of each length does C contain? The answer to such a question can be a formula giving this number cn in terms of the length n, or it may be a generating function