On growth rates of hereditary permutation classes

A class of permutations is called hereditary if implies where the relation is the natural containment of permutations Let n be the set of all permutations of n belonging to We investigate the counting functions n j nj of hereditary classes Our main result says that if j nj n for at least one n then there is a unique k such that Fn k j nj Fn k n c holds for all n with a constant c Here Fn k are the generalized Fibonacci numbers which grow like powers of the largest positive root of xk xk We characterize also the constant and the polynomial growth of hereditary permutation classes and give two more results on these