  We construct a sequence of finite automata that accept subclasses of the
class of 4231-avoiding permutations. We thereby show that the Wilf-Stanley
limit for the class of 4231-avoiding permutations is bounded below by 9.35.
This bound shows that this class has the largest such limit among all classes
of permutations avoiding a single permutation of length 4 and refutes the
conjecture that the Wilf-Stanley limit of a class of permutations avoiding a
single permutation of length k cannot exceed (k-1)^2.
