  In this paper we prove that among the permutations of length n with i fixed
points and j excedances, the number of 321-avoiding ones equals the number of
132-avoiding ones, for all given i,j<=n. We use a new technique involving
diagonals of non-rational generating functions. This theorem generalizes a
recent result of Robertson, Saracino and Zeilberger, for which we also give
another, more direct proof.
