On the rate of convergence of the distribution of the number of cycles of given length in a random permutation with known number of cycles to the limit distributions

Let on the set S-n,S-N of all different permutations of degree n with N cycles the uniform distribution be given. We obtain estimates of the rate of convergence of the distribution of the number of cycles of given length in a random permutation of S-n,S-N to the limit distributions as n, N -> infinity in such a way that either n/N -> 1 or n/N -> infinity.