Limit distributions of the number of cycles of given length in a random permutation with a known number of cycles

We give a complete description of the limit behaviour of the number of cycles of length $r$ in a random permutation of degree $n$ with $N$ cycles in all domains of variations of the parameters $n$, $N$, $r$, thus essentially extending the known results concerning the limit behaviour of the number of such cycles.
This research was supported by the grant 1758.2003.1 of support of leading scientific schools of Russian Federation.