Limit Theorem for the Middle Members of Ordered Cycle Lengths in Random A -Permutations

In this article, random permutation $\tau_n$ is considered uniformly distributed on the set of all permutations with degree $n$ and with cycle lengths from fixed set $A$ (so-called $A$-permutations). Let ζ^sub n^ be the general number of cycles and ... be the ordered cycle lengths in a random permutation τ^sub n^. The central limit theorem is obtained here for the middle members of this sequence, i.e., for random variables η^sub n(m) with numbers ... as n[arrow right]∞ for fixed α...(0,σ) and for some class of the sets A with positive asymptotic density σ. The basic approach to the proof is the new three-dimensional Tauberian theorem. Asymptotic behavior of extreme left and extreme right members of this sequence was investigated earlier by the author.(ProQuest: ... denotes formulae/symbols omitted.)