ON THE LIMIT DISTRIBUTION OF THE NUMBER OF CYCLES AND THE LOGARITHM OF THE ORDER OF A CLASS OF PERMUTATIONS
Alexander Ivanovich Pavlov · Mathematics of the USSR-Sbornik · 1982
Let be the symmetric group of degree and let be the set of permutations such that the equation has a solution . Consider the uniform probability distribution on the set . This article investigates the limit distributions on , as and for fixed , of the random variables , , and , where is the number of cycles of length , is the number of all cycles, and is the logarithm of the order of a random permutation . Bibliography: 5 titles.