2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/215904Answering a question of Bona, it is shown that for n>1 the probability that 1 and 2 are in the same cycle of a product of two n-cycles on the set {1,2,...,n} is 1/2 if n is odd and 1/2 - 2/(n-1){n+2) if n is even. Another result concerns the generating function P_h(q) for the number of cycles of the product (1,2,...,n)w, where w ranges over all permutations of 1,2,...,n of cycle type h. A formula is obtained for P_h(q) from which it is proved that the zeros of P_h(q) have real part 0.10 pagesCombinatorics05A15; 05E05text