On a problem raised by P.J. Cameron Original Research Article

At the problem session of the 14th British Combinatorial Conference, Cameron asked for a bijection between the set of permutations of 1, 2, …, n with all cycles of even length and the set of permutations of 1, 2, …,n with all cycles odd (where n is even). Here we give bijections between more general sets of permutations.