Translation sets of permutations: Enumeration of selfcomplementary step-cycles

For given integern>2, there corresponds to each step-cycle a set of permutations, called a translation set. All the translation sets of permutations on the setS={1, 2, ...,n?1} form a set of equivalence classes on the set of all permutations onS. The selfcomplementary step-cycles are described and enumerated. A more general introduction to translation sets may be found in 4] and 3].