Representation of permutations as products of two cycles Original Research Article

Given a permutation σ on n letters, we determine for which values of the integers l1 and l2 it is possible to represent σ as a product of two cycles of sizes l1 and l2, respectively. Our results are of a constructive nature. We also deal with the special cases l1=l2 for even permutations and l1=l2+1 for odd permutations, which were solved differently by Bertram in (J. Combin. Theory 12 (1972) 368).