A Representation of Even Permutations

We give a combinatorial proof of the formula giving the number of representations of an even permutation σ inSnas a product of ann-cycle by an (n − 2)-cycle, such a number being (n − χ (σ))(n − 3)!, where χ(σ is the number of fixed points of σ. This proof relies on the fact that any odd permutation inSnis the product of ann-cycle by an (n − 1)-cycle in exactly 2(n − 2)! different ways.