Hamiltonicity of the Cayley Digraph on the Symmetric Group Generated by {σ} = (1 2 ... n) and {τ} = (1 2)

The symmetric group is generated by {\sigma} = (1 2 ... n) and {\tau} = (1 2). We answer an open problem of Nijenhuis and Wilf by constructing a Hamilton path in the directed Cayley graph for all n, and a Hamilton cycle for odd n.