  We give a bijective proof of the fact that the number of k-prefixes of
minimal factorisations of the n-cycle (1...n) as a product of n-1
transpositions is n^{k-1}\binom{n}{k+1}. Rather than a bijection, we construct
a surjection with fibres of constant size. This surjection is inspired by a
bijection exhibited by Stanley between minimal factorisations of an n-cycle and
parking functions, and by a counting argument for parking functions due to
Pollak.
