  For odd n, the alternating group on n elements is generated by the
permutations that jump an element from any odd position to position 1. We prove
Hamiltonicity of the associated directed Cayley graph for all odd n not equal
to 5. (A result of Rankin implies that the graph is not Hamiltonian for n=5.)
This solves a problem arising in rank modulation schemes for flash memory. Our
result disproves a conjecture of Horovitz and Etzion, and proves another
conjecture of Yehezkeally and Schwartz.
