Of great interest to me is the Hamiltonian path over some set of data. Pseudo-random number generators follow a fixed Hamiltonian path, visiting all elements of a set of results exactly one time before visiting any element a second time. There are a factorial number of different Hamiltonian paths that exist for any set of data S. Hence, for a pseudo-random number generator (of values over some range 0 to n), there are n! different Hamiltonian paths that might be used, alternatives to each other, that govern visitation of the elements of the set S, and so the generation of a pseudo-random sequence.

The concern in this discussion is that there is also a set of Super-Hamiltonian paths over the set of all possible Hamiltonian paths of S. Specifically, the concern is the predictability of the next visited element of S for such Super-Hamiltonian paths.