Given a natural number N, one may ask what configuration of N points on the
two-sphere minimizes the discrete generalized Coulomb energy. If one applies a
gradient-based numerical optimization to this problem, one encounters many
configurations that are stable but not globally minimal. This led the authors
of this manuscript to the question, how many stable configurations are there?
In this manuscript we report methods for identifying and counting observed
stable configurations, and estimating the actual number of stable
configurations. These estimates indicate that for N approaching two hundred,
there are at least tens of thousands of stable configurations.Comment: The final publication is available at Springer via
http://dx.doi.org/10.1007/s10955-015-1245-
