  We developed a novel experimental technique to generate mechanically stable
(MS) packings of frictionless granular disks. We performed a series of
coordinated experiments and numerical simulations to enumerate the MS packings
in small 2D systems composed of bidisperse disks. We find that frictionless MS
packings occur as discrete, well-separated points in configuration space and
obtain excellent quantitative agreement between MS packings generated in
experiments and simulations. In addition, we observe that MS packing
probabilities can vary by many orders of magnitude and are robust with respect
to the packing-generation procedure. These results suggest that the most
frequent MS packings may dominate the structural and mechanical properties of
granular systems. We argue that these results for small systems represent a
crucial first-step in constructing a statistical description for large granular
systems from the `bottom-up'.
