  In 1969, Andreev and Lifshitz have conjectured the existence of a supersolid
phase taking place at zero temperature between the quantum liquid and the
solid. In this and a succeeding paper, we re-visit this issue for a few
polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion
on a two dimensional L * L square lattice with periodic boundary conditions and
nearest neighbor hopping.
