  Employing the Haldane-Rezayi periodic representation, the crystalline
determinantal Hall crystal mean field solutions derived in previous works are
used to construct variational wavefunctions for the FQHE at $\nu=1/q$. The
proposed states optimize the short range correlations in a similar measure as
the Laughlin ones, since the zero of the states when the coordinates of two
particles join is of order $q$. However, the proposed wavefunctions also
incorporate the crystalline correlations of the mean field problem, through a
determinantal mean field function entering their construction. The above
properties, lead to the expectation that the considered states can be
competitive in energy per particle with the Laughlin ones. Their similar
structure also could explain way the breaking of the translation invariance in
the FQHE ground states can result to be a weak one, which after disregarded,
produce the Laughlin states as good approximations. Calculation for checking
these possibilities are under consideration.
