  We consider the action of the modular group $\Gamma (2)$ on the set of
positive rational fractions. From this, we derive a model for a classification
of fractional (as well as integer) Hall states which can be visualized on two
``visibility" diagrams, the first one being associated with even denominator
fractions whereas the second one is linked to odd denominator fractions. We use
this model to predict, among some interesting physical quantities, the relative
ratios of the width of the different transversal resistivity plateaus. A
numerical simulation of the tranversal resistivity plot based on this last
prediction fits well with the present experimental data.
