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The pseudopotentials describing the interactions of quasiparticles infractional quantum Hall (FQH) states are studied. Rules for the identificationof incompressible quantum fluid ground states are found, based upon the form ofthe pseudopotentials. States belonging to the Jain sequence nu=n/(1+2pn), wheren and p are integers, appear to be the only incompressible states in thethermodynamic limit, although other FQH hierarchy states occur for finite sizesystems. This explains the success of the composite Fermion picture.Comment: RevTeX, 10 pages, 7 EPS figures, submitted fo Phys.Rev.

Quasiparticle interactions in fractional quantum Hall systems: Justification of different hierarchy schemes