The hierarchy schemes for the fractional quantum Hall effect are reexamined and it is shown that different schemes all give the same lattice of excitations whose statistics is determined by the norm of the corresponding vector, and hence have equivalent Ginzburg-Landau theories. Similar ideas apply to the anyon liquid. The schemes can be generalized by using different lattices; many inequivalent states can be obtained at any filling factor (or value of the statistics parameter).

• Received 29 June 1990

DOI:https://doi.org/10.1103/PhysRevLett.65.1502