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Highly nonlocal interparticle correlations in quantum Hall states of 2Dcharged system exposed to the perpendicular strong magnetic field are detailedby application of the commensurability condition upon path-integralquantization approach and examined by Monte-Carlo Metropolis simulations inperfect consistence with exact diagonalization of the Coulomb interaction insmall models and with experimental data. In this way refined filling ratehierarchy in the lowest Landau level fully explains the experimentallycollected features for FQHE at filling ratios predicted by the conventionalcomposite fermion model as well as for those beyond the composite fermion modelbut also visible in the experiment. The trial wave functions for FQHE statesare proposed using a systematic topological method revealing the differentsymmetry for different correlated states depending on filling fraction. Aviolation of fermionic antisymmetry for 2D electrons is evidenced for somefilling rates related to specific correlations in FQHE.

Topological correlations and breaking of fermionic antisymmetry of electrons in FQHE