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A new procedure for large-scale calculations of the coefficients of fractional parentage (CFP) for many-particle systems is presented. The approach is based on a simple enumeration scheme for antisymmetric N particle states, and we suggest an efficient method for constructing the eigenvectors of two-particle transposition operator $$P_{N_1 ,N}$$ in a subspace where N1 and N2 = N − N1 nucleons basis states are already antisymmetrized. The main result of this paper is that according to permutation operators $$P_{N_1 ,N}$$ eigenvalues we can distinguish totally asymmetrical N particle states from the other states with lower degree of asymmetry.

Method simplifying calculation of coefficients of fractional parentage for translationally invariant shell-model