Abstract
A recurrent formula of fractional parentage coefficients (CFPs) with explicit seniorities for identical fermions in the coupling scheme is given. The multiplicity of states with fixed seniority and angular momentum is also given. Using irreducible tensor method, the CFPs are factorized completely along a group chain. It is found that the CFPs are directly related to the group reduction coefficients. Them are useful for constructing an efficient iteration method of calculating the CFPs.
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