New relations for coefficients of fractional parentage-The Redmond recursion formula with seniority

We find a relationship between coefficients of fractional parentage (cfp) obtained on the one hand from the principal-parent method and on the other hand from a seniority classification. We apply this to the Redmond recursion formula which relates n → n + 1 cfp's to n − 1 → n cfp's where the principal-parent classification is used. We transform this to the seniority scheme. Our formula differs from the Redmond formula inasmuch as we have a sum over the possible seniorities for the n → n + 1 cfp's, whereas Redmond has only one term. We show that there are useful applications of both the principal-parent and the seniority classification.