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Number of spin I states of identical particles

In this article we study the enumeration of number (denoted as D{sub I}) of spin I states for fermions in a single-j shell and bosons with spin l. We show that D{sub I} can be enumerated by the reduction from SU(n+1) to SO(3). New regularities of D{sub I} are discerned. As an example of our new algorithm, we obtained analytical expressions of D{sub I} for four particles.