2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/82392In this paper we study the enumeration of number (denoted as ${D_I}$) of spin $I$ states for fermions in a single-$j$ shell and bosons with spin $l$. We show that $D_I$ can be enumerated by the reduction from SU$(n+1)$ to SO(3). New regularities of $D_I$ are discerned.3 pages, no figures. to be publishedNuclear Theorytext