Till now we have mainly been concerned with the coupling of two angular momenta \( j_{a} \) and \( j_{b} \) to a final angular momentum \( J \). If we wish to describe a three-body state with a final angular momentum \( J \), we need to couple three angular momenta, say the two momenta \( j_a,j_b \) to a third one \( j_c \). The coupling order is important and leads to a less trivial implementation of the Pauli principle. With three angular momenta there are obviously \( 3! \) ways by which we can combine the angular momenta. In \( m \)-scheme a three-body Slater determinant is represented as (say for the case of \( {}^{19}\mbox{O} \), three neutrons outside the core of \( {}^{16}\mbox{O} \)), $$ |^{19}\mathrm{O}\rangle =|(abc)M\rangle = a^{\dagger}_aa^{\dagger}_ba^{\dagger}_c|^{16}\mathrm{O}\rangle=|\Phi^{abc}\rangle. $$ The Pauli principle is automagically implemented via the anti-commutation relations.