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.