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^{++}particle led to the introduction of the missing degree of freedom, or color. It states that free particles are colorless so they must be in color singlet states. From there, it just lists the unnormalized anti-symmetric color singlet state as

rbg-rgb+grb-gbr+bgr-brg

I don't understand how they jumped from that statement to the equation. Where does this come from? Does it have to do with SU(3) symmetry? Any help would be greatly appreciated