Prove that Eq. (19.34) gives the simplest multi-gluon and gluon-quark states that contain an (mathrm{SU}(3)) color singlet

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Prove that Eq. (19.34) gives the simplest multi-gluon and gluon-quark states that contain an \(\mathrm{SU}(3)\) color singlet in the decomposition.

Data from Eq. 19.34

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