 Pauli constraint on three-quark flavour multiplets

In a three-quark colour singlet, a symmetric spatial state requires symmetric spin-flavour symmetry. Completely symmetric decuplet flavour couples to symmetric spin $3/2$; mixed octet flavour couples to mixed spin $1/2$ in the symmetric permutation combination. Antisymmetric singlet flavour cannot have a symmetric S-wave orbital state, since ${\bigwedge }^3{\mathbb{C}}^2=0$ forbids a completely antisymmetric state of three spin-$1/2$ quarks. Mixed orbital and spin states can instead realize the required antisymmetry.