Irreducible representations of $SU(3)$ for nucleons in a oscillator shell $η$ with $η\le 8$: Application to nuclei with proxy-$SU(4)$ symmetry

Applying some simple rules, established in group theory literature, generated are codes (easy to modify as required) for obtaining $SU(3)$ irreducible representations (irreps) for a given number of nucleons in a given oscillator shell $η$ with $η\le 8$. In this approach, first the $SU(3)$ irreps are