  It has recently been proven that in rank three tensor models, the
anti-symmetric and symmetric traceless sectors both support a large $N$
expansion dominated by melon diagrams [arXiv:1712.00249 [hep-th]]. We show how
to extend these results to the last irreducible $O(N)$ tensor representation
available in this context, which carries a two-dimensional representation of
the symmetric group $S_3$. Along the way, we emphasize the role of the
irreducibility condition: it prevents the generation of vector modes which are
not compatible with the large $N$ scaling of the tensor interaction. This
example supports the conjecture that a melonic large $N$ limit should exist
more generally for higher rank tensor models, provided that they are
appropriately restricted to an irreducible subspace.
