Addendum to `Bosonic formulas for $(k,l)$-admissible partitions'

In our earlier paper we made a combinatorial study of (k,l)-admissible partitions. This object appeared already in the work of M. Primc as a label of a basis of level k-integrable modules over ${\widehat{sl}}_l$. We clarify the relation between these two works. As a byproduct we obtain an explicit parameterization of the affine Weyl group of ${\widehat{sl}}_l$ by a simple combinatorial set.