A combinatorial proof and refinement of a partition identity of Siladić

Rogers-Ramanujan type partition identities establish equalities between certain types of partitions with difference conditions and partitions whose generating functions is an infinite product. Since the 1980’s, many connections between representations of Lie algebras and RogersRamanujan type partition identities have emerged. Lepowsky and Wilson [6] were the first to establish this link by giving an interpretation of Theorem 1.1 in terms of representations of the affine Lie algebra sl(2,C)∼. Similar methods were subsequently applied to other representations of affine Lie algebras, yielding new partition identities of the