We implement an advanced technique to provide combinatorial interpretations of some Rogers--Ramanujan type identities, also known as sum--product identities. Specifically, we elaborate on the notion of modular Ferrers diagrams to explain these identities in terms of $n$--color overpartitions. Additionally, we reveal the interdependence between split part $n$--color partitions, $2$--color $F$--partitions, and $n$--color overpartitions.
Keywords and Phrases
Rogers--Ramanujan type identities; $n$--color overpartitions; Split part $n$--color partition; $2$--color $F$--partition; Modular Ferrers diagram; Combinatorial interpretation.
A.M.S. subject classiﬁcation
05A17, 19, 11P81, 84.