R. Tauraso

Franklin's identity for $n$-color partitions and companion Beck-type identities

We show that some classical identities valid for ordinary partitions have precise analogues for $n$-color partitions, that is partitions in which a part of size $n\geq 1$ can occur in colors $1, 2, \ldots, n$. For $r \ge 2$ and $j \ge 0$, we write $\mathcal{O}_{j,r}(m)$ and $\mathcal{D}_{j,r}(m)$ for the sets of $n$-co...