Abstract :
Recently, several authors have been treating partitions by considering the gaps between their consecutive parts. Many of the existing results involving “partitions with parts in the gaps” bear a striking resemblance to certain weighted partition identities that also arise from the gaps of partitions. In this paper, we show that this is not merely a coincidence, and we demonstrate that many of these weighted partition identities are equivalent to identities involving partitions with parts in the gaps. We intend that this brief note will more or less act as a Rosetta Stone for some of the literature on the gap-theoretic study of partitions.
