Linked partition ideals and gap-frequency partitions
arXiv:2606.16739
Abstract
Recently, linked partition ideals have attracted renewed attention. In this paper, we embed the gap-frequency partitions in which each part appears at most twice or three times into the framework of span one linked partition ideals, and derive refined generating functions for both cases. Furthermore, for gap-frequency partitions in which every part appears at most k times, we provide a purely combinatorial proof of the corresponding refined generating function.
18 pages, to appear in Discrete Mathematics