English

Linked partition ideals and a family of quadruple summations

Combinatorics 2023-01-27 v1 Number Theory

Abstract

Recently, 44-regular partitions into distinct parts are connected with a family of overpartitions. In this paper, we provide a uniform extension of two relations due to Andrews for the two types of partitions. Such an extension is made possible with recourse to a new trivariate Rogers--Ramanujan type identity, which concerns a family of quadruple summations appearing as generating functions for the aforementioned overpartitions. More interestingly, the derivation of this Rogers--Ramanujan type identity is relevant to a certain well-poised basic hypergeometric series.

Keywords

Cite

@article{arxiv.2301.11137,
  title  = {Linked partition ideals and a family of quadruple summations},
  author = {George E. Andrews and Shane Chern},
  journal= {arXiv preprint arXiv:2301.11137},
  year   = {2023}
}