Linked partition ideals and a family of quadruple summations
Combinatorics
2023-01-27 v1 Number Theory
Abstract
Recently, -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}
}