Linked partition ideals and a family of quadruple summations

Recently, 4-regular partitions into distinct parts were 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. (c) 2023 Elsevier Inc. All rights reserved.