A generalisation of a partition theorem of Andrews to overpartitions

TL;DR

This paper extends Andrews' 1969 partition theorem, originally about partitions with difference conditions, to the broader context of overpartitions, using q-differential equations and recurrences.

Contribution

It introduces a generalisation of Andrews' theorem to overpartitions, expanding the scope of partition identities.

Findings

Generalisation of Andrews' theorem to overpartitions

Use of q-differential equations and recurrences in proof

Enhanced understanding of partition identities

Abstract

In 1969, Andrews proved a theorem on partitions with difference conditions which generalises Schur's celebrated partition identity. In this paper, we generalise Andrews' theorem to overpartitions. The proof uses q-differential equations and recurrences.