Partitions related to positive definite binary quadratic forms

TL;DR

This paper explores generating functions for partitions linked to positive definite binary quadratic forms and introduces new Bailey pairs, contributing to the understanding of their mathematical relationships.

Contribution

It presents new generating functions and Bailey pairs connecting partitions to positive definite binary quadratic forms.

Findings

New generating functions for partitions related to quadratic forms

Introduction of novel Bailey pairs

Enhanced understanding of partition and quadratic form connections

Abstract

The purpose of this paper is to present a collection of interesting generating functions for partitions which have connections to positive definite binary quadratic forms. In establishing our results we obtain some new Bailey pairs.