A note on Some Partitions Related to Ternary Quadratic Forms

TL;DR

This paper introduces partition functions connected to ternary quadratic forms, explores their upper bounds and properties, and demonstrates the utility of a simple method based on conjugate Bailey pairs.

Contribution

It presents new partition functions related to ternary quadratic forms and applies a simple conjugate Bailey pair method to analyze their properties.

Findings

Partition functions related to ternary quadratic forms are introduced.

Upper bounds and properties of these partition functions are established.

The conjugate Bailey pair method proves effective in this context.

Abstract

We offer some partition functions related to ternary quadratic forms, and note on their upper bounds and related properties. We offer these results as an application of a simple method related to conjugate Bailey pairs presented in a prior study, further illustrating its utility.