Truncated theta series and partitions into distinct parts

TL;DR

This paper introduces new linear inequalities for the partition function counting distinct parts using truncated theta series, offering novel insights and interpretations in partition theory.

Contribution

It presents four infinite families of inequalities for the distinct-part partition function using truncated theta series, with new partition theoretic interpretations.

Findings

Four infinite families of inequalities for Q(n)

Partition theoretic interpretations provided

Advances understanding of partitions into distinct parts

Abstract

Linear inequalities involving Euler's partition function $p(n)$ have been the subject of recent studies. In this article, we consider the partition function $Q(n)$ counting the partitions of $n$ into distinct parts. Using truncated theta series, we provide four infinite families of linear inequalities for $Q(n)$ and partition theoretic interpretations for these results.