Truncated theta series and 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.

Some of the results obtained in this article were presented at Transient Transcendence In Transylvania, Brasov, Romania, May 13-17, 2019. https://specfun.inria.fr/bostan/trans19/slides/Merca.pdf