Truncated theta series and partitions into distinct parts

Mircea Merca

Truncated theta series and partitions into distinct parts

Combinatorics 2020-06-16 v1

Authors: Mircea Merca

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.

Keywords

truncated theta series partitions into distinct parts linear inequalities partition function Q(n) Euler's partition function

Cite

@article{arxiv.2006.07704,
  title  = {Truncated theta series and partitions into distinct parts},
  author = {Mircea Merca},
  journal= {arXiv preprint arXiv:2006.07704},
  year   = {2020}
}

Comments

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

Truncated theta series and partitions into distinct parts

Abstract

Keywords

Cite

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