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arXiv · 2507.09276

Certain positive $q$-series and inequalities for two-color partitions

George E. Andrews·Mohamed El Bachraoui
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Abstract

We consider some $q$-series which depend on a pair of positive integers $(k,m)$. While positivity of these series holds for the first few values of $(k,m)$, the situation is quite unclear for other values of $(k,m)$. In addition, our series generate the number of certain two-color integer partitions weighted by $(-1)^j$ where $j$ is the number of even parts. Therefore, inequalities involving these partitions will be deduced from the positivity of their generating functions.

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George E. Andrews, Mohamed El Bachraoui. 2025-07-12. Certain positive $q$-series and inequalities for two-color partitions. https://arxiv.org/abs/2507.09276

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