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arXiv · 2204.07961

Higher order log-concavity of the overpartition function and its consequences

Gargi Mukherjee·Helen W. J. Zhang·Ying Zhong
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Abstract

Let $\bar{p}(n)$ denote the overpartition function. In this paper, we study the asymptotic higher order $\log$-concavity property of the overpatition function in a similar framework done by Hou and Zhang for the partition function. This will enable us to move on further in order to prove $\log$-concavity of overpartitions, explicitly by studying the asymptotic expansion of the quotient $\bar{p}(n-1)\bar{p}(n+1)/\bar{p}(n)^2$ upto a certain order so that one can finally ends up with the phenomena of $2$-$\log$-concavity and higher order Turán property of $\bar{p}(n)$ by following a sort of unified approach.

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Gargi Mukherjee, Helen W. J. Zhang, Ying Zhong. 2022-04-17. Higher order log-concavity of the overpartition function and its consequences. https://arxiv.org/abs/2204.07961

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