A positivity conjecture related first positive rank and crank moments for overpartitions

@article{Xiong2016APC,
  title={A positivity conjecture related first positive rank and crank moments for overpartitions},
  author={Xinhua Xiong},
  journal={arXiv: Number Theory},
  year={2016}
}
  • Xinhua Xiong
  • Published 30 May 2016
  • Mathematics
  • arXiv: Number Theory
Recently, Andrews, Chan, Kim and Osburn introduced a $q$-series $h(q)$ for the study of the first positive rank and crank moments for overpartitions. They conjectured that for all integers $m \geq 3$, \begin{equation*}\label{hqcon} \frac{1}{(q)_{\infty}} (h(q) - m h(q^{m})) \end{equation*} has positive power series coefficients for all powers of $q$. Byungchan Kim, Eunmi Kim and Jeehyeon Seo provided a combinatorial interpretation and proved it is asymptotically true by circle method. In this… 

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