# 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…

## References

SHOWING 1-6 OF 6 REFERENCES

### Asymptotic inequalities for positive crank and rank moments

• Mathematics
• 2012
Andrews, Chan, and Kim recently introduced a modified definition of crank and rank moments for integer partitions that allows the study of both even and odd moments. In this paper, we prove the

### The First Positive Rank and Crank Moments for Overpartitions

• Mathematics
• 2013
In 2003, Atkin and Garvan initiated the study of rank and crank moments for ordinary partitions. These moments satisfy a strict inequality. We prove that a strict inequality also holds for the first

### On the number of even and odd strings along the overpartitions of n

• Mathematics
• 2013
AbstractRecently, Andrews, Chan, Kim, and Osburn introduced the even strings and the odd strings in the overpartitions. We show that their conjecture $$A_k (n) \geq B_k (n)$$Ak(n)≥Bk(n)holds for