由行列式引起的超配分函数的不等式
Inequalities for the overpartition function arising from determinants
摘要：
令$\overline{p}(n)$表示过划分函数。本文通过考虑一个更一般的不等式\begin{equation*} \begin{vmatrix} \overline{p}(n) & \overline{p}(n+1) & \overline{p}(n+2) \\ \overline{p}(n-1) & \overline{p}(n) & \overline{p}(n+1) \\ \overline{p}(n-2) & \overline{p}(n-1) & \overline{p}(n) \end{vmatrix} > 0, \end{equation*}，证明了$\overline{p}(n)$的$2$ - $\log$ -性质，该不等式对所有$n \geq 42$都成立.
英文摘要：
Let $\overline{p}(n)$ denote the overpartition funtion. This paper presents the $2$-$\log$-concavity property of $\overline{p}(n)$ by considering a more general inequality of the following form \begin{equation*} \begin{vmatrix} \overline{p}(n) & \overline{p}(n+1) & \overline{p}(n+2) \\ \overline{p}(n-1) & \overline{p}(n) & \overline{p}(n+1) \\ \overline{p}(n-2) & \overline{p}(n-1) & \overline{p}(n) \end{vmatrix} > 0, \end{equation*} which holds for all $n \geq 42$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
