Higher order log-concavity of the overpartition function and its consequences
Higher order log-concavity of the overpartition function and its consequences
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DOI：
10.1017/s0013091523000093
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发表时间：
2022-04
影响因子：
0.7
通讯作者：
G. Mukherjee;Helen W. J. Zhang;Ying Zhong
中科院分区：
文献类型：
--
作者：
G. Mukherjee;Helen W. J. Zhang;Ying Zhong
摘要设${\overline{p}}(N)$表示过分划函数。本文在Hou和Zhang关于配分函数的类似框架下，研究了超配分函数的渐近高阶对数凹性。这将使我们能够进一步证明过划分的对数凹性，明确地通过研究商${\overline{p}}(n-1){\overline{p}}(n+1)/{\overline{p}}(n)^2$到某一阶的渐近展开来证明。这使得我们能够用统一的方法另外证明2-对数凹性和高阶Turán不等式。
Abstract Let ${\overline{p}}(n)$ denote the overpartition function. In this paper, we study the asymptotic higher-order log-concavity property of the overpartition 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 ${\overline{p}}(n-1){\overline{p}}(n+1)/{\overline{p}}(n)^2$ up to a certain order. This enables us to additionally prove 2-log-concavity and higher Turán inequalities with a unified approach.