Determinantal inequalities for the partition function

被引：9

作者：

Jia, Dennis X. Q. ^{[1
]}

Wang, Larry X. W. ^{[1
]}

机构：

[1] Nankai Univ, Ctr Combinatorics, Tianjin 300071, Peoples R China

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2020年 / 150卷 / 03期

基金：

美国国家科学基金会;

关键词：

Partition function; log-concavity; determinant; the Hardy-Ramanujan-Rademacher formula; double Turan inequality; LOG-CONCAVITY;

D O I：

10.1017/prm.2018.144

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let p(n) denote the partition function. In this paper, we will prove that for n222, p(n) p(n + 1) p(n + 2) p(n - 1) p(n) p(n + 1) p(n - 2) p(n - 1) p(n) > 0. As a corollary, we deduce that p(n) satisfies the double Tur ' an inequalities, that is, for n222, (p(n)2 - p(n - 1)p(n + 1))2 - (p(n - 1)2 - p(n - 2)p(n))(p(n + 1)2 - p(n)p(n + 2)) > 0.

引用

页码：1451 / 1466

页数：16

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