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
收藏
页码：1451 / 1466
页数：16
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