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
相关论文
共 50 条
  • [1] Determinantal inequalities for the psi function
    Palumbo, B
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 1999, 2 (02): : 223 - 231
  • [2] ON DETERMINANTAL AND PERMANENTAL INEQUALITIES
    GYIRES, B
    ACTA MATHEMATICA HUNGARICA, 1995, 66 (03) : 255 - 268
  • [3] Some determinantal inequalities
    Mond, B
    Pecaric, J
    Tepes, B
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2005, 8 (02): : 331 - 336
  • [4] ON SOME DETERMINANTAL INEQUALITIES
    CARLSON, D
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1968, 19 (02) : 462 - &
  • [5] Higher order Laguerre inequalities for the partition function
    Dou, Li-Mei
    Wang, Larry X. W.
    DISCRETE MATHEMATICS, 2023, 346 (06)
  • [6] Tur?n inequalities for the plane partition function
    Ono, Ken
    Pujahari, Sudhir
    Rolen, Larry
    ADVANCES IN MATHEMATICS, 2022, 409
  • [7] HIGHER ORDER TURAN INEQUALITIES FOR THE PARTITION FUNCTION
    Chen, William Y. C.
    Jia, Dennis X. Q.
    Wang, Larry X. W.
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2019, 372 (03) : 2143 - 2165
  • [8] The Laguerre inequality and determinantal inequality for the broken k-diamond partition function
    Yang, Eve Y. Y.
    RAMANUJAN JOURNAL, 2024, 64 (03): : 857 - 880
  • [9] REMARKS ON TWO DETERMINANTAL INEQUALITIES
    Tam, Tin-Yau
    Zhang, Pingping
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2019, 22 (03): : 815 - 823
  • [10] Reversed Fischer determinantal inequalities
    Drury, Stephen
    Lin, Minghua
    LINEAR & MULTILINEAR ALGEBRA, 2014, 62 (08): : 1069 - 1075
12345