Tur?n inequalities for the plane partition function

被引：17

作者：

Ono, Ken ^{[1
]}

Pujahari, Sudhir ^{[2
]}

Rolen, Larry ^{[3
]}

机构：

[1] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA

[2] HBNI, Natl Inst Sci Educ & Res Bhubaneswar, Sch Math Sci, PO Jatni, Bhubaneswar 752050, Odisha, India

[3] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

来源：

ADVANCES IN MATHEMATICS | 2022年 / 409卷

关键词：

Plane partition function; Log-concavity; Tur?n inequalities;

D O I：

10.1016/j.aim.2022.108692

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Heim, Neuhauser and Troger recently established some inequalities for MacMahon's plane partition function PL(n) that generalize known results for Euler's partition function p(n). They also conjectured that PL(n) is log-concave for all n > 12. We prove this conjecture. Moreover, for every d > 1, we prove their speculation that PL(n) satisfies the degree d Turan inequalities for sufficiently large n. The case where d = 2 is the case of log-concavity.(c) 2022 Elsevier Inc. All rights reserved.

引用

页数：31

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