Determinantal inequalities for the partition function

DOI10.1017/prm.2018.144zbMath1437.05023OpenAlexW2914380314WikidataQ128501182 ScholiaQ128501182MaRDI QIDQ4961017

Dennis X. Q. Jia, Larry X. W. Wang

Publication date: 24 April 2020

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/prm.2018.144

zbMATH Keywords

partition functiondeterminantlog-concavityHardy-Ramanujan-Rademacher formuladouble Turán inequality

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Combinatorial inequalities (05A20) Analytic theory of partitions (11P82) Matrices, determinants in number theory (11C20)

Related Items (6)

Laguerre inequalities for discrete sequences ⋮ Inequalities for the overpartition function arising from determinants ⋮ Higher order Turán inequalities for the distinct partition function ⋮ Higher order log-concavity of the overpartition function and its consequences ⋮ On a new class of Laguerre-Pólya type functions with applications in number theory ⋮ Positivity of the determinants of the partition function and the overpartition function

Cites Work

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• Log-concavity of the partition function
• Jensen polynomials and the Turán and Laguerre inequalities
• \(r\)-log-concavity of partition functions
• Karlin's conjecture and a question of Pólya
• Finite differences of the logarithm of the partition function
• Unimodal, log-concave and Pólya frequency sequences in combinatorics
• Higher order Turán inequalities for the partition function
• On the Generating Functions of Totally Positive Sequences
• Conjectures and theorems in the theory of entire functions

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