Sequences with Inequalities

We consider infinite sequences of positive numbers. The connection between log-concavity and the Bessenrodt--Ono inequality had been in the focus of several papers. This has applications in the white noise distribution theory and combinatorics. We improve a recent result of Benfield and Roy and show...

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Bibliographic Details
Published in:arXiv.org 2024-08
Main Author: Bernhard Heim und Markus Neuhauser
Format: Article
Language:English
Subjects:
Combinatorial analysis
Concavity
White noise
Online Access:Get full text
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Summary:We consider infinite sequences of positive numbers. The connection between log-concavity and the Bessenrodt--Ono inequality had been in the focus of several papers. This has applications in the white noise distribution theory and combinatorics. We improve a recent result of Benfield and Roy and show that for the sequence of partition numbers \(\{p(n)\}\) Nicolas' log-concavity result implies the result of Bessenrodt and Ono towards \(p(n) \, p(m) > p(n+m)\).
ISSN:2331-8422