Sequences with Inequalities

2024/08/01 by Bernhard Heim und Markus Neuhauser, Neuhauser, Bernhard Heim und Markus
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Approximation and Integration #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2408.00319

openalex publication_date 2024/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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). We provide several examples. Benfield and Roy gave a conjecture related to ℓ -ary partition numbers. We prove part of this conjecture.

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