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arXiv · 2408.00319

Sequences with Inequalities

Bernhard Heim und Markus Neuhauser
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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 $\ell $-ary partition numbers. We prove part of this conjecture.

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Bernhard Heim und Markus Neuhauser. 2025-12-09. Sequences with Inequalities. https://arxiv.org/abs/2408.00319

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