Sequences with Inequalities
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908700647620608 |
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| author | Neuhauser, Bernhard Heim und Markus |
| author_facet | Neuhauser, Bernhard Heim und Markus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00319 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sequences with Inequalities Neuhauser, Bernhard Heim und Markus Combinatorics Number Theory 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. |
| title | Sequences with Inequalities |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2408.00319 |