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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2505.15236 |
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| _version_ | 1866916844920635392 |
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| author | Banerjee, Koustav Bringmann, Kathrin Kane, Ben |
| author_facet | Banerjee, Koustav Bringmann, Kathrin Kane, Ben |
| contents | We derive an asymptotic expansion with effective error bound for $u(n)$, counting the number of unimodal sequences of size $n$. We prove that $u(n)$ satisfies the higher order Turán inequalities for $n\geq33$ and that certain second $j$-shifted difference of $u(n)$ are positive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15236 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A generic approach to proving Turán-type inequalities for sequences that admit exact formulas, with an application to unimodal sequences Banerjee, Koustav Bringmann, Kathrin Kane, Ben Number Theory We derive an asymptotic expansion with effective error bound for $u(n)$, counting the number of unimodal sequences of size $n$. We prove that $u(n)$ satisfies the higher order Turán inequalities for $n\geq33$ and that certain second $j$-shifted difference of $u(n)$ are positive. |
| title | A generic approach to proving Turán-type inequalities for sequences that admit exact formulas, with an application to unimodal sequences |
| topic | Number Theory |
| url | https://arxiv.org/abs/2505.15236 |