Asymptotics and inequalities for the distinct partition function
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917168983048192 |
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| author | Mukherjee, Gargi Zhang, Helen W. J. Zhong, Ying |
| author_facet | Mukherjee, Gargi Zhang, Helen W. J. Zhong, Ying |
| contents | In this paper, we give explicit error bounds for the asymptotic expansion of the shifted distinct partition function $q(n +s)$ for any nonnegative integer $s$. Then based on this refined asymptotic formula, we give the exact thresholds of $n$ for the inequalities derived from the invariants of the quartic binary form, the double Turán inequalities, the Laguerre inequalities and their corresponding companion versions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21205 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotics and inequalities for the distinct partition function Mukherjee, Gargi Zhang, Helen W. J. Zhong, Ying Combinatorics Number Theory 05A16, 05A20, 11P82 In this paper, we give explicit error bounds for the asymptotic expansion of the shifted distinct partition function $q(n +s)$ for any nonnegative integer $s$. Then based on this refined asymptotic formula, we give the exact thresholds of $n$ for the inequalities derived from the invariants of the quartic binary form, the double Turán inequalities, the Laguerre inequalities and their corresponding companion versions. |
| title | Asymptotics and inequalities for the distinct partition function |
| topic | Combinatorics Number Theory 05A16, 05A20, 11P82 |
| url | https://arxiv.org/abs/2512.21205 |