Asymptotic Formula for $(t+1)$-Regular Partitions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914410288644096 |
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| author | Barman, Jayanta Mahatab, Kamalakshya |
| author_facet | Barman, Jayanta Mahatab, Kamalakshya |
| contents | A partition is $t$-regular if none of its parts is divisible by $t$. Let $p(N,t)$ be the number of $(t+1)$-regular partitions of a positive integer $N$. In 1971, Hagis proved an asymptotic formula for $p(N,t)$ using the circle method, when $t$ fixed. In this article, we use the saddle point method and extend the result of Hagis in different ranges of $t$, obtaining explicit bounds. We also discuss an application of our result to estimate zeros in the character table of the symmetric group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19691 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic Formula for $(t+1)$-Regular Partitions Barman, Jayanta Mahatab, Kamalakshya Number Theory Combinatorics 11P82, 11P55, 11N37 A partition is $t$-regular if none of its parts is divisible by $t$. Let $p(N,t)$ be the number of $(t+1)$-regular partitions of a positive integer $N$. In 1971, Hagis proved an asymptotic formula for $p(N,t)$ using the circle method, when $t$ fixed. In this article, we use the saddle point method and extend the result of Hagis in different ranges of $t$, obtaining explicit bounds. We also discuss an application of our result to estimate zeros in the character table of the symmetric group. |
| title | Asymptotic Formula for $(t+1)$-Regular Partitions |
| topic | Number Theory Combinatorics 11P82, 11P55, 11N37 |
| url | https://arxiv.org/abs/2603.19691 |