A note on the exact formulas for certain $2$-color partitions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912119821172736 |
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| author | Guadalupe, Russelle |
| author_facet | Guadalupe, Russelle |
| contents | Let $p\leq 23$ be a prime and $a_p(n)$ counts the number of partitions of $n$ where parts that are multiple of $p$ come up with $2$ colors. Using a result of Sussman, we derive the exact formula for $a_p(n)$ and obtain an asymptotic formula for $\log a_p(n)$. Our results partially extend the work of Mauth, who proved the asymptotic formula for $\log a_2(n)$ conjectured by Banerjee et al. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_02367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the exact formulas for certain $2$-color partitions Guadalupe, Russelle Combinatorics Number Theory 11P55, 11P82, 05A16 Let $p\leq 23$ be a prime and $a_p(n)$ counts the number of partitions of $n$ where parts that are multiple of $p$ come up with $2$ colors. Using a result of Sussman, we derive the exact formula for $a_p(n)$ and obtain an asymptotic formula for $\log a_p(n)$. Our results partially extend the work of Mauth, who proved the asymptotic formula for $\log a_2(n)$ conjectured by Banerjee et al. |
| title | A note on the exact formulas for certain $2$-color partitions |
| topic | Combinatorics Number Theory 11P55, 11P82, 05A16 |
| url | https://arxiv.org/abs/2404.02367 |