A note on the exact formulas for certain $2$-color partitions
Let $p\le 23$ be a prime and $a_p(n)$ count 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 M...
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.658/ |
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| author | Guadalupe, Russelle |
| author_facet | Guadalupe, Russelle |
| author_sort | Guadalupe, Russelle |
| collection | DOAJ |
| description | Let $p\le 23$ be a prime and $a_p(n)$ count 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 | Article |
| id | doaj-art-2b49b5617c054db0a34f02d67c318e55 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-2b49b5617c054db0a34f02d67c318e552025-02-07T11:23:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G111485149010.5802/crmath.65810.5802/crmath.658A note on the exact formulas for certain $2$-color partitionsGuadalupe, Russelle0https://orcid.org/0009-0001-8974-4502Institute of Mathematics, University of the Philippines-Diliman, Quezon City, 1101, PhilippinesLet $p\le 23$ be a prime and $a_p(n)$ count 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.658/Circle method$\eta $-quotientspartitionsasymptotic formula |
| spellingShingle | Guadalupe, Russelle A note on the exact formulas for certain $2$-color partitions Comptes Rendus. Mathématique Circle method $\eta $-quotients partitions asymptotic formula |
| title | A note on the exact formulas for certain $2$-color partitions |
| title_full | A note on the exact formulas for certain $2$-color partitions |
| title_fullStr | A note on the exact formulas for certain $2$-color partitions |
| title_full_unstemmed | A note on the exact formulas for certain $2$-color partitions |
| title_short | A note on the exact formulas for certain $2$-color partitions |
| title_sort | note on the exact formulas for certain 2 color partitions |
| topic | Circle method $\eta $-quotients partitions asymptotic formula |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.658/ |
| work_keys_str_mv | AT guadaluperusselle anoteontheexactformulasforcertain2colorpartitions AT guadaluperusselle noteontheexactformulasforcertain2colorpartitions |