Congruences modulo powers of $3$ for $6$-colored generalized Frobenius partitions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908935259160576 |
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| author | Chen, Dandan Yin, Siyu |
| author_facet | Chen, Dandan Yin, Siyu |
| contents | In $1984$, Andrews introduced the family of partition functions $cϕ_k(n)$, which enumerate generalized Frobenius partitions of $n$ with $k$ colors. In $2016$, Gu, Wang, and Xia established several congruences for $cϕ_6(n)$ and proposed a conjecture concerning congruences modulo powers of $3$ for this function. In this paper, we resolve a revised version of their conjecture by employing an approach analogous to that developed by Banerjee and Smoot. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04983 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Congruences modulo powers of $3$ for $6$-colored generalized Frobenius partitions Chen, Dandan Yin, Siyu Combinatorics Number Theory 11P83, 05A17 In $1984$, Andrews introduced the family of partition functions $cϕ_k(n)$, which enumerate generalized Frobenius partitions of $n$ with $k$ colors. In $2016$, Gu, Wang, and Xia established several congruences for $cϕ_6(n)$ and proposed a conjecture concerning congruences modulo powers of $3$ for this function. In this paper, we resolve a revised version of their conjecture by employing an approach analogous to that developed by Banerjee and Smoot. |
| title | Congruences modulo powers of $3$ for $6$-colored generalized Frobenius partitions |
| topic | Combinatorics Number Theory 11P83, 05A17 |
| url | https://arxiv.org/abs/2504.04983 |