On 2-color partitions where one of the colors is multiples of $7^k$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916671563759616 |
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| author | Gireesh, D. S. C., Shivashankar B, HemanthKumar |
| author_facet | Gireesh, D. S. C., Shivashankar B, HemanthKumar |
| contents | In this work, we investigate the arithmetic properties of $p_{1,7^k}(n)$, which counts 2-color partitions of $n$ where one of the colors appears only in parts that are multiples of $7^k$. By constructing generating functions for $p_{1,7^k}(n)$ across specific arithmetic progressions, we establish a set of Ramanujan-type infinite family of congruences modulo powers of $7$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_01518 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On 2-color partitions where one of the colors is multiples of $7^k$ Gireesh, D. S. C., Shivashankar B, HemanthKumar Number Theory primary 11P83, secondary 05A15, 05A17 In this work, we investigate the arithmetic properties of $p_{1,7^k}(n)$, which counts 2-color partitions of $n$ where one of the colors appears only in parts that are multiples of $7^k$. By constructing generating functions for $p_{1,7^k}(n)$ across specific arithmetic progressions, we establish a set of Ramanujan-type infinite family of congruences modulo powers of $7$. |
| title | On 2-color partitions where one of the colors is multiples of $7^k$ |
| topic | Number Theory primary 11P83, secondary 05A15, 05A17 |
| url | https://arxiv.org/abs/2504.01518 |