Arithmetic Properties of Partitions with 1-colored Even Parts and r-colored Odd Parts
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911273010069504 |
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| author | Thejitha, M. P. Fathima, S. N. |
| author_facet | Thejitha, M. P. Fathima, S. N. |
| contents | Recently, Hirschhorn and Sellers defined the partition function $a_r(n)$, which counts the number of partitions of $n$ wherein even parts come in only one color, while the odd parts may appear in one of $r$-colors for fixed $r\ge1$. The aim of this paper is to prove several new infinite families of congruences modulo 3 and 5 by employing a result of Newman and theory of modular forms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_24324 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Arithmetic Properties of Partitions with 1-colored Even Parts and r-colored Odd Parts Thejitha, M. P. Fathima, S. N. Number Theory 05A17 (Primary), 11P83 (Secondary) Recently, Hirschhorn and Sellers defined the partition function $a_r(n)$, which counts the number of partitions of $n$ wherein even parts come in only one color, while the odd parts may appear in one of $r$-colors for fixed $r\ge1$. The aim of this paper is to prove several new infinite families of congruences modulo 3 and 5 by employing a result of Newman and theory of modular forms. |
| title | Arithmetic Properties of Partitions with 1-colored Even Parts and r-colored Odd Parts |
| topic | Number Theory 05A17 (Primary), 11P83 (Secondary) |
| url | https://arxiv.org/abs/2509.24324 |