Congruences modulo $7$ and $11$ for certain two restricted partition functions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918277271257088 |
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| author | Guadalupe, Russelle |
| author_facet | Guadalupe, Russelle |
| contents | For an integer $c\geq 1$, let $a_c(n)$ count the number of generalized cubic partitions of $n$, which are partitions of $n$ whose even parts may appear in $c$ different colors, and $d_c(n)$ count the number of partitions obtained by adding the links of the $c$-elongated plane partition diamonds of length $n$. We prove in this note infinite families of congruences modulo $7$ and $11$ for $a_c(n)$ and $d_c(n)$ by employing elementary $q$-series techniques. These results generalize particular congruences modulo $7$ and $11$ for $a_c(n)$ and $d_c(n)$ recently found by Dockery, and Baruah, Das, and Talukdar, respectively, using modular forms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_18286 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Congruences modulo $7$ and $11$ for certain two restricted partition functions Guadalupe, Russelle Number Theory Combinatorics 11P83, 05A17, 11P81 For an integer $c\geq 1$, let $a_c(n)$ count the number of generalized cubic partitions of $n$, which are partitions of $n$ whose even parts may appear in $c$ different colors, and $d_c(n)$ count the number of partitions obtained by adding the links of the $c$-elongated plane partition diamonds of length $n$. We prove in this note infinite families of congruences modulo $7$ and $11$ for $a_c(n)$ and $d_c(n)$ by employing elementary $q$-series techniques. These results generalize particular congruences modulo $7$ and $11$ for $a_c(n)$ and $d_c(n)$ recently found by Dockery, and Baruah, Das, and Talukdar, respectively, using modular forms. |
| title | Congruences modulo $7$ and $11$ for certain two restricted partition functions |
| topic | Number Theory Combinatorics 11P83, 05A17, 11P81 |
| url | https://arxiv.org/abs/2508.18286 |