On $\ell-$regular and $2-$color partition triples modulo powers of $3$
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| Format: | Preprint |
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2025
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| _version_ | 1866915249919098880 |
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| author | Hemanthkumar, B. Gireesh, D. S. |
| author_facet | Hemanthkumar, B. Gireesh, D. S. |
| contents | Let $T_\ell(n)$ denote the number of $\ell-$regular partition triples of $n$ and let $p_{\ell, 3}(n)$ enumerates the number of 2--color partition triples of $n$ where one of the colors appear only in parts that are multiples of $\ell$. In this paper, we prove several infinite families of congruences modulo powers of 3 for $T_\ell(n)$ and $p_{\ell, 3}(n)$, where $\ell \geq 1$ and $\equiv 0\pmod{3^k}$, and $\equiv \pm 3^k \pmod{3^{k+1}}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_13507 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On $\ell-$regular and $2-$color partition triples modulo powers of $3$ Hemanthkumar, B. Gireesh, D. S. Combinatorics Number Theory primary 11P83, secondary 05A15, 05A17 Let $T_\ell(n)$ denote the number of $\ell-$regular partition triples of $n$ and let $p_{\ell, 3}(n)$ enumerates the number of 2--color partition triples of $n$ where one of the colors appear only in parts that are multiples of $\ell$. In this paper, we prove several infinite families of congruences modulo powers of 3 for $T_\ell(n)$ and $p_{\ell, 3}(n)$, where $\ell \geq 1$ and $\equiv 0\pmod{3^k}$, and $\equiv \pm 3^k \pmod{3^{k+1}}$. |
| title | On $\ell-$regular and $2-$color partition triples modulo powers of $3$ |
| topic | Combinatorics Number Theory primary 11P83, secondary 05A15, 05A17 |
| url | https://arxiv.org/abs/2504.13507 |