Extending recent work of Nath, Saikia, and Sarma on $k$-tuple $\ell$-regular partitions
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912277341405184 |
|---|---|
| author | Paudel, Bishnu Sellers, James A. Wang, Haiyang |
| author_facet | Paudel, Bishnu Sellers, James A. Wang, Haiyang |
| contents | Let $T_{\ell,k}(n)$ denote the number of $\ell$-regular $k$-tuple partitions of $n$. In a recent work, Nath, Saikia, and Sarma derived several families of congruences for $T_{\ell,k}(n)$, with particular emphasis on the cases $T_{2,3}(n)$ and $T_{4,3}(n)$. In the concluding remarks of their paper, they conjectured that $T_{2,3}(n)$ satisfies an infinite set of congruences modulo 6. In this paper, we confirm their conjecture by proving a much more general result using elementary $q$-series techniques. We also present new families of congruences satisfied by $T_{\ell,k}(n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12583 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extending recent work of Nath, Saikia, and Sarma on $k$-tuple $\ell$-regular partitions Paudel, Bishnu Sellers, James A. Wang, Haiyang Number Theory Combinatorics 11P83, 05A17 Let $T_{\ell,k}(n)$ denote the number of $\ell$-regular $k$-tuple partitions of $n$. In a recent work, Nath, Saikia, and Sarma derived several families of congruences for $T_{\ell,k}(n)$, with particular emphasis on the cases $T_{2,3}(n)$ and $T_{4,3}(n)$. In the concluding remarks of their paper, they conjectured that $T_{2,3}(n)$ satisfies an infinite set of congruences modulo 6. In this paper, we confirm their conjecture by proving a much more general result using elementary $q$-series techniques. We also present new families of congruences satisfied by $T_{\ell,k}(n)$. |
| title | Extending recent work of Nath, Saikia, and Sarma on $k$-tuple $\ell$-regular partitions |
| topic | Number Theory Combinatorics 11P83, 05A17 |
| url | https://arxiv.org/abs/2503.12583 |