Congruences modulo powers of $7$ for $k$-elongated plane 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_ | 1866916901996724224 |
|---|---|
| author | Chen, Dandan Xu, Tianjian Yin, Siyu |
| author_facet | Chen, Dandan Xu, Tianjian Yin, Siyu |
| contents | The enumeration $d_k(n)$ of $k$-elongated plane partition diamonds has emerged as a generalization of the classical integer partition function $p(n)$. Congruences for $d_k(n)$ modulo certain powers of primes have been proven via elementary means and modular forms by many authors. Recently, Banerjee and Smoot established an infinite family of congruences for $d_5(n)$ modulo powers of 5. In this paper we have discovered an infinite congruence family for $d_3(n)$ and $d_5(n)$ modulo powers of 7. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09723 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Congruences modulo powers of $7$ for $k$-elongated plane partitions Chen, Dandan Xu, Tianjian Yin, Siyu Number Theory Combinatorics 11P83, 05A17 The enumeration $d_k(n)$ of $k$-elongated plane partition diamonds has emerged as a generalization of the classical integer partition function $p(n)$. Congruences for $d_k(n)$ modulo certain powers of primes have been proven via elementary means and modular forms by many authors. Recently, Banerjee and Smoot established an infinite family of congruences for $d_5(n)$ modulo powers of 5. In this paper we have discovered an infinite congruence family for $d_3(n)$ and $d_5(n)$ modulo powers of 7. |
| title | Congruences modulo powers of $7$ for $k$-elongated plane partitions |
| topic | Number Theory Combinatorics 11P83, 05A17 |
| url | https://arxiv.org/abs/2508.09723 |