The Localization Method Applied to $k$-Elongated Plane Partitions and Divisibility by 5
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913604692869120 |
|---|---|
| author | Banerjee, Koustav Smoot, Nicolas Allen |
| author_facet | Banerjee, Koustav Smoot, Nicolas Allen |
| contents | The enumeration $d_k(n)$ of $k$-elongated plane partition diamonds has emerged as a generalization of the classical integer partition function $p(n)$. We have discovered an infinite congruence family for $d_5(n)$ modulo powers of 5. Classical methods cannot be used to prove this family of congruences. Indeed, the proof employs the recently developed localization method, and utilizes a striking internal algebraic structure which has not yet been seen in the proof of any congruence family. We believe that this discovery poses important implications on future work in partition congruences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_07065 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Localization Method Applied to $k$-Elongated Plane Partitions and Divisibility by 5 Banerjee, Koustav Smoot, Nicolas Allen Number Theory The enumeration $d_k(n)$ of $k$-elongated plane partition diamonds has emerged as a generalization of the classical integer partition function $p(n)$. We have discovered an infinite congruence family for $d_5(n)$ modulo powers of 5. Classical methods cannot be used to prove this family of congruences. Indeed, the proof employs the recently developed localization method, and utilizes a striking internal algebraic structure which has not yet been seen in the proof of any congruence family. We believe that this discovery poses important implications on future work in partition congruences. |
| title | The Localization Method Applied to $k$-Elongated Plane Partitions and Divisibility by 5 |
| topic | Number Theory |
| url | https://arxiv.org/abs/2208.07065 |