Congruences modulo powers of $3$ for generalized Frobenius partitions $CΨ_{6,0}$
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_ | 1866918449209409536 |
|---|---|
| author | Chen, Dandan Yin, Siyu |
| author_facet | Chen, Dandan Yin, Siyu |
| contents | In 1984, Andrews introduced the family of partition functions \(cϕ_k(n)\), which counts the number of generalized Frobenius partitions of \(n\) with \(k\) colors. In previous work, we proved a conjecture on congruences for \(cϕ_6(n)\) modulo powers of 3. In this paper, we consider the \((6,0)\)-colored Frobenius partition functions \(cψ_{6,0}(n)\). We establish a connection between the generating functions of \(cψ_{6,3}(n)\) and \(cψ_{6,0}(n)\) via an Atkin-Lehner involution, and prove congruences modulo powers of 3 for \(cψ_{6,0}(n)\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19242 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Congruences modulo powers of $3$ for generalized Frobenius partitions $CΨ_{6,0}$ Chen, Dandan Yin, Siyu Combinatorics Number Theory 11P83, 05A17 In 1984, Andrews introduced the family of partition functions \(cϕ_k(n)\), which counts the number of generalized Frobenius partitions of \(n\) with \(k\) colors. In previous work, we proved a conjecture on congruences for \(cϕ_6(n)\) modulo powers of 3. In this paper, we consider the \((6,0)\)-colored Frobenius partition functions \(cψ_{6,0}(n)\). We establish a connection between the generating functions of \(cψ_{6,3}(n)\) and \(cψ_{6,0}(n)\) via an Atkin-Lehner involution, and prove congruences modulo powers of 3 for \(cψ_{6,0}(n)\). |
| title | Congruences modulo powers of $3$ for generalized Frobenius partitions $CΨ_{6,0}$ |
| topic | Combinatorics Number Theory 11P83, 05A17 |
| url | https://arxiv.org/abs/2510.19242 |