PreprintCC BY 4.0arXiv
On Congruences modulo powers of 3 for Simultaneously l-Regular and t-Distinct Partitions in k-Colors
Abstract
In 2017, Keith defined and studied a multi-restricted partition function RDl,t(n), the number of integer partitions of n into parts that are simultaneously l-regular and t-distinct if none of the parts is divisible by l and parts appear fewer than t times. Thereafter, in a series of papers Buragohain et al. and Nadji et al. examined combinatorial and arithmetic properties of RDl,t(n). In this article, we focus on simultaneously l-regular and t-distinct partitions in 3-colors, RDl,t3(n) and establish infinite families of congruences modulo powers of 3 for specific values of (l,t). For instance, for positive integers n and k, we have ∑n=0∞RD33,3(3kn+(3k+1)/2)qn≡0 pmod3k+1. Our approach involves Hirschhorn's H operator technique.
Related
- A uniform proof approach for congruences modulo 3 for partitions with k-colored odd parts
- Congruences modulo powers of $7$ for partitions with colored odd parts
- Congruences modulo powers of 5 and 7 for the crank and rank parity functions and related mock theta-functions
- Internal congruences modulo powers of 2 for k-colored overpartitions into odd parts
- Elementary proofs of congruences modulo 5 for overpartitions with restricted odd differences
BibTeX
@misc{johnson2026congruences,
title = {{On Congruences modulo powers of 3 for Simultaneously $l$-Regular and $t$-Distinct Partitions in $k$-Colors}},
author = {Anjelin Mariya Johnson and S. N. Fathima},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2607.11499},
eprint = {2607.11499},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.11499},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On Congruences modulo powers of 3 for Simultaneously l-Regular and t-Distinct Partitions in k-Colors
AU - Anjelin Mariya Johnson
AU - S. N. Fathima
PY - 2026
DA - 2026/11/06
PB - arXiv
DO - 10.48550/arxiv.2607.11499
UR - https://arxiv.org/abs/2607.11499
AB - In 2017, Keith defined and studied a multi-restricted partition function RD^l,t(n), the number of integer partitions of n into parts that are simultaneously l-regular and t-distinct if none of the parts is divisible by l and parts appear fewer than t times. Thereafter, in a series of papers Buragohain et al. and Nadji et al. examined combinatorial and arithmetic properties of RD^l,t(n). In this article, we focus on simultaneously l-regular and t-distinct partitions in 3-colors, RD^l,t_3(n) and establish infinite families of congruences modulo powers of 3 for specific values of (l,t). For instance, for positive integers n and k, we have ∑_n=0^∞RD_3^3,3(3^kn+(3^k+1)/2)q^n≡0 pmod3^k+1. Our approach involves Hirschhorn's H operator technique.
ER -