Congruences for Overcubic Partition k-Tuples
Abstract
In the last few years, a number of authors have proved divisibility properties satisfied by various functions which count the number of overcubic partition k--tuples of weight n for small values of k. In this work, we use generating functions to prove some of their results as well as multiple infinite families of new congruences for overcubic partition k-tuples which do not yet appear in the literature. In particular, we focus on a new perspective which provides insights as to why these functions are often divisible by powers of 2, and we also prove families of congruences whose moduli are odd. For example, we prove that, for all m≥ 0, OLb4(22m + 11) ≡ 0 pmod11 and we also prove infinite families such as OLb9l+2(9m+3) ≡ 0 pmod3 for all m,l≥0.
Related
- On Certain Congruences for Partition k-Tuples with $5$-Cores
- Congruences for Overcolored Partition k-tuples Restricted by Parity of the Parts
- Overcolored Partition k-tuples Restricted by Parity of the Parts
- Nonexistence of Constant Congruences for the Cumulative Partition Function
- Congruences for the Andrews--Uncu partition function ℰ𝒪u(n)
BibTeX
@misc{chacon2026congruences,
title = {{Congruences for Overcubic Partition $k$-Tuples}},
author = {Daniel Chacón and James A. Sellers},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.21780},
eprint = {2606.21780},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.21780},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Congruences for Overcubic Partition k-Tuples
AU - Daniel Chacón
AU - James A. Sellers
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2606.21780
UR - https://arxiv.org/abs/2606.21780
AB - In the last few years, a number of authors have proved divisibility properties satisfied by various functions which count the number of overcubic partition k--tuples of weight n for small values of k. In this work, we use generating functions to prove some of their results as well as multiple infinite families of new congruences for overcubic partition k-tuples which do not yet appear in the literature. In particular, we focus on a new perspective which provides insights as to why these functions are often divisible by powers of 2, and we also prove families of congruences whose moduli are odd. For example, we prove that, for all m≥ 0, OLb_4(22m + 11) ≡ 0 pmod11 and we also prove infinite families such as OLb_9l+2(9m+3) ≡ 0 pmod3 for all m,l≥0.
ER -