Arithmetic properties for generalized cubic partitions and overpartitions modulo a prime
Number Theory
2025-05-19 v1 Combinatorics
Abstract
A cubic partition is an integer partition wherein the even parts can appear in two colors. In this paper, we introduce the notion of generalized cubic partitions and prove a number of new congruences akin to the classical Ramanujan-type. We emphasize two methods of proofs, one elementary (relying significantly on functional equations) and the other based on modular forms. We close by proving analogous results for generalized overcubic partitions.
Cite
@article{arxiv.2407.00058,
title = {Arithmetic properties for generalized cubic partitions and overpartitions modulo a prime},
author = {Tewodros Amdeberhan and James A. Sellers and Ajit Singh},
journal= {arXiv preprint arXiv:2407.00058},
year = {2025}
}
Comments
11 pages