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arXiv · 2407.00058

Arithmetic properties for generalized cubic partitions and overpartitions modulo a prime

Tewodros Amdeberhan·James A. Sellers·Ajit Singh
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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.

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Tewodros Amdeberhan, James A. Sellers, Ajit Singh. 2024-06-15. Arithmetic properties for generalized cubic partitions and overpartitions modulo a prime. https://arxiv.org/abs/2407.00058

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