Combinatorial proof of a result on generalized overcubic partitions and related conjectures

TL;DR

This paper provides a combinatorial proof for a modulo 4 result on generalized overcubic partitions and confirms some related conjectures, extending previous work using theta functions.

Contribution

It offers a combinatorial proof of a key result and verifies several conjectures in the study of generalized overcubic partitions.

Findings

Proved a modulo 4 result combinatorially

Confirmed several conjectures related to overcubic partitions

Extended previous results using theta functions

Abstract

Extending Sellers' result, Das et al. recently proved some congruence results for generalized overcubic partitions using theta functions and posed some related conjectures. In this paper, we provide a combinatorial proof of a result in modulo $4$ of Das et al. and confirm some of their conjectures.