Abstract Andrews and El Bachraoui ‘On two-color partitions with odd smallest part’, Preprint (2024), arXiv:2410. 14190 recently investigated identities involving two-colour partitions, with particular emphasis on their connection to overpartitions, and posed questions regarding possible companion results. Subsequently, Chen and Zou ‘Combinatorial proofs for two-colour partitions’, Bull. Aust. Math. Soc. 113 (1) (2025), to appear obtained some companion results by employing q -series identities and generating functions. In addition, they presented a combinatorial proof for one of their own results and one of the results of Andrews and El Bachraoui. They posed questions regarding combinatorial proofs of the remaining companion results. In this paper, we provide such proofs.
Ghoshal et al. (2026) studied this question.