This work provides combinatorial proofs for distinct parts in two-colored partitions and overpartitions, addressing previously raised questions.
Andrews and El Bachraoui recently studied various two-colored integer partitions, including those related to two-colored partitions into distinct parts with constraints and overpartitions. Their work raised questions about the existence of combinatorial proofs for these results, which were partially addressed by the first author and Zou. This paper provides combinatorial proofs for the remaining results concerning two-colored partitions and overpartitions with constraints.
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Chen et al. (2025) studied this question.
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