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<p>George Andrews and Mohamed El Bachraoui recently explored identities for two-color partitions (Andrews and Bachraoui (2024) On two-color partitions with odd smallest part). In particular, they studied the connection between two-colored partitions and overpartitions. Their proofs were analytical, but they also conjectured combinatorial proofs of their results. In this paper we use two-modular diagrams to give a combinatorial proof of their main result.</p>

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Two-color partitions and overpartitions: a combinatorial proof

  • 期刊论文

  • 发表日期：

    2026年4月7日

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  • Anton Bugleev

摘要

George Andrews and Mohamed El Bachraoui recently explored identities for two-color partitions (Andrews and Bachraoui (2024) On two-color partitions with odd smallest part). In particular, they studied the connection between two-colored partitions and overpartitions. Their proofs were analytical, but they also conjectured combinatorial proofs of their results. In this paper we use two-modular diagrams to give a combinatorial proof of their main result.