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<p>Recently, Andrews and EI Bachraoui obtained several identities on two-colored partitions. While solving open problems they posed, Chen and Zhou derived a number of identities using analytic methods and asked for combinatorial proofs. In this note, we provide the requested combinatorial proofs. Additionally, we derive several new identities and provide combinatorial proofs for them.</p>

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The combinatorics of some two-color partition identities

  • 期刊论文

  • 发表日期：

    2026年1月20日

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  • Yong-Chao Shen

摘要

Recently, Andrews and EI Bachraoui obtained several identities on two-colored partitions. While solving open problems they posed, Chen and Zhou derived a number of identities using analytic methods and asked for combinatorial proofs. In this note, we provide the requested combinatorial proofs. Additionally, we derive several new identities and provide combinatorial proofs for them.