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<p>Recently, Andrews and El Bachraoui discovered several companions for some well-known <i>q</i>-series formulas and derived new identities involving partitions and overpartitions with distinct parts. In this paper, we shall refine their results by considering the number of restricted parts in partitions and furthermore, provide combinatorial proofs for these partition identities. Our results answer the combinatorial problem posed by Andrews and El Bachraoui.</p>

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The combinatorics of identities involving overpartitions with distinct parts

  • 期刊论文

  • 发表日期：

    2026年3月7日

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  • Haijun Li

摘要

Recently, Andrews and El Bachraoui discovered several companions for some well-known q-series formulas and derived new identities involving partitions and overpartitions with distinct parts. In this paper, we shall refine their results by considering the number of restricted parts in partitions and furthermore, provide combinatorial proofs for these partition identities. Our results answer the combinatorial problem posed by Andrews and El Bachraoui.