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<p>Recently, Andrews and El Bachraoui (Rev Real Acad Cienc Exactas Fis Nat Ser A Mat 119:4, 2024) proved three very interesting <i>q</i>-series identities, from which three simple looking identities involving certain restricted partitions into distinct even parts and 4-regular partitions follow. In this short note, we give combinatorial proofs of these identities. We also prove the counterpart identities for the restricted partitions into distinct odd parts.</p>

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Combinatorial proofs of some results of Andrews and El Bachraoui

  • 期刊论文

  • 发表日期：

    2025年2月24日

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  • Pankaj Jyoti Mahanta,
  • Manjil P. Saikia

摘要

Recently, Andrews and El Bachraoui (Rev Real Acad Cienc Exactas Fis Nat Ser A Mat 119:4, 2024) proved three very interesting q-series identities, from which three simple looking identities involving certain restricted partitions into distinct even parts and 4-regular partitions follow. In this short note, we give combinatorial proofs of these identities. We also prove the counterpart identities for the restricted partitions into distinct odd parts.