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<p>Euler’s classic partition identity states that the number of partitions of <i>n</i> into odd parts equals the number of partitions of <i>n</i> into distinct parts. We develop a new generalization of this identity, which yields a previous generalization of Franklin as a special case, and prove an accompanying Beck-type companion identity.</p>

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A generalization of Franklin’s partition identity and a Beck-type companion identity

  • 期刊论文

  • 发表日期：

    2025年7月16日

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  • Gabriel Gray,
  • David Hovey,
  • Brandt Kronholm,
  • Emily Payne,
  • Holly Swisher,
  • Ren Watson

摘要

Euler’s classic partition identity states that the number of partitions of n into odd parts equals the number of partitions of n into distinct parts. We develop a new generalization of this identity, which yields a previous generalization of Franklin as a special case, and prove an accompanying Beck-type companion identity.