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<p>It is proved that the number of partitions of <i>n</i> with odd mex and <i>k</i> parts that aren’t ones equals the number of partitions of <i>n</i> with nonnegative crank and <i>k</i> parts that aren’t ones.</p>

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A refinement of the Crank-Mex theorem

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年11月6日

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  • George E. Andrews,
  • Moshe Newman

摘要

It is proved that the number of partitions of n with odd mex and k parts that aren’t ones equals the number of partitions of n with nonnegative crank and k parts that aren’t ones.