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<p>This paper completes the classification of maximal unrefinable partitions, extending a previous work of Aragona et al. devoted only to the case of triangular numbers. We show that the number of maximal unrefinable partitions of an integer coincides with the number of suitable partitions into distinct parts, depending on the distance from the successive triangular number.</p>

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The number of maximal unrefinable partitions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月13日

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  • Riccardo Aragona,
  • Lorenzo Campioni,
  • Roberto Civino

摘要

This paper completes the classification of maximal unrefinable partitions, extending a previous work of Aragona et al. devoted only to the case of triangular numbers. We show that the number of maximal unrefinable partitions of an integer coincides with the number of suitable partitions into distinct parts, depending on the distance from the successive triangular number.