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<p>Recently, many authors have investigated how various partition statistics distribute as the size of the partition grows. In this work, we look at a particular statistic arising from the recent rejuvenation of MacMahon’s partition analysis. More specifically, we compute all the moments of the alternating sum statistic for partitions. We prove these results using the Circle Method. We also propose a general framework for studying further questions of this type that may avoid some of the complications that arise in traditional approaches to the distributions of partition statistics, and we comment on the utility, comparative ease and opportunities to generalize to very broad settings.</p>

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Distribution of alternating sums of parts in partitions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月17日

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  • William Craig,
  • Runqiao Li

摘要

Recently, many authors have investigated how various partition statistics distribute as the size of the partition grows. In this work, we look at a particular statistic arising from the recent rejuvenation of MacMahon’s partition analysis. More specifically, we compute all the moments of the alternating sum statistic for partitions. We prove these results using the Circle Method. We also propose a general framework for studying further questions of this type that may avoid some of the complications that arise in traditional approaches to the distributions of partition statistics, and we comment on the utility, comparative ease and opportunities to generalize to very broad settings.