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<p>Recently, Bachraoui proved four positivity results for alternating sums involving the ordinary partition function and the overpartition function by using Bailey’s transform. At the end of his paper, Bachraoui asked for partition-theoretic interpretations of those alternating sums. In this paper, we settle Bachraoui’s open problem based on the minimal excludant in congruence classes of partitions.</p>

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Partition-theoretic interpretations of some truncated sums of integer partitions

  • 期刊论文

  • 发表日期：

    2025年12月17日

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  • Jing Jin,
  • Eric H. Liu,
  • Olivia X. M. Yao

摘要

Recently, Bachraoui proved four positivity results for alternating sums involving the ordinary partition function and the overpartition function by using Bailey’s transform. At the end of his paper, Bachraoui asked for partition-theoretic interpretations of those alternating sums. In this paper, we settle Bachraoui’s open problem based on the minimal excludant in congruence classes of partitions.