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<p>BG-ranks and GBG-ranks, introduced by Berkovich and Garvan, are combinatorial statistics that have been used to prove some partition congruences and refinements. In this paper, we give a thorough study on these statistics and obtain formulas for the GBG-rank generating functions for ordinary partitions, self-conjugate partitions, and doubled distinct partitions.</p>

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GBG-rank generating functions for ordinary, self-conjugate, and doubled distinct partitions

  • 期刊论文

  • 发表日期：

    2025年11月7日

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  • Hyunsoo Cho,
  • Eunmi Kim,
  • Ho-Hyeong Lee,
  • Kyeongjun Lee,
  • Ae Ja Yee,
  • Jaeyeong Yoo

摘要

BG-ranks and GBG-ranks, introduced by Berkovich and Garvan, are combinatorial statistics that have been used to prove some partition congruences and refinements. In this paper, we give a thorough study on these statistics and obtain formulas for the GBG-rank generating functions for ordinary partitions, self-conjugate partitions, and doubled distinct partitions.