Séminaire Lotharingien de Combinatoire, 93B.35 (2025), 12 pp.
Hyunsoo Cho, Eunmi Kim, Ho-Hyeong Lee, Kyeongjun Lee, Ae Ja Yee and Jaeyeong Yoo
GBG-rank Generating Functions for Ordinary, Self-Conjugate, and Doubled Distinct Partitions
Abstract.
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.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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