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

Hyunsoo Cho; Eunmi Kim; Ho Hyeong Lee; Kyeongjun Lee; Ae Ja Yee; Jaeyeong Yoo

doi:10.1007/s11139-025-01227-y

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

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Article number	94
Journal	Ramanujan Journal
Volume	68
Issue number	4
DOIs	https://doi.org/10.1007/s11139-025-01227-y
State	Published - Dec 2025

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1007/s11139-025-01227-y

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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.",

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AU - Kim, Eunmi

AU - Lee, Ho Hyeong

AU - Lee, Kyeongjun

AU - Yee, Ae Ja

AU - Yoo, Jaeyeong

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

PY - 2025/12

Y1 - 2025/12

N2 - 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.

AB - 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.

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

Abstract

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