Overpartitions and Bressoud's Conjecture, I

He, Thomas Y.; Ji, Kathy Q.; Zhao, Alice X.H.

doi:10.1016/j.aim.2022.108449

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2023

2024

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Cited by 5 publications

(2 citation statements)

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“…Recently, Kim [10] proved Bressoud's conjecture for j = 1. Bressoud's conjecture for j = 0 was resolved by He, Ji and Zhao [9]. To this end, Kim [10] and He, Ji and Zhao [9] established the following theorem for j = 1 and j = 0 respectively.…”

Section: Introductionmentioning

confidence: 99%

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An overpartition analogue of Bressoud's conjecture for even moduli

Chen,

Gu,

et al. 2023

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In 1980, Bressoud conjectured a combinatorial identity $A_j=B_j$ for $j=0$ or $1$. In this paper, we introduce a new partition function $\overline{B}_0$ which can be viewed as an overpartition analogue of the partition function $B_0$. An overpartition is apartition such that the last occurrence of a part can be overlined. We build a bijection to get a relationship between $\overline{B}_0$ and $B_1$, based on which an overpartition analogue of Bressoud's conjecture for $j=0$ is obtained. AMS Classifications: 05A17, 11P84

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Section: Introductionmentioning

confidence: 99%

“…In recent years, overpartitions have been heavily studied. He, Ji and Zhao gave overpartitions analogues of Bressoud's conjecture for j = 1 and j = 0 in [8] and [9] respectively. In [8,9], an overpartition is a partition such that the first occurrence of a part can be overlined and the parts in an overpartition are ordered as follows:…”

Section: Introductionmentioning

confidence: 99%