An overpartition analogue of Bressoud’s conjecture for even moduli

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发表日期：

2024年6月28日

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Y. H. Chen,
T. T. Gu,
T. Y. He,
F. Tang,
J. J. Wei

摘要

In 1980, Bressoud conjectured a combinatorial identity $A_j=B_j$ $A_{j} = B_{j}$ for $j=0$ $j = 0$ or 1. In this paper, we introduce a new partition function $\widetilde{B}_0$ ${\tilde{B}}_{0}$ which can be viewed as an overpartition analogue of the partition function $B_0$ $B_{0}$ . An overpartition is a partition such that the last occurrence of a part can be overlined. We build a bijection to get a relationship between $\widetilde{B}_0$ ${\tilde{B}}_{0}$ and $B_1$ $B_{1}$ , based on which an overpartition analogue of Bressoud’s conjecture for $j=0$ $j = 0$ is obtained.