An overpartition analogue of Bressoud conjecture for even moduli

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 a partition 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.