An overpartition analogue of Bressoud’s conjecture for even moduli

Abstract

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 \(\widetilde{B}_0\) 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 \(\widetilde{B}_0\) and \(B_1\), based on which an overpartition analogue of Bressoud’s conjecture for \(j=0\) is obtained.