An overpartition analogue of Bressoud's 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 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 B ~ 0 and B 1 , based on which an overpartition analogue of Bressoud's conjecture for j = 0 is obtained. [ABSTRACT FROM AUTHOR]