Overpartitions and Bressoud's Conjecture, I

In 1980, Bressoud conjectured a combinatorial identity A j = B for 0 or 1, where the function counts number of partitions with certain congruence conditions and difference conditions. Bressoud's conjecture specializes to wide variety well-known theorems in theory partitions. Special cases his have been subsequently proved by Bressoud, Andrews, Kim Yee. Recently, resolved case 1 . this paper, we introduce new partition ‾ which can be viewed as an overpartition analogue introduced Bressoud. By means Gordon markings, build bijections obtain relationship between Based on these former relationships, further give analogues many classical including Euler's theorem, Rogers-Ramanujan-Gordon identities, Bressoud-Rogers-Ramanujan Andrews-Göllnitz-Gordon identities Bressoud-Göllnitz-Gordon identities.