Bressoud's conjecture

In 1980, D. M. Bressoud obtained an analytic generalization of the Rogers-Ramanujan-Gordon identities. He then tried to establish a combinatorial interpretation of his identity, which specializes to many well-known Rogers-Ramanujan type identities. He proved that a certain partition identity follows from his identity in a very restrictive case and conjectured that the partition identity holds true in general. In this paper, we prove Bressoud's conjecture for the general case by providing bijective proofs.