Overpartitions and Bressoud's conjecture, II

The main objective of this paper is to present an answer to Bressoud's conjecture for the case j = 0, resulting in a complete solution to Bressoud's conjecture. The case for j = 1 has been recently resolved by Kim. Using the connection established in our previous paper between the ordinary partition function B0 and the overpartition function B1, we found that the proof of Bressoud's conjecture for the case j = 0 is equivalent to establishing an overpartition analogue of the conjecture for the case j = 1. By generalizing Kim's method, we obtain the desired overpartition analogue of Bressoud's conjecture for the case j = 1, which eventually enables us to confirm Bressoud's conjecture for the case j=0. (c) 2024 Elsevier Ltd. All rights reserved.