A bijection related to Bressoud's conjecture

Abstract

Bressoud introduced the partition function $B(\hat{I}{\pm }_1,\dots ,\hat{I}{\pm }_{\hat{I}}»;\hat{I}\cdot ,k,r;n)$, which counts the number of partitions with certain difference conditions. Bressoud posed a conjecture on the generating function for the partition function $B(\hat{I}{\pm }_1,\dots ,\hat{I}{\pm }_{\hat{I}}»;\hat{I}\cdot ,k,r;n)$ in multi-summation form. In this article, we introduce a bijection related to Bressoud's conjecture. As an application, we give a new companion to the Göllnitz-Gordon identities.