A bijection related to Bressoud's conjecture

TL;DR

This paper introduces a bijection related to Bressoud's conjecture on partition functions with difference conditions, providing new insights and a companion to the G"ollnitz-Gordon identities.

Contribution

The paper presents a novel bijection that advances understanding of Bressoud's conjecture and offers a new perspective on related partition identities.

Findings

Established a new bijection related to Bressoud's conjecture

Provided a new companion to the G"ollnitz-Gordon identities

Enhanced the combinatorial understanding of partition functions

Abstract

Bressoud introduced the partition function $B(\alpha_1,\ldots,\alpha_\lambda;\eta,k,r;n)$, which counts the number of partitions with certain difference conditions. Bressoud posed a conjecture on the generating function for the partition function $B(\alpha_1,\ldots,\alpha_\lambda;\eta,k,r;n)$ 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 G\"ollnitz-Gordon identities.