标题： 幽灵级数和布雷索德-戈尔尼茨-戈登恒等式的有动机证明 显示英文标题

标题： Ghost series and a motivated proof of the Bressoud-Göllnitz-Gordon identities

摘要： 我们提出一种称为“有动机的证明”的布雷索-戈尔尼茨-戈登分拆恒等式的证明。 类似的“有动机的证明”已由安德鲁斯和巴克斯对罗格斯-拉马努金恒等式进行了证明，以及由莱波夫斯基和朱对戈登恒等式进行了证明。 此外，“有动机的证明”也已被用于安德鲁斯-布雷索的分拆恒等式，由卡纳德、莱波夫斯基、拉塞尔和希尔完成，以及用于戈尔尼茨-戈登-安德鲁斯恒等式，由科尔森、卡纳德、莱波夫斯基、麦克雷、齐、拉塞尔和第三作者完成。 我们的证明既借鉴了安德鲁斯-布雷索恒等式“有动机的证明”中“幽灵级数”的使用，又使用了类似于戈尔尼茨-戈登-安德鲁斯恒等式“有动机的证明”中的递归关系。 我们预计这种对布雷索-戈尔尼茨-戈登恒等式的“有动机的证明”将阐明某些扭曲顶点代数构造。 显示英文摘要

摘要： We present what we call a "motivated proof" of the Bressoud-G\"ollnitz-Gordon partition identities. Similar "motivated proofs" have been given by Andrews and Baxter for the Rogers-Ramanujan identities and by Lepowsky and Zhu for Gordon's identities. Additionally, "motivated proofs" have also been given for the Andrews-Bressoud partition identities by Kanade, Lepowsky, Russell, and Sills and for the G\"ollnitz-Gordon-Andrews identities by Coulson, Kanade, Lepowsky, McRae, Qi, Russell, and the third author. Our proof borrows both the use of "ghost series" from the "motivated proof" of the Andrews-Bressoud identities and uses recursions similar to those found in the "motivated proof" of the G\"ollnitz-Gordon-Andrews identities. We anticipate that this "motivated proof" of the Bressoud-G\"ollnitz-Gordon identities will illuminate certain twisted vertex-algebraic constructions.