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arXiv · 2311.01992

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

John Layne·Samuel Marshall·Christopher Sadowski·Emily Shambaugh
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Abstract

We present what we call a "motivated proof" of the Bressoud-Göllnitz-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 Göllnitz-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 Göllnitz-Gordon-Andrews identities. We anticipate that this "motivated proof" of the Bressoud-Göllnitz-Gordon identities will illuminate certain twisted vertex-algebraic constructions.

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John Layne, Samuel Marshall, Christopher Sadowski, Emily Shambaugh. 2023-11-03. Ghost series and a motivated proof of the Bressoud-Göllnitz-Gordon identities. https://arxiv.org/abs/2311.01992

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