2023/11/03 by John Layne, Samuel F. Marshall, Layne, John +5
Mathematics · #05A15 #05A17 #11P84 #17B69 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2311.01992
openalex publication_date 2023/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.