Séminaire Lotharingien de Combinatoire, 95B.67 (2026), 12 pp.
Jehanne Dousse, Jihyeug Jang and Frédéric Jouhet
Particle Motion Methods for Andrews-Gordon and Stanton Type Identities
Abstract.
In 2018, Stanton proved generalisations of the celebrated Andrews-Gordon and Bressoud identities (in their q-series version). In this extended abstract, we give combinatorial proofs of these identities. They are based on particle motion introduced by Warnaar and extended by the first and third authors and Konan, and use the original Andrews-Gordon and Bressoud identities as ingredients. We also find new Stanton-type generalisations of classical identities.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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