2024/03/08 by Jehanne Dousse, Dousse, Jehanne, Frédéric Jouhet +3
Mathematics · #05A15 #05A17 #05A19 #05A30 #11P81 #11P84 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2403.05414
openalex publication_date 2024/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide combinatorial tools inspired by work of Warnaar to give combinatorial interpretations of the sum sides of the Andrews-Gordon and Bressoud identities. More precisely, we give an explicit weight- and length-preserving bijection between sets related to integer partitions, which provides these interpretations. In passing, we discover the q-series version of an identity of Kurşungöz, similar to the Bressoud identity but with opposite parity conditions, which we prove combinatorially using the classical Bressoud identity and our bijection. We also use this bijection to prove combinatorially many identities, some known and other new, of the Andrews-Gordon and Bressoud type.