Bressoud's identities for even moduli. New companions and related positivity results

TL;DR

This paper advances the understanding of Bressoud's identities for even moduli by proving new cases of the conjecture, refining related identities, and deriving all identities for mod 20, using positivity-preserving transformations.

Contribution

It introduces new proofs for infinitely many cases of Bressoud's conjecture and develops refined identities, including all mod 20 cases, expanding the theoretical framework.

Findings

Proved infinitely many new cases of Bressoud's conjecture

Established a doubly-bounded refinement of Foda-Quano identities

Derived all 10 identities for mod 20

Abstract

I revisit Bressoud's generalised Borwein conjecture. Making use of certain positivity-preserving transformations for q-binomial coefficients, I establish the truth of infinitely many new cases of the Bressoud conjecture. In addition, I prove new doubly-bounded refinement of the Foda-Quano identities. Finally, I discuss new companions to the Bressoud even moduli identities. In particular, all 10 mod 20 identities are derived.