Extension of Bressoud's generalization of Borwein's conjecture and some exact results

Fuente: arXiv
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Main Authors: Berkovich, Alexander, Dhar, Aritram
Format: Preprint
Published: 2024
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author Berkovich, Alexander
Dhar, Aritram
author_facet Berkovich, Alexander
Dhar, Aritram
contents In this paper, we conjecture an extension to Bressoud's 1996 generalization of Borwein's famous 1990 conjecture. We then state a few infinite hierarchies of non-negative $q$-series identities which are interesting examples of our proposed conjecture and Bressoud's generalized conjecture. Finally, using certain positivity-preserving transformations for $q$-binomial coefficients, we prove the non-negativity of the infinite families.
format Preprint
id arxiv_https___arxiv_org_abs_2402_15886
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Extension of Bressoud's generalization of Borwein's conjecture and some exact results
Berkovich, Alexander
Dhar, Aritram
Combinatorics
Number Theory
05A15, 05A17, 05A30, 11P81, 11P84
In this paper, we conjecture an extension to Bressoud's 1996 generalization of Borwein's famous 1990 conjecture. We then state a few infinite hierarchies of non-negative $q$-series identities which are interesting examples of our proposed conjecture and Bressoud's generalized conjecture. Finally, using certain positivity-preserving transformations for $q$-binomial coefficients, we prove the non-negativity of the infinite families.
title Extension of Bressoud's generalization of Borwein's conjecture and some exact results
topic Combinatorics
Number Theory
05A15, 05A17, 05A30, 11P81, 11P84
url https://arxiv.org/abs/2402.15886