Extension of Bressoud's generalization of Borwein's conjecture and some exact results
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908347834302464 |
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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 |
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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 |