Certain positive $q$-series and inequalities for two-color partitions
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913939064881152 |
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| author | Andrews, George E. Bachraoui, Mohamed El |
| author_facet | Andrews, George E. Bachraoui, Mohamed El |
| contents | We consider some $q$-series which depend on a pair of positive integers $(k,m)$. While positivity of these series holds for the first few values of $(k,m)$, the situation is quite unclear for other values of $(k,m)$. In addition, our series generate the number of certain two-color integer partitions weighted by $(-1)^j$ where $j$ is the number of even parts. Therefore, inequalities involving these partitions will be deduced from the positivity of their generating functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09276 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Certain positive $q$-series and inequalities for two-color partitions Andrews, George E. Bachraoui, Mohamed El Number Theory 11P81 We consider some $q$-series which depend on a pair of positive integers $(k,m)$. While positivity of these series holds for the first few values of $(k,m)$, the situation is quite unclear for other values of $(k,m)$. In addition, our series generate the number of certain two-color integer partitions weighted by $(-1)^j$ where $j$ is the number of even parts. Therefore, inequalities involving these partitions will be deduced from the positivity of their generating functions. |
| title | Certain positive $q$-series and inequalities for two-color partitions |
| topic | Number Theory 11P81 |
| url | https://arxiv.org/abs/2507.09276 |