Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2601.04014 |
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Inhaltsangabe:
- Recently, Andrews and Bachraoui considered a generating function $F_{k,m}(q)$ associated with certain two-color partitions, and conjectured that this function has non-negative coefficients for $m=1$. They showed this property for $1 \leq k \leq 4$. In this note, we prove that $F_{k,1}(q)$ has non-negative coefficients for $5 \leq k \leq 10$. Moreover, we show that, as $k\to\infty$, $F_{k,1}(q)$ is related to Ramanujan's third order mock theta function $ω(q)$ and to quotients of certain $q$-binomial coefficients.