关于无穷乘积展开式中消失系数的进一步结果
Further Results on Vanishing Coefficients in Infinite Product Expansions
摘要：
推广了Andrews和Bressoud关于某些无穷乘积级数展开式中系数为零的结果.这些结果具有如下形式：如果对于某些整数$k$、$m$、$s$和$t$，有\begin{equation*} \frac{(q^{r-tk}, q^{mk-(r-tk)}; q^{mk})_\infty}{(q^r,q^{mk-r}; q^{mk})_\infty} =: \sum_{n=0}^\infty c_nq^n, \end{equation*}，其中$r=sm+t$，则$c_{kn-rs}$总是零。我们的定理也部分地给出了一个简单的重新表述的结果的Alladi和戈登，但也给出了结果的情况下不包括定理的Alladi和戈登。我们也给出了一些解释的分析结果的整数分割。
英文摘要：
We extend results of Andrews and Bressoud on the vanishing of coefficients in the series expansions of certain infinite products. These results have the form that if \begin{equation*} \frac{(q^{r-tk}, q^{mk-(r-tk)}; q^{mk})_\infty}{(q^r,q^{mk-r}; q^{mk})_\infty} =: \sum_{n=0}^\infty c_nq^n, \end{equation*} for certain integers $k$, $m$ $s$ and $t$, where $r=sm+t$, then $c_{kn-rs}$ is always zero. Our theorems also partly give a simpler reformulation of results of Alladi and Gordon, but also give results for cases not covered by the theorems of Alladi and Gordon. We also give some interpretations of the analytic results in terms of integer partitions.
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