论文标题
一系列普通矩阵的分母
Denominators for One Variable Poincaré Series of Generic Matrices
论文作者
论文摘要
我们研究了普通矩阵的混合和纯正痕迹的庞加莱系列。这些系列被称为理性功能。在$ 2 \ times2 $矩阵的情况下，我们以最低的方式获得了一个明确的公式；我们认为，在$ 3 \ times3 $矩阵的情况下，我们认为这是一种分母，但无法证明是最低的；在一般情况下，猜想分母。
We study the Poincaré series of the mixed and pure trace rings of generic matrices. These series are known to be rational functions. We obtain an explicit formula in lowest terms in the case of $2\times2$ matrices; a denominator, which we presume but have not been able to prove to be in lowest terms, in the case of $3\times3$ matrices; and a conjectured denominator in the general case.
