We prove that a generic homogeneous polynomial of degree $d$ is determined, up to a nonzero constant multiplicative factor, by the vector space spanned by its partial derivatives of order $k$ whenever $k\leq\frac{d}{2}-1$.

中文翻译：

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关于由偏导数确定的齐次多项式 – 勘误表

我们证明，当 $k\leq\frac{d}{2} -1$。