Geodesic
On Homogeneous Polynomials Determined by their Partial Derivatives
Canadian mathematical bulletin, Tome 63 (2020) no. 2, pp. 358-365

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DOI

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 $k$ for $k\leqslant \frac{d}{2}-1$.
DOI : 10.4153/S0008439519000419
Mots-clés : homogeneous polynomial, derivative 
Wang, Zhenjian. On Homogeneous Polynomials Determined by their Partial Derivatives. Canadian mathematical bulletin, Tome 63 (2020) no. 2, pp. 358-365. doi: 10.4153/S0008439519000419
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     title = {On {Homogeneous} {Polynomials} {Determined} by their {Partial} {Derivatives}},
     journal = {Canadian mathematical bulletin},
     pages = {358--365},
     year = {2020},
     volume = {63},
     number = {2},
     doi = {10.4153/S0008439519000419},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000419/}
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