Geodesic
On the minimal number of nodes uniquely determining algebraic curves
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2015), pp. 17-22

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It is well-known that the number of $n$-independent nodes determining uniquely the curve of degree $n$ passing through them equals to $N-1$, where $N=\dfrac{1}{2}(n+1)(n+2)$. It was proved in [1], that the minimal number of $n$-independent nodes determining uniquely the curve of degree $n-1$ equals to $N-4$. The paper also posed a conjecture concerning the analogous problem for general degree $k\leq n$. In the present paper the conjecture is proved, establishing that the minimal number of $n$-independent nodes determining uniquely the curve of degree $k\leq n$ equals to $\dfrac{(k-1)(2n+4-k)}{2}+2$.
Keywords: poised, independent nodes, algebraic curves.
Mots-clés : polynomial interpolation 
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H. A. Hakopian; S. Z. Toroyan. On the minimal number of nodes uniquely determining algebraic curves. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2015), pp. 17-22. http://geodesic.mathdoc.fr/item/UZERU_2015_3_a2/