@article{Hakopian_Malinyan_2013, place={Yerevan, Armenia}, title={ON $n$-INDEPENDENT SETS LOCATED ON QUARTICS}, volume={47}, url={https://journals.ysu.am/index.php/proceedings-phys-math/article/view/vol47_no1_2013_pp006-012}, DOI={10.46991/PYSU:A/2013.47.1.006}, abstractNote={<p>Denote the space of all bivariate polynomials of total degree $\leq n$ by $\Pi_n$. We study the $n$-independence of points sets on quartics, i.e. on algebraic curves of degree 4. The $n$-independent sets $\mathcal X$ are characterized by the fact that the dimension of the space ${\mathcal P}_{\mathcal X}:=\{p\in \Pi_n : p(x)=0, \forall x\in \mathcal X\}$ equals $\dim \Pi_n-\#\mathcal X.$ Next, polynomial interpolation of degree $n$ is solvable only with these sets. Also the $n$-independent sets are exactly the subsets of $\Pi_n$-poised sets. In this paper we characterize all $n$-independent sets on quartics. We also characterize the set of points that are $n$-complete in quartics, i.e. the subsets ${\mathcal X}$ of quartic $\delta,$ having the property $p\in\Pi_n,~p(x)=0~\forall x\in {\mathcal X} \Rightarrow p=\delta q,~q\in \Pi_{n-4}.$</p>}, number={1 (230)}, journal={Proceedings of the YSU A: Physical and Mathematical Sciences}, author={Hakopian, H.A. and Malinyan, A.R.}, year={2013}, month={Apr.}, pages={6–12} }