On Radon's recipe for choosing correct sites for multivariate polynomial interpolation (Q655450)

Let \({\mathbb F}\) be either \({\mathbb R}\) or \({\mathbb C}\). A set \(X\subset {\mathbb F}^s\) is called \(n\)-correct if, for every \(a:X\rightarrow {\mathbb F}\), there exists exactly one polynomial \(p\) of degree \(\leq n\) on the affine hull of \(X\) such that \(p(x) = a(x)\), \(\forall\;x\in X\). The main result of this article is a characterization of the class of all correct sets that are constructible by recursive application of Radon's recipe. Two types of \(n\)-correct sets introduced previously by the authors are also shown to belong to this class.