Finite Sets in \(R^n\) Given up to Translation have Reconstruction Number Three.

Abstract

We prove that a finite set \(A\) of points in the \(n\)-dimensional Euclidean space \(\mathcal{R}^n\) is uniquely determined up to translation by three of its subsets of cardinality \(|A|-1\) given up to translation, i.e. the Reconstruction Number of such objects is three. This result is best-possible.