Mapping $n$ grid points onto a square forces an arbitrarily large Lipschitz constant

Michael Dymond, Vojtěch Kaluža, Eva Kopecká

We prove that the regular $n\times n$ square grid of points in the integer lattice ${\mathbb{Z}}^2$ cannot be recovered from an arbitrary $n^2$-element subset of ${\mathbb{Z}}^2$…