COVARIOGRAM OF NON-CONVEX SETS

The covariogram of a compact subset A of R(n) is the function that to each x associates the volume of the intersection of A and (A+x). Recently it has been proved that the covariogram determines any planar convex body, in the class of all convex bodies. We extend the class of sets in which a planar convex body is determined by its covariogram. Moreover, we prove that there is no pair of non-congruent planar polyominoes consisting of less than nine points that have equal discrete covariograms.