Covariogram of non-convex sets
Metric Geometry
2010-09-06 v1
Abstract
The covariogram of a compact set A contained in R^n is the function that to each x in R^n associates the volume of A intersected with (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 9 points that have equal discrete covariogram.
Cite
@article{arxiv.1003.4122,
title = {Covariogram of non-convex sets},
author = {Carlo Benassi and Gabriele Bianchi and Giuliana D'Ercole},
journal= {arXiv preprint arXiv:1003.4122},
year = {2010}
}
Comments
15 pages, 7 figures, accepted for publication on Mathematika