Covariogram of non-convex sets

Details Covariogram of non-convex sets Covariogram of non-convex sets

2010-03-22

arxiv.org/abs/1003.4122v1

Mathematika 56 (2010) pp 267-284

Mathematics

Metric Geometry

15 pages, 7 figures, accepted for publication on Mathematika

Scientific paper

10.1112/S0025579310000549

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.

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