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arXiv · 1003.4122

Covariogram of non-convex sets

Carlo Benassi·Gabriele Bianchi·Giuliana D'Ercole
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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.

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Carlo Benassi, Gabriele Bianchi, Giuliana D'Ercole. 2010-03-22. Covariogram of non-convex sets. https://doi.org/10.1112/s0025579310000549

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