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.
COVARIOGRAM OF NON-CONVEX SETS / Benassi, Carlo 6/8/1962; G., Bianchi; G., D’Ercole. - In: MATHEMATIKA. - ISSN 0025-5793. - STAMPA. - 56:(2010), pp. 267-284. [10.1112/S0025579310000549]
COVARIOGRAM OF NON-CONVEX SETS
BENASSI, Carlo 6/8/1962;
2010
Abstract
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.
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