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. - 56:2(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.
2010
56
2
267
284
COVARIOGRAM OF NON-CONVEX SETS / Benassi, Carlo 6/8/1962; G., Bianchi; G., D’Ercole. - In: MATHEMATIKA. - ISSN 0025-5793. - STAMPA. - 56:2(2010), pp. 267-284. [10.1112/S0025579310000549]
Benassi, Carlo 6/8/1962; G., Bianchi; G., D’Ercole
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/706144
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