Reconstructing sets from interpoint distances (extended abstract)
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Sums, Projections, and Sections of Lattice Sets, and the Discrete Covariogram
Discrete & Computational Geometry
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Two discrete point sets in R^n are said to be homometric if their difference sets coincide. Homometric point sets were first studied in the 1930s in connection with the interpretation of x-ray diffraction patterns; today they appear in many contexts. Open questions still abound, even for point sets on the line. Under what conditions does a difference set S-S characterize S uniquely? If it does not, how can we find all the sets S"i,i=1,..., that give rise to it, and how are these sets related?