volume 27, issue 3, P303-351 2002
DOI: 10.1007/s00454-001-0073-4
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## Abstract: For each pair (Q i , Q j ) of reference points and each real number r there is a unique hyperplane h ⊥ Q i Q j such that d(P, Q i ) 2 − d(P, Q j ) 2 = r for points P in h. Take n reference points in d-space and for each pair (Q i , Q j ) a finite set of real numbers. The corresponding perpendiculars form an arrangement of hyperplanes. We explore the structure of the semilattice of intersections of the hyperplanes for generic reference points. The main theorem is that there is a real, additive gain graph (this…

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