Geometry of Cuts and Metrics
The 22 minimal dichotomy decompositions of the K5-distance
Discrete Applied Mathematics
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Itis conjectured that there exist at most 2k equidistantpoints in the k-dimensional rectilinear space.This conjecture has been verified for k\leq 3; weshow here its validity in dimension k=4. We alsodiscuss a number of related questions. For instance, what isthe maximum number of equidistant points lying in the hyperplane:\sum^k_{i=1}x_i = 0? If this number would be equalto k, then the above conjecture would follow. Weshow, however, that this number is \geq k+1 for k\geq 4.