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math.MG2014
On the distribution of distances in homogeneous compact metric spaces
Mark Herman, Jonathan Pakianathan
We provide a simple proof that in any homogeneous, compact metric space of diameter , if one finds the average distance achieved in with respect to some isometry invaria…
math.MG2014
A note on the unit distance problem for planar configurations with Q-independent direction set
Mark Herman, Jonathan Pakianathan
Let denote the maximum number of unit distances that a set of points in the Euclidean plane can determine with the additional condition that the distinct…