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The number of different distances determined by n points in the plane
 J. Combin. Theory Ser. A
, 1984
"... A classical problem in combinatorial geometry is that of determining the minimum number f(n) of different distances determined by n points in the Euclidean plane. In 1952, L. Moser proved thatf(n)> n”‘/(2 fi) 1 and this has remained for 30 years as the best lower bound known for f(n). It is show ..."
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A classical problem in combinatorial geometry is that of determining the minimum number f(n) of different distances determined by n points in the Euclidean plane. In 1952, L. Moser proved thatf(n)> n”‘/(2 fi) 1 and this has remained for 30 years as the best lower bound known for f(n). It is shown that f(n)> cn “ ’ for some fixed constant c. I.
private communication
, 1983
"... The ndimensional lattices that contain fewest distances are characterized for all n # 2. 0 1991 Academic Press, Inc. 1. ..."
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The ndimensional lattices that contain fewest distances are characterized for all n # 2. 0 1991 Academic Press, Inc. 1.