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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

$ n$-clusters for $ 1<n<7$


Authors: Landon Curt Noll and David I. Bell
Journal: Math. Comp. 53 (1989), 439-444
MSC: Primary 52A37
MathSciNet review: 970702
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Abstract: An n-cluster is a set of n lattice points in $ {{\mathbf{R}}^2}$ with no 3 points collinear, no 4 points concyclic, and where all mutual distances are nonzero integers. The initial discoveries of n-clusters for $ 1 < n < 7$ are reported. A progress report on small 6-clusters and the search for a 7-cluster is described. A question on the impact of the lattice point restriction is raised, and the definition of n-cluster is generalized to $ {{\mathbf{R}}^m}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1989-0970702-0
PII: S 0025-5718(1989)0970702-0
Article copyright: © Copyright 1989 American Mathematical Society