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Multiplicities of interpoint distances in finite planar sets |
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| Authors: | Paul Erd s Peter C Fishburn |
| Institution: | a Mathematical Institute, Hungarian Academy of Sciences, Budapest, Hungary b AT&T Bell Laboratories, Murray Hill, NJ 07974, USA |
| Abstract: | What is the maximum number of unit distances between the vertices of a convex n-gon in the plane? We review known partial results for this and other open questions on multiple occurrences of the same interpoint distance in finite planar subsets. Some new results are proved for small n. Challenging conjectures, both old and new, are highlighted. |
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