volume 28, issue 4, P467-473 2002
DOI: 10.1007/s00454-002-2882-5
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Abstract: Let f (n) be the maximum number of unit distances determined by the vertices of a convex n-gon. Erdős and Moser conjectured that this function is linear. Supporting this conjecture we prove that f sym (n) ∼ 2n where f sym (n) is the restriction of f (n) to centrally symmetric convex n-gons. We also present two applications of this result. Given a strictly convex domain K with smooth boundary, if f K (n) denotes the maximum number of unit segments spanned by n points in the boundary of K , then f K (n) = O(n) …

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