On 5-isosceles sets in the plane, with linear restriction. (English) Zbl 1149.52015

Summary: A finite planar set is \(k\)-isosceles for \(k\geq 3\) if every \(k\)-point subset of the set contains a point equidistant from two others. We show that an 8-set on a line is 5-isosceles if and only if its adjacent interpoint distances are equal to each other, and no 5-isosceles 9-set has 9 points on a line. We also show that the maximum 5-isosceles set with 8 points on a line contains at most 10 points.


52C20 Tilings in \(2\) dimensions (aspects of discrete geometry)
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