Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 831.52008
Autor: Erdös, Paul; Fishburn, Peter C.
Title: Multiplicities of interpoint distances in finite planar sets. (In English)
Source: Discrete Appl. Math. 60, No.1-3, 141-147 (1995).
Review: For a set X of n points in the plane, let d1, ..., dm denote the different positive distances between the points of X, and rk the multiplicity of dk. The authors study the vector r(X) = (r1, ..., rm), where the numbering is chosen such that r1 \geq r2 \geq ··· \geq rm. The case where X is the set V of vertices of a convex polygon is considered particularly. For n = 5 and m in {2,3}, the possible vectors r(X) and r(V) are completely specified. For n = 6, it is shown that r(X) cannot be equal to (7,7,1). There is a discussion of some known results and several challenging conjectures which are related to this topic.
Reviewer: J.Linhart (Salzburg)
Classif.: * 52C10 Erdoes problems and related topics of discrete geometry
Keywords: minimum number of different distances; multiplicity vector
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