Distinct Distances from Three Points. (30th September 2015)

• Record Type: Journal Article
• Authors: SHARIR, MICHA; SOLYMOSI, JÓZSEF
• Is Part Of: Combinatorics, probability and computing. Volume 25:Number 4(2016:Jul.)
• Page Start: 623
• Page End: 632
• Publication Date: 2015-09-30
• Subjects: Primary 52C10, -- Secondary 52C45, -- 05C35; Combinatorial analysis -- Periodicals; Probabilities -- Periodicals; Computer science -- Mathematics -- Periodicals; 511.6
• DOI: 10.1017/S0963548315000231
• Languages: English
• ISSNs: 0963-5483

Abstract

Abstract : Let p 1, p 2, p 3 be three noncollinear points in the plane, and let P be a set of n other points in the plane. We show that the number of distinct distances between p 1, p 2, p 3 and the points of P is Ω( n 6/11 ), improving the lower bound Ω( n 0.502 ) of Elekes and Szabó [4 ] (and considerably simplifying the analysis).