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RATIONAL DISTANCES WITH RATIONAL ANGLES

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 28 Nov 2011Embargo end date: 01 Jan 2010 English Publisher:WileyJournal:Mathematika, volume 58, pages 409-418 (issn: 0025-5793, eissn: 2041-7942,

Authors: József Solymosi; Frank de Zeeuw; Ryan Schwartz;

doi: 10.1112/s0025579311001847 , 10.48550/arxiv.1008.3671

arXiv: http://arxiv.org/abs/1008.3671

RATIONAL DISTANCES WITH RATIONAL ANGLES

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Abstract

In 1946 Erd\H os asked for the maximum number of unit distances, $u(n)$, among $n$ points in the plane. He showed that $u(n)> n^{1+c/\log\log n}$ and conjectured that this was the true magnitude. The best known upper bound is $u(n)

12 pages; corrected typos, updated references; corrected results in Sections 3 and 4; added/updated statement of main results in Section 2; added new section containing lower bounds

Related Organizations

University of British Columbia
Canada

Keywords

52C10 (Primary) 12E05 (Secondary), FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)

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