Few distinct distances implies no heavy lines or circles

Few distinct distances implies no heavy lines or circles

We study the structure of planar point sets that determine a small number of distinct distances. Specifically, we show that if a set PP of n points determines o(n) distinct distances, then no line contains Ω(n[superscript 7/8]) points of PP and no circle contains Ω(n[superscript 5/6]) points of...

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Bibliographic Details
Main Authors: Sheffer, Adam, Zahl, Joshua, de Zeeuw, Frank
Other Authors: Massachusetts Institute of Technology. Department of Mathematics
Format: Article
Language:English
Published: Springer Berlin Heidelberg 2017
Online Access:http://hdl.handle.net/1721.1/106218
https://orcid.org/0000-0001-5129-8300

Internet

http://hdl.handle.net/1721.1/106218
https://orcid.org/0000-0001-5129-8300

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