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