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Distance set
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<h2 id="see-also">See also</h2> <ul><li><a href="/facts/Distance_matrix/2ptk07Y7">Distance matrix</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Arutyunyants, G.; Iosevich, A. (2004), "Falconer conjecture, spherical averages and discrete analogs", in Pach, János (ed.), Towards a Theory of Geometric Graphs, Contemp. Math., vol. 342, Amer. Math. Soc., Providence, RI, pp. 15–24, doi:10.1090/conm/342/06127, MR 2065249 <a href="/wiki/J%C3%A1nos_Pach" target="_blank">/wiki/J%C3%A1nos_Pach</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Klee, Victor; Wagon, Stan (1991), "Problem 10 Does the plane contain a dense rational set?", Old and New Unsolved Problems in Plane Geometry and Number Theory, Dolciani mathematical expositions, vol. 11, Cambridge University Press, pp. 132–135, ISBN 978-0-88385-315-3. <a href="978-0-88385-315-3" target="_blank">978-0-88385-315-3</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Magyar, Ákos (2008), "On distance sets of large sets of integer points", Israel Journal of Mathematics, 164: 251–263, doi:10.1007/s11856-008-0028-z, MR 2391148, S2CID 17629304 <a href="/wiki/Israel_Journal_of_Mathematics" target="_blank">/wiki/Israel_Journal_of_Mathematics</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Anning, Norman H.; Erdős, Paul (1945), "Integral distances", Bulletin of the American Mathematical Society, 51 (8): 598–600, doi:10.1090/S0002-9904-1945-08407-9. <a href="/wiki/Paul_Erd%C5%91s" target="_blank">/wiki/Paul_Erd%C5%91s</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>Guth, Larry; Katz, Nets Hawk (2015), "On the Erdős distinct distances problem in the plane", Annals of Mathematics, 181 (1): 155–190, arXiv:1011.4105, doi:10.4007/annals.2015.181.1.2, MR 3272924, S2CID 43051852 <a href="/wiki/Annals_of_Mathematics" target="_blank">/wiki/Annals_of_Mathematics</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Bekir, Ahmad; Golomb, Solomon W. (2007), "There are no further counterexamples to S. Piccard's theorem", IEEE Transactions on Information Theory, 53 (8): 2864–2867, doi:10.1109/TIT.2007.899468, MR 2400501, S2CID 16689687 <a href="/wiki/Solomon_W._Golomb" target="_blank">/wiki/Solomon_W._Golomb</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Koolen, Jack; Laurent, Monique; Schrijver, Alexander (2000), "Equilateral dimension of the rectilinear space", Designs, Codes and Cryptography, 21 (1): 149–164, doi:10.1023/A:1008391712305, MR 1801196, S2CID 9391925 <a href="/wiki/Monique_Laurent" target="_blank">/wiki/Monique_Laurent</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Szöllösi, Ferenc (2018), "The Two-Distance Sets in Dimension Four", in Akiyama, Jin; Marcelo, Reginaldo M.; Ruiz, Mari-Jo P.; Uno, Yushi (eds.), Discrete and Computational Geometry, Graphs, and Games - 21st Japanese Conference, JCDCGGG 2018, Quezon City, Philippines, September 1-3, 2018, Revised Selected Papers, Lecture Notes in Computer Science, vol. 13034, Springer, pp. 18–27, arXiv:1806.07861, doi:10.1007/978-3-030-90048-9_2, MR 4390269 <a href="/wiki/Jin_Akiyama" target="_blank">/wiki/Jin_Akiyama</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Blokhuis, A. (1983), "Chapter 7: Isosceles point sets", Few-Distance Sets (Ph.D. thesis), Eindhoven University of Technology, pp. 46–49, doi:10.6100/IR53747, Zbl 0516.05017 <a href="/wiki/Eindhoven_University_of_Technology" target="_blank">/wiki/Eindhoven_University_of_Technology</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>Grigorescu, C.; Petkov, N. (October 2003), "Distance sets for shape filters and shape recognition" (PDF), IEEE Transactions on Image Processing, 12 (10): 1274–1286, doi:10.1109/tip.2003.816010, hdl:11370/dd4f402f-91b0-47ae-94ec-29428a2d8fb9, PMID 18237892 <a href="https://pure.rug.nl/ws/files/2998573/2003IEEETIPGrigorescuC2.pdf" target="_blank">https://pure.rug.nl/ws/files/2998573/2003IEEETIPGrigorescuC2.pdf</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> </ol>