Timeline for Distribution of pairwise distances
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Nov 28, 2019 at 13:45 | comment | added | Joseph O'Rourke | This is great, Matt! My only concern is that maybe some of your conjectures are in the literature in a form not easily recognized, as with the Harborth result. But this is what I was seeking, so: Thanks! | |
| Nov 28, 2019 at 10:08 | history | edited | user44143 | CC BY-SA 4.0 |
added full references to Erdos and Harborth
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| Nov 28, 2019 at 6:38 | comment | added | Ilya Bogdanov | The maximal number of diameters was found in P. Erdos, On sets of distances of $n$ points. Am. Math. Mon. 53 , 248–250 (1946). It is indeed $n$, and there are many other examples (e.g., the vertices of a regular $n$-gon with $n$ odd also work). | |
| Nov 28, 2019 at 0:37 | vote | accept | Joseph O'Rourke | ||
| Nov 27, 2019 at 23:26 | history | edited | user44143 | CC BY-SA 4.0 |
updated to reflect Yoav Kallus's comments
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| Nov 27, 2019 at 14:55 | comment | added | user44143 | @YoavKallus, you are correct! | |
| Nov 27, 2019 at 14:50 | comment | added | Yoav Kallus | For your "maxima" conjecture, am I missing something or can you get 2n-2 ordered pairs by putting one point in the center of a circle and n-1 along a small circular arc? If you make the arc 60 degrees, you get up to 2n. | |
| Nov 27, 2019 at 14:46 | comment | added | Yoav Kallus | Your "minima" conjecture is apparently a theorem of Harborth, according to arxiv.org/abs/1210.5756 | |
| Nov 27, 2019 at 14:35 | history | edited | user44143 | CC BY-SA 4.0 |
added 312 characters in body
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| Nov 27, 2019 at 13:42 | history | answered | user44143 | CC BY-SA 4.0 |