Timeline for Largest number of vectors with pairwise negative dot product
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 6 at 16:52 | history | edited | LSpice | CC BY-SA 4.0 |
While this is on the front page, removing redundant whitespace introduced to prevent "too few changes"
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| Jan 6 at 16:52 | comment | added | LSpice | @WlodAA, re, there and there you mention an argument by @YuichiroFujiwara, but I can't find it. Where is it? | |
| Apr 20, 2020 at 19:58 | comment | added | Dmitry Vaintrob | Another way of saying this geometrically: op is asking about covers of an n-1 sphere by hemispheres satisfying a certain property. If n>1, you can assume no two hemispheres are opposite. Now observe that such a cover induced another cover of the boundary of a given hemisphere, satisfying the same property. It follows that the maximal number of hemispheres can grow by at most 1 when you add 1 to the dimension. | |
| Apr 20, 2020 at 17:17 | comment | added | Wlod AA | Actually, you don't need to know about the perfect example for n+1 vectors. The above Yuichiro argument induces plenty of specific generic examples. For the sake of the theorem, these generic examples are much simpler. | |
| S Jan 7, 2015 at 9:48 | history | edited | Yuichiro Fujiwara | CC BY-SA 3.0 |
Removed a LaTeX remark. The strange $\ \ \ \ $ is to avoid the "too few changes" restriction.
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| S Jan 7, 2015 at 9:48 | history | suggested | CommunityBot | CC BY-SA 3.0 |
remove the silly and incomprehensible LaTeX remark
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| Jan 7, 2015 at 9:42 | review | Suggested edits | |||
| S Jan 7, 2015 at 9:48 | |||||
| Jul 11, 2010 at 18:10 | comment | added | Benoît Kloeckner | Note that the lower bound holds by Robin Chapman's argument, of course. | |
| Jul 11, 2010 at 18:09 | history | answered | Benoît Kloeckner | CC BY-SA 2.5 |