Consider $m$ unit vectors in $\mathbb{R}^n$ with positive coordinates so that $m>n$. How does one pick the $m$ unit vectors so that the largest inner product of them is the smallest?
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4$\begingroup$ It is equivalent to placing $m$ points on the sphere $\mathbb{S}^{n-1}$ so that the minimal distance between them is a maximal. This have been studied a lot. Only in few cases the complete answer is known. $\endgroup$– Fedor PetrovCommented Nov 8, 2016 at 13:47
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$\begingroup$ Dear Fedor Petrov, thank you for the information. Maybe there is a standard reference or paper that deals with this problem? $\endgroup$– TOMCommented Nov 8, 2016 at 13:50
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5$\begingroup$ One reference, which also discusses a lot of related problems, is arxiv.org/pdf/math/0607446v2.pdf. $\endgroup$– Richard StanleyCommented Nov 8, 2016 at 16:31
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