Timeline for What is the minimum of this quantity on $S^{n-2}\times S^{n-2}$?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Oct 11, 2018 at 20:33 | comment | added | Mostafa - Free Palestine | Thanks Noam, I learnt so much from your answer! | |
| Oct 11, 2018 at 20:28 | history | bounty ended | Mostafa - Free Palestine | ||
| Oct 11, 2018 at 20:28 | vote | accept | Mostafa - Free Palestine | ||
| Oct 10, 2018 at 17:34 | comment | added | Noam D. Elkies | Thanks / you're welcome. I've now incorporated some of the explanation into my answer. | |
| Oct 10, 2018 at 17:33 | history | edited | Noam D. Elkies | CC BY-SA 4.0 |
added 272 characters in body
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| Oct 10, 2018 at 16:16 | comment | added | Iosif Pinelis | Very nice, thank you for this detail! | |
| Oct 10, 2018 at 16:10 | comment | added | Noam D. Elkies | Sorry, I meant the image of those vectors $(1,\ldots,1,1-n)$ etc. under the appropriate permutation. If $x_1 \geq x_2 \geq \ldots \geq x_n$ then the map taking $x$ to $(x_1-x_2,x_2-x_3,\ldots,x_{n-1}-x_n)$ identifies the this cone with the closed positive orthant, and those extreme rays with the coordinate axes. | |
| Oct 10, 2018 at 15:53 | comment | added | Iosif Pinelis | I like the homogenization idea, as well as the idea of fixing an order of the coordinates. However, it is unclear to me how and why "[s]uch a choice limits each of $x$ and $y$ to a cone whose extreme rays are generated by $(1,\ldots,1,1-n)$, $(2,\ldots,2,2-n,2-n)$, etc."; for any choice of "one of the $n!^2$ possible orders of the coordinates of $x$ and $y$"? In particular, the vectors $(1,\ldots,1,1-n)$, $(2,\ldots,2,2-n,2-n)$, etc. are compatible only with some of the $n!^2$ possible orders. Can you provide details on this? | |
| Oct 10, 2018 at 15:02 | history | answered | Noam D. Elkies | CC BY-SA 4.0 |