Timeline for What is the maximal diameter of a cell in a particular partition of the simplex?
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Dec 21, 2015 at 6:07 | vote | accept | User123321 | ||
| Dec 21, 2015 at 6:07 | history | edited | User123321 | CC BY-SA 3.0 |
Asked for an upper bound on the diameter too.
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| Dec 18, 2015 at 13:55 | answer | added | Joseph O'Rourke | timeline score: 3 | |
| Dec 18, 2015 at 3:44 | comment | added | User123321 | @JosephO'Rourke: Thanks for the comment. I edited the question. I am considering the standard simplex and using the hyperspaces defined by the planes to partition the simplex. | |
| Dec 18, 2015 at 3:43 | history | edited | User123321 | CC BY-SA 3.0 |
added 192 characters in body
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| Dec 18, 2015 at 0:00 | comment | added | Joseph O'Rourke | "I only intended for the simplex to contain points whose coordinates sum to exactly 1." So is your simplex defined by the $p_i$ summing to $1$, or do the $p_i$ determine the partition of the simplex? I feel like you are leaving out some information that makes your question clear. Perhaps you could define your simplex first, and then define its partition? | |
| Dec 17, 2015 at 21:14 | comment | added | User123321 | @JosephO'Rourke: Yes, that is correct. (Note: I edited the notation above so as the faces are not counted as part of the hyperplanes.) | |
| Dec 17, 2015 at 21:14 | history | edited | User123321 | CC BY-SA 3.0 |
added 4 characters in body
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| Dec 17, 2015 at 21:12 | comment | added | User123321 | @user35593: I only intended for the simplex to contain points whose coordinates sum to exactly 1. | |
| Dec 17, 2015 at 21:04 | comment | added | User123321 | Sorry, I hadn't realized it was forum convention to link to previous questions. As you mentioned, the previous question asked for the optimal partitioning on the simplex. This one asks for a bound on the cell diameter for a particular partitioning. | |
| Dec 17, 2015 at 18:54 | review | Close votes | |||
| Dec 18, 2015 at 10:16 | |||||
| Dec 17, 2015 at 18:37 | comment | added | Sebastian Goette | Possible duplicate of What is the minimal number of lines needed to partition a simplex into cells of diameter at most $\epsilon$? Since you are the same OP, why did you not even refer to that question of yours? The only difference is that now you ask for evenly space intersection points on the opposite edge. | |
| Dec 17, 2015 at 17:54 | comment | added | Joseph O'Rourke | So there are $K \binom{n}{2}$ hyperplanes? For a triangle, $3 \binom{n}{2} $ lines forming the partition? | |
| Dec 17, 2015 at 17:51 | comment | added | user35593 | All cells contain the origin $(0,\dots,0)$ so the diameter is at least $1$. Or did I missunderstand something? | |
| Dec 17, 2015 at 17:30 | history | asked | User123321 | CC BY-SA 3.0 |