Timeline for Divide Euclidean space by surfaces
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 10, 2023 at 10:15 | comment | added | Martin Tancer | There is Milnor-Thom theorem bounding the total number of faces of the arrangement. This must be, for example, in Matousek's book Lectures on Discrete Geometry. I do not have it with me now. Thus for a lack of better reference, here is a PDF containing the statement (Thm. 6.2.1). kam.mff.cuni.cz/~matousek/kvg1-tb.pdf Of course, counting all faces is probably an overkill. But at least it provides some bound. | |
| Sep 9, 2023 at 1:06 | comment | added | Hao Yu | the result I wrote is for hyperplane not surface | |
| Sep 8, 2023 at 8:55 | comment | added | YCor | Do you know for a single hypersurface ($n=1$)? For instance $xy=1$ divides the Euclidean plane into 3 components (here $d=2$, $k=2$). | |
| Sep 8, 2023 at 8:32 | comment | added | Hao Yu | @YCor, yes,it is | |
| Sep 7, 2023 at 9:22 | comment | added | YCor | What is $C_n^k$? is it the binomial coefficient $\binom{n}{k}$? | |
| Sep 7, 2023 at 9:22 | history | edited | YCor | CC BY-SA 4.0 |
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| Sep 7, 2023 at 7:19 | comment | added | Ali Taghavi | It is some how similar to the first part of the Hilbert 16th problem | |
| Sep 7, 2023 at 6:06 | history | asked | Hao Yu | CC BY-SA 4.0 |