Timeline for Making 'circles' on a lattice/ Making distinct fractions from partitions of a number
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
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| Jun 17, 2022 at 15:00 | comment | added | The Amplitwist |
The links to the articles at springerlink.com and sciencedirect.com are broken. Perhaps you could take a look, whenever possible…
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| Jun 11, 2010 at 18:56 | comment | added | Tom Boardman | PPs. Hey, does this mean i have just proved something in number theory?! | |
| Jun 11, 2010 at 18:51 | comment | added | Tom Boardman | Bah... that last result looks like the business but I can't see it without forking out $30. Damn those journal subscription fees... it really bugs me when I don't get to see the solution- it's like watching half of a movie- +1 though. Ps. I think your index might be upside-down- my bound isn't great- but it's nowhere near as bad as o(n^2) vs o(n^2/3) ! | |
| Jun 11, 2010 at 15:42 | comment | added | David Eppstein | +1 I came here to point to Barany's work on exactly this problem (I saw him speak on it at IPAM last fall) but I see you've already done so. | |
| Jun 11, 2010 at 14:45 | history | edited | Gjergji Zaimi | CC BY-SA 2.5 |
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| Jun 11, 2010 at 14:38 | comment | added | Gjergji Zaimi | Oh, in that case I believe he is only considering width in one direction, which shouldn't be of much interest to you, since you are considering points in convex position in a confined area (square). I was referring to the section "maximal polytopes in K", being of interest, but I figured the new article I added above is a much better reference. | |
| Jun 11, 2010 at 14:25 | history | edited | Gjergji Zaimi | CC BY-SA 2.5 |
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| Jun 11, 2010 at 14:23 | comment | added | Tom Boardman | I mean, you can do it easily if you don't need general position- but he seems to use g.p. in his definition of convex "since every lattice line contains at most 2 vertices of P...". | |
| Jun 11, 2010 at 14:17 | comment | added | Tom Boardman | The first one seems more asymptotic than my query, the second though does seem to cover it... Although, and maybe I'm being a bit thick here, I can't seem to get his bound for the width of a lattice 10-gon: he says "The reader will have no diffculty finding a convex lattice polygon with n vertices having lattice width exactly $\lciel n/2 \rceil- 1$". I am having difficulty. Is it possible he saw n=1-8 attaining his lower bound and assumed the rest? I am probably just being a pillock- can you fit a convex 10-gon in a lattice width of 4? | |
| Jun 11, 2010 at 13:14 | history | edited | Gjergji Zaimi | CC BY-SA 2.5 |
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| Jun 11, 2010 at 13:09 | history | answered | Gjergji Zaimi | CC BY-SA 2.5 |