Timeline for What is the smallest number of subsets in such a subdivision?
Current License: CC BY-SA 3.0
11 events
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| Jan 25, 2013 at 19:28 | comment | added | Aaron Meyerowitz | Sorry, I don't have those two pages. The review in Math Reviews for MR1330906 (96b:52016) Kalbfleisch, J. G. ; Stanton, R. G. On the maximum number of coplanar points containing no convex n-gons. Utilitas Math. 47 (1995), 235--245. Says that the construction by Erdos-Szekeres is igenious but "not quite adequate. The authors of this paper modify that construction to give a complete proof." So maybe look there. | |
| Jan 11, 2013 at 5:57 | comment | added | Aaron Meyerowitz | Sorry, I haven't read the paper but it seems unlikely that the example would recursively designate an all 0 sequence. | |
| Jan 11, 2013 at 4:31 | comment | added | Diorn | I am wondering if that is a valid example. | |
| Jan 10, 2013 at 7:37 | comment | added | Diorn | Aaron, that's okay. I found the missing two pages, but it seems that their inductive construction is based on $g_{k,1}(1)=g_{1,l}=0$ and $g_{k,l}$ linearly depends on $g_{k,1}(1)$ and $g_{1,l}(1)$, which means that all $g_{k,l}$'s would be $0$. Then how would that form a example of a set of $2^{N−2}$ points so that no $N$ are the vertices of a convex $N$-gon? Thanks! | |
| Dec 25, 2012 at 9:53 | comment | added | Aaron Meyerowitz | I have spent more time with that paper and understand what I did not before: pages 55 and 56 are not there! So seek out a complete copy of the paper. Sorry that I did not notice before. | |
| Dec 25, 2012 at 7:07 | comment | added | Diorn | I mean at the top of the 3rd page of that paper. | |
| Dec 25, 2012 at 7:02 | comment | added | Diorn | Aaron, I looked into that paper, but in that paper, are $S_{k_i}$ any subsets or subsets in special configurations? Thanks! | |
| Dec 25, 2012 at 5:30 | comment | added | Aaron Meyerowitz | No I do not. However I just checked and the construction is just a few lines in 193.224.79.10/~p_erdos/1960-09.pdf It may take more than a few minutes to understand it though. | |
| Dec 24, 2012 at 22:28 | comment | added | Diorn | Dear Aaron, thank you for your answer, but do you know, specifically, what is an concrete example of a set of $2^{N-2}$ points so that no $N$ are the vertices of a convex $N$-gon? Thanks! | |
| Dec 14, 2012 at 0:16 | history | edited | Aaron Meyerowitz | CC BY-SA 3.0 |
added 195 characters in body
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| Dec 13, 2012 at 19:38 | history | answered | Aaron Meyerowitz | CC BY-SA 3.0 |