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I'd seriously like to see a source for V(2,6)=1132. I'm flagging it, and if a source does not come up, I'm removing it, because that number is seriously beyond calculation as far as I know, especially if it's that high, unless someone has come up with a new way of doing things (in which case, I'd still like to see a reference before I let it stand). Cheeser1 03:54, 18 February 2007 (UTC)
This entry by Bill Gasarch at the computational complexity blog points to the following recent work on van der Waerden numbers: Lower Bounds for van der Waerden Numbers, By: Tamara Giorgadze, 6/15/08 [1] I refrained from putting these into the table, since I am not an expert in the field and thus cannot judge about the correctness of the results. Thus I only point to the announcement at this page and let anyone interested judge for himself. Hermel ( talk) 12:23, 26 September 2008 (UTC)
The sequence is 2, 9, 293, 29799 coming from the formula W(k) = (2*k^2 -1)^(k -1) +2^(k -1) where k= 1, 2, 3, 4, ... It would require lots of computer time to verify the fourth value in the sequence, but I'm confident. Searching for boundary would be an over-rated and unsatisfactory experience. Also, the table should be changed to reflect the first item: 2 in the sequence with only one color. By: William Bouris 2601:249:500:73FD:7079:FA87:7A1F:5A00 ( talk) 16:51, 15 October 2017 (UTC)
[2] Ron Graham apparently conjectured a while back that W(k,t) for fixed K grows as O(t2). Ben Green recently disproved this conjecture and shows that for any n, for sufficiently large k, W(k,t) grows faster than O(tn). This was a surprising result and seems worth writing up in the article. 2602:24A:DE47:B8E0:1B43:29FD:A863:33CA ( talk) 00:49, 17 December 2021 (UTC)
Never again should you revert a revision that explicitly quotes your own reference number without reading and referring to your own reference number. 2603:7000:8C00:43E2:E47B:CE39:B457:D651 ( talk) 21:08, 23 April 2024 (UTC)
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
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I'd seriously like to see a source for V(2,6)=1132. I'm flagging it, and if a source does not come up, I'm removing it, because that number is seriously beyond calculation as far as I know, especially if it's that high, unless someone has come up with a new way of doing things (in which case, I'd still like to see a reference before I let it stand). Cheeser1 03:54, 18 February 2007 (UTC)
This entry by Bill Gasarch at the computational complexity blog points to the following recent work on van der Waerden numbers: Lower Bounds for van der Waerden Numbers, By: Tamara Giorgadze, 6/15/08 [1] I refrained from putting these into the table, since I am not an expert in the field and thus cannot judge about the correctness of the results. Thus I only point to the announcement at this page and let anyone interested judge for himself. Hermel ( talk) 12:23, 26 September 2008 (UTC)
The sequence is 2, 9, 293, 29799 coming from the formula W(k) = (2*k^2 -1)^(k -1) +2^(k -1) where k= 1, 2, 3, 4, ... It would require lots of computer time to verify the fourth value in the sequence, but I'm confident. Searching for boundary would be an over-rated and unsatisfactory experience. Also, the table should be changed to reflect the first item: 2 in the sequence with only one color. By: William Bouris 2601:249:500:73FD:7079:FA87:7A1F:5A00 ( talk) 16:51, 15 October 2017 (UTC)
[2] Ron Graham apparently conjectured a while back that W(k,t) for fixed K grows as O(t2). Ben Green recently disproved this conjecture and shows that for any n, for sufficiently large k, W(k,t) grows faster than O(tn). This was a surprising result and seems worth writing up in the article. 2602:24A:DE47:B8E0:1B43:29FD:A863:33CA ( talk) 00:49, 17 December 2021 (UTC)
Never again should you revert a revision that explicitly quotes your own reference number without reading and referring to your own reference number. 2603:7000:8C00:43E2:E47B:CE39:B457:D651 ( talk) 21:08, 23 April 2024 (UTC)