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Thursday, May 03, 2007
Coda to idiot-post
Posted by GASARCH
Coda to idiot.
- The posting idiot was a test case for the newly-fixed mechanism to email posts to people (some people had been getting this blog via email instead of going to the web.) It did not work. Nobody knows why.
- I had written:
computers have gotten VDW(4,2) more complicated.One of the comments was:For the "Ramsey-theory idiots" out there, the technical translation of VDW(4,2) is "I don't know exactly how much more complicated computers have gotten, but its a while hell of a lot!" :-)The commenter is correct in clarifying what I meant; however, both the commentator and I are incorrect in the details. Inspired by the commenter, I looked up what is known about the VDW numbers. VDW(4,2) is known and is only 35. VDW(5,2) is known, and is only 178. I should have written VDW(5,5) which is unknown but quite likely quite large.- VDW(k,c) is the least number W such that no matter how you c-color the elements {1,2,...,W} there will be k numbers equally spaced (e.g., 3,7,11,15 is 4 numbers equally spaced) that are the same color. W(k,c) exists by van der Waerden's Theorem. See van der Waerden's Theorem-Wikipedia or van der Waerden's theorem-my posting in Luca's blog
- I believe the only VDW numbers that are known are as follows: (see this paper) by Landman, Robertson, Culver from 2005.
- VDW(3,2)=9, (easy)
- VDW(3,3)=27, (Chvátal, 1970, math review entry, article not online.
- VDW(3,4)=76, (Brown, Some new van der Warden numbers (prelim report), Notices of the AMS, Vol 21, (1974), A-432. Article, review not online!
- VDW(4,2)=35, Chvátal ref above
- VDW(5,2)=178, Stevens and Shantarum, 1978 full article!
10:43 AM #
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You'll use any excuse possible to talk VDW!!! =)
--Yarden
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what is "coda" mean?
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It's an alternative spelling of 'kudos'. Check it out at
http://dictionary.reference.com/browse/coda
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