Coda to idiot-post

Coda to idiot.

1. 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.
2. 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.
3. 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
4. I believe the only VDW numbers that are known are as follows: (see this paper) by Landman, Robertson, Culver from 2005.
   1. VDW(3,2)=9, (easy)
   2. VDW(3,3)=27, (Chvátal, 1970, math review entry, article not online.
   3. 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!
   4. VDW(4,2)=35, Chvátal ref above
   5. VDW(5,2)=178, Stevens and Shantarum, 1978 full article!