tag:blogger.com,1999:blog-3722233.post8808163209655813563..comments2024-03-04T02:59:26.350-06:00Comments on Computational Complexity: A Complete History of the LVDW conjectureLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-3722233.post-21177204203367861242009-01-14T19:45:00.000-06:002009-01-14T19:45:00.000-06:00Anonymous 3: Yes, the statement of VDW's theor...Anonymous 3: Yes, the statement of VDW's theorem should say "there exists a monochromatic arithmetic progression of length k."<BR/><BR/>In the statement of the (false) LVDW conjecture, we color the numbers beginning at k and look for a "large" AP. But the k here and the k in VDW are not entirely different. Any large AP would have to have at least k elements (since a large AP beginning at m needs to have m terms, and m >= k.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-9110279824103846922009-01-13T07:58:00.000-06:002009-01-13T07:58:00.000-06:00What is k in the statement of VDW's theorem? If I'...What is k in the statement of VDW's theorem? If I'm not mistaken it's the length of the arithmetic progression.<BR/><BR/>So then the k in the LVDW theorem has a different meaning than the k of the VDW theorem?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-2624948424333232572009-01-12T12:10:00.000-06:002009-01-12T12:10:00.000-06:00AH- I mean the LENGTH of the sequence is \ge itsle...AH- I mean the LENGTH of the sequence is \ge its<BR/>least element.<BR/><BR/>Sorry about that.GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-78585511538376345072009-01-12T10:53:00.000-06:002009-01-12T10:53:00.000-06:00Definitional question: What does it mean for an ar...Definitional question: What does it mean for an arithmetic sequence to be larger than its least element? For example, under the interpretations of that definition that I'm imagining, I don't see why (4,5,6,7) would be large.Anonymousnoreply@blogger.com