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simont

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[personal profile] simont Fri 2014-03-14 14:56
This seems to disagree with my version of your bound above in some cases. The smallest is s(5,7). The true optimum is 5/3; my version of your bound also gives 5/3 (that's the point at which my second range for P switches from [14,21] to [14,14] while the first was at [15,20] and hence they stop overlapping). But the version in your comment here, as I calculate it, gives us p=2 and s' = min { 5-7/2, 7/3 } = min { 3/2, 7/3 } = 3/2, which isn't even a correct upper bound at all.

Incidentally, I'm starting to think about putting up a web page containing all the data I have so far, and trying to tabulate it so as to show at a glance where answers are known, where bounds are tight, and what's still uncertain. Your bounding technique will form an important part of that table, and you obviously deserve credit for coming up with it; would you like me to credit you as [livejournal.com profile] writinghawk, or under some other name?
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