Timeline for Lower bounds for the density variant of the Hilbert cube problem
Current License: CC BY-SA 4.0
4 events
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| Feb 7, 2023 at 22:34 | comment | added | Zach Hunter | indeed. a minor tweak to this is the solution. basically you take a random dense subset of the construction in this post (which was known before Salem-Spencer and Behrend constructions). to my knowledge, said construction is the only way we know how to make dense subset of $[n]$ where all APs have length $o(\log n)$. | |
| Feb 7, 2023 at 22:22 | comment | added | Terry Tao | Fair enough. I guess a random density 1/2 set in $[n]$ will already contain an arithmetic progression of length about $\log_2 n$ or so, so some other construction will be needed to do better than exponential. | |
| Feb 7, 2023 at 18:59 | comment | added | Zach Hunter | due the presence of the term “non-degenerate”, I fear this is not what what I seek. the only restriction on the integers $d_1,\dots,d_k$ i meant to impose was that they are non-zero (i.e., the subset sums need not be distinct). I will update the question accordingly. | |
| Feb 7, 2023 at 18:47 | history | answered | Terry Tao | CC BY-SA 4.0 |