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Sep 14, 2021 at 20:11 history edited David E Speyer CC BY-SA 4.0
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Sep 14, 2021 at 19:23 comment added David E Speyer @WillSawin I found a lower bound; see the edit.
Sep 14, 2021 at 19:22 history edited David E Speyer CC BY-SA 4.0
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Sep 14, 2021 at 18:55 comment added H A Helfgott Hah, this ties in with the subject of my B.A. thesis.
Sep 14, 2021 at 18:18 comment added David E Speyer Good question! My first thought is to try to find a partial tiling with $c n^2$ many hexagonal holes in it, each of which can be filled in two ways. @WillSawin
Sep 14, 2021 at 18:16 comment added Will Sawin Interesting! Can you see a "cheap" argument that gets a lower bound of the form $e^{ \delta n^2 + O(n)}$ for some $\delta>0$ by embedding a simpler problem in this one? I tried to do that briefly and failed...
Sep 14, 2021 at 17:29 history edited David E Speyer CC BY-SA 4.0
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Sep 14, 2021 at 15:51 comment added LSpice @‍RichardStanley's comment referenced by @SamHopkins.
Sep 14, 2021 at 15:37 comment added Sam Hopkins $\ln(\sqrt{27/16})\approx 0.262$, not far from what Richard Stanley wrote in a comment above.
Sep 14, 2021 at 15:31 history edited David E Speyer CC BY-SA 4.0
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Sep 14, 2021 at 15:26 history answered David E Speyer CC BY-SA 4.0