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Jul 29, 2012 at 0:39 comment added Douglas Zare For $k=3$, it looks like $(1/3 + o(1))n$ is the limit of this technique, with about $n/4$ pairs and $n/6$ triplets.
Jul 28, 2012 at 13:24 history edited Douglas Zare CC BY-SA 3.0
Solved 3-independent case.
Jul 19, 2012 at 17:30 vote accept Raphael
Jul 15, 2012 at 8:36 comment added Douglas Zare Earlier I had overlooked that you only need the sum from about $\sqrt{2n}$ to $n$, which is why I didn't obtain the $O(\sqrt{n})$ result from this technique.
Jul 14, 2012 at 10:21 history answered Douglas Zare CC BY-SA 3.0