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Dec 28, 2014 at 7:33 comment added Yuval Filmus @QiangLi Thanks for spotting the error. The lower bound does hold, however, once the argument is suitably modified.
Dec 28, 2014 at 7:32 history edited Yuval Filmus CC BY-SA 3.0
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Dec 28, 2014 at 6:14 comment added Qiang Li It seems that $\log^k(2n) = (\log 2 + \log n)^k$. The Lower bound doesn't hold.
Dec 8, 2014 at 21:22 history answered Yuval Filmus CC BY-SA 3.0