Lower Bounds for the Number of Small Convex k-Holes
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چکیده
Let S be a set of n points in the plane in general position, that is, no three points of S are on a line. We consider an Erdős-type question on the least number hk(n) of convex k-holes in S, and give improved lower bounds on hk(n), for 3 ≤ k ≤ 5. Specifically, we show that h3(n) ≥ n − 32n 7 + 22 7 , h4(n) ≥ n 2 2 − 9n 4 − o(n), and h5(n) ≥ 3n 4 − o(n).
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تاریخ انتشار 2012