论文信息 - The number of small semispaces of a finite set of points in the plane

The number of small semispaces of a finite set of points in the plane

Abstract For a configuration S of n points in the plane, let gk(S) denote the number of subsets of cardinality ⩽k cut off by a line. Let gk,n = max{gk(S): |S| = n}. Goodman and Pollack (J. Combin. Theory Ser. A 36 (1984) , 101–104) showed that if k n 2 then gk,n ⩽ 2nk − 2k2 − k. Here we show that gk,n = k·n for k n 2 .

Noga Alon | Ervin Györi | N. Alon | E. Györi

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