TY - JOUR

T1 - The number of small semispaces of a finite set of points in the plane

AU - Alon, Noga

AU - Györi, E.

PY - 1986/1

Y1 - 1986/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=38249043947&partnerID=8YFLogxK

U2 - 10.1016/0097-3165(86)90122-6

DO - 10.1016/0097-3165(86)90122-6

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AN - SCOPUS:38249043947

SN - 0097-3165

VL - 41

SP - 154

EP - 157

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 1

ER -